Transcript: Scott Tremaine on The Stability of the Solar System | Nov 06, 2004

Scott Tremaine stands on a stage in a dimly lit auditorium, behind a podium that reads “P.I.”
A giant screen next to him reads “The stability of the solar system. Scott Tremaine. Princeton University.”
Scott is in his fifties, clean-shaven and balding. He’s wearing glasses, a brown suit with a matching tie, and a white shirt.

Scott says THE
UNDERSTANDING OF THE GEOMETRY
AND THE DYNAMICS OF THE SOLAR
SYSTEM IN WHICH WE LIVE WAS ONE
OF THE MOST SUCCESSFUL AND MOST
IMPORTANT INTELLECTUAL
ACCOMPLISHMENTS OF THE LAST
MILLENNIUM.

An old black and white drawing pops up of a man reaching out to the celestial vault as the sun and stars shine.
Then, ancient Egyptian hieroglyphs appear.
Other black and white drawings representing the Earth and solar system flash by in quick succession.

Scott continues FOR THOUSAND OF YEARS AS
CIVILIZATION DEVELOPED HUMANS
BELIEVED THAT THE EARTH WAS
FLAT AND SAT AT THE CENTRE OF
THE UNIVERSE AND THAT THE SUN
AND THE STARS AND THE OTHER
PLANETS REVOLVED AROUND IT.
EVEN AFTER RECOGNIZING THAT THE
EARTH WAS A SPHERE RATHER THAN
BEING FLAT, THEY STILL
CONTINUED TO BELIEVE THAT THE
SUN AND THE PLANETS REVOLVED
AROUND IT.
THE RECOGNITION THAT THIS WAS
IN FACT NOT CORRECT UM, UH, AND
THAT THE GEOMETRY OF THE SOLAR
SYSTEM WAS QUITE DIFFERENT FROM
WHAT EVERYONE HAD BELIEVED FOR
MANY, MANY YEARS WAS REALLY DUE
TO THREE FIGURES.
UM...

A painting depicting Nicolaus Copernicus appears next to the caption “Nicolaus Copernicus. 1473-1543. Copernicus showed that the Sun, not the Earth, was the centre of the solar system.”

Scott continues THE FIRST OF THESE WAS NICHOLAS
COPERNICUS WHO MADE THE FIRST
PERSUASIVE CASE THAT THE EARTH
WAS NOT AT THE CENTRE OF THE
SOLAR SYSTEM.
IN FACT, THE SUN WAS AT THE
CENTRE.
THAT VENUS AND MERCURY ORBITED
INSIDE THE EARTH.
THE EARTH WAS THE THIRD PLANET
FROM THE CENTRE.
THE MOON REVOLVED IT AND THEN
THE OTHER PLANETS MARS, JUPITER
AND SATURN WERE IN TURN OUTSIDE
IT.
THE REALLY IMPORTANT PART OF
COPERNICUS' INSIGHT AND WHY
THIS IS SOMETIMES CALLED THE
COPERNICAN REVOLUTION WAS NOT
SO MUCH THAT THE SUN WAS AT THE
CENTRE OF THE SOLAR SYSTEM BUT
THAT HE DEPOSED THE EARTH FROM
ITS PRIMARY POSITION AS BEING
THE CENTRE OF EVERYTHING IN THE
UNIVERSE AND THAT RECOGNITION
WAS SO IMPORTANT AND IT TURNED
OUT TO BE UH, SUCH A USEFUL
GUIDING PRINCIPLE IN ASTRONOMY
IN THE LAST 400 YEARS THAT IT'S
BEEN ELEVATED TO THE STATUS OF
A PRINCIPLE CALLED THE
COPERNICAN PRINCIPLE WHICH SAYS:

The slide reappears and now reads “The Copernican Principle: We are not located at a special place in the Universe, or at a special time in the history of the Universe.”

Scott continues SO FOR
EXAMPLE THE EARTH REVOLVES
AROUND THE SUN UH, THE SUN IS
ONLY ONE OF SOMETHING LIKE 10
BILLION STARS.

A caption appears on screen. It reads "Scott Tremaine. Princeton University. The stability of the Solar System and the future of Planet Earth. Perimeter Institute for Theoretical Physics. June 2, 2004."

Scott continues THE SUN IS
AN ORDINARY, MIDDLE AGED,
UNREMARKABLE STAR. ONE OF THESE
10 BILLION STARS THAT ORBITS UH,
THE MILKY WAY GALAXY AND IN TURN
THE MILKY WAY IS AN AVERAGE
SIZED GALAXY ONE OF SOMETHING
LIKE 100 BILLION GALAXIES
THROUGHOUT THE UNIVERSE
AS A WHOLE.
THE SECOND UH, GREAT FIGURE IN
UNDERSTANDING THE SOLAR SYSTEM
WAS JOHANNES KEPLER.

A new slate shows a painting of Kepler and reads “Johannes Kepler. 1571-1630. Kepler showed that the motions of the planets obeyed three empirical laws.”

Scott continues KEPLER STUDIED HISTORICAL DATA
ON THE POSITIONS OF THE PLANETS
THAT HAD BEEN GATHERED OVER
MANY YEARS AND HE RECOGNIZED
THAT YOU COULD DISTIL ALL OF
THIS DATA INTO THREE VERY
SIMPLE EMPIRICAL LAWS TO
DESCRIBE THE MOTION OF THE
PLANETS.
ONE IS THAT THE ORBIT OF A
PLANET IS AN ELLIPSE.
THAT'S PARTICULARLY IMPORTANT
BECAUSE MANY INTELLECTUALS FOR
EXAMPLE THE GREEKS BELIEVED
THAT YOU KNOW, THINGS THAT WENT
ON IN THE HEAVENS WERE PERFECT.
THE ONLY PERFECT FIGURE IS A
CIRCLE AND SO THE PLANETS HAVE
TO MOVE IN CIRCLES AND UH,
KEPLER RECOGNIZED THAT THAT WAS
WRONG THAT THE ORBITS WERE
ELLIPSES AND IN PARTICULAR THAT
THE SUN IS NOT AT THE CENTRE OF
THE ELLIPSE BUT IT'S AT ONE OF
THE GEOMETRICAL POINTS CALLED
THE FOCUS OF THE ELLIPSE.
HE ALSO RECOGNIZED THE PLANETS
DON'T MOVE AROUND THE SUN AT
UNIFORM SPEED.
THEY GO FASTER UH, WHEN THEY'RE
CLOSER TO THE SUN SO THAT IF
YOU HAD AN IMAGINARY LINE
JOINING THE PLANET AND THE SUN
SWEEP OUT EQUAL AREAS AND EQUAL
TIMES.
AND THIRD HE RECOGNIZED THAT
THERE WAS A RELATION BETWEEN
THE ORBITAL PERIOD, THE TIME
THAT TAKES THE PLANET TO GO
AROUND ONCE AND THE SIZE OF THE
PLANET'S ORBIT, THE SQUARE OF
THE PERIOD WAS PROPORTIONAL TO
THE CUBE OF THE DISTANCE.
THESE WERE EMPIRICAL LAWS.
THEY HAD NO BASIS IN PHYSICS
AND THAT BASIS WAS ONLY
PROVIDED BY ISAAC NEWTON WHO
UH, MANY PEOPLE REGARD AS THE
GREATEST PHYSICIST WHO EVER
LIVED...

A new slide shows a painting of Newton and reads “Isaac Newton. 1642-1727.”

Scott continues UH, NEWTON FORMULATED TWO
OF THE MOST BASIC LAWS OF
PHYSICS THAT WE USE TO THIS DAY
HIS LAW OF MOTION WHICH SAYS
THAT FORCE IS MASS TIMES
ACCELERATION AND HIS LAW OF
GRAVITY WHICH SAYS THAT ANY TWO
BODIES UH, ATTRACT ONE ANOTHER
WITH A GRAVITATIONAL FORCE
THAT'S PROPORTIONAL TO THE
PRODUCT OF THEIR MASSES UH, THE
SQUARE OF THE DISTANCE BETWEEN THEM.
AND THIS INVERSE SQUARE LAW OF
NEWTON'S HAS BEEN MODIFIED
SLIGHTLY BY EINSTEIN'S GENERAL
THEORY OF RELATIVITY BUT IN
ALMOST ALL ASTRONOMICAL CONTEXT
NEWTON'S LAW IS STILL ACCURATE
ENOUGH AND IT'S CERTAINLY
ACCURATE FOR ANYTHING WE HAVE
TO DO WITH THE SOLAR SYSTEM.
IN ADDITION TO FORMULATING
THESE TWO LAWS NEWTON HAD
APPLIED THEM TO SHOW THAT THE
EMPIRICAL LAWS THAT KEPLER HAD
DESCRIBED COULD BE ENTIRELY
EXPLAINED AS MATHEMATICAL
CONSEQUENCES OF THE EQUATIONS
OF MOTION DETERMINED BY
NEWTON'S FIRST TWO LAWS.
NEWTON WAS A REMARKABLE GUY.
NOT ONLY DID HE DO THIS BUT UM,
HE DID THIS IN ONLY PART OF HIS
CAREER UH, A LARGE PART OF HIS
LATER CAREER HE SPENT AS MASTER
OF THE ROYAL MINT SO IT'S
PARTICULARLY APPROPRIATE THAT
FOR MANY YEARS THE ONE POUND
NOTE IN THE UNITED KINGDOM HAD
A PICTURE OF NEWTON ON THE
OPPOSITE SIDE FROM THE PICTURE
OF THE QUEEN...

A picture of the one pound note pops up.

Scott continues UM, HOWEVER THIS
HONOUR IS A LITTLE IRONIC
BECAUSE YOU CAN SEE THAT THE
ENGRAVER WHO DREW THE BEAUTIFUL
PICTURE OF THESE ELLIPTICAL
ORBITS ACTUALLY PUT THE SUN AT
THE CENTRE RATHER THAN AT ONE
FOCUS WHICH OF COURSE AND OF
COURSE EXPLAINING WHY THE FOCUS
WAS ONE OF NEWTON'S PRIMARY
ACCOMPLISHMENTS WHICH JUST
SHOWS WHY YOU SHOULDN'T GO AND
WORK FOR THE GOVERNMENT I GUESS.

[Laughter]

Scott continues BUT NEWTON
WAS NOT ABLE TO SOLVE FOR THE
PHYSICS OF THE SOLAR SYSTEM
COMPLETELY UM, ALL HE WAS ABLE
TO DO WAS TO SOLVE FOR THE
MOTION OF ONE PLANET AND THE
SUN BUT NEWTON'S LAW OF GRAVITY
SAYS THAT EVERY BODY ATTRACTS
EVERY OTHER BODY AND THAT MEANS
THAT NOT ONLY IS THE SUN
ATTRACTING THE EARTH IN ITS
ORBIT BUT JUPITER IS ATTRACTING
IT AND MARS IS ATTRACTING IT.
EVERY PLANET ATTRACTS EVERY
OTHER PLANET.
AND THAT MEANS THAT THE MOTION
IS MORE COMPLICATED UH, THAN
THE MOTION AROUND JUST ONE
PLANET AROUND THE SUN WOULD BE.
UM, NEWTON TRIED TO SOLVE THIS
MORE COMPLICATED PROBLEM AND
FAILED.
IT WAS A REASONABLE
APPROXIMATION FOR HIM TO IGNORE
THE OTHER PLANETS BECAUSE THE
MASSES OF THE OTHER PLANETS ARE
MUCH SMALLER THAN THE MASS OF
THE SUN BUT HE ALWAYS SORT OF
WONDERED WELL, IF THE SOLAR
SYSTEM GOES ON FOR MILLENNIA
INTO THE FUTURE FOR THOUSANDS
AND MILLIONS OF YEARS THERE ARE
ALL THESE TINY TUGS SAY FROM
JUPITER ON THE ORBIT OF THE
EARTH AND THE QUESTION IS OVER
OVER MILLIONS AND BILLIONS
OF ORBITS DO THOSE TUGS UM,
CANCEL EACH OTHER OUT SO THAT
THE ORBIT OF THE EARTH STAYS
THE SAME OR DO THEY GRADUALLY
ADD UP SO THAT THEY GRADUALLY
CHANGE AND CHANGE THE ORBIT OF
THE EARTH AND DESTROY
IRREGULARITY OF THE SOLAR SYSTEM.
UM, NEWTON WASN'T THE ONLY ONE
WHO TRIED TO SOLVE THIS PROBLEM.
MANY OF THE BEST PHYSICISTS AND
MATHEMATICIANS OVER THE NEXT
300 YEARS TRIED TO SOLVE THE
SAME PROBLEM.
UH, IT'S BECOME DIGNIFIED WITH
THE TITLE OF THE GRAVITATIONAL N-body problem

A slide pops up that reads “The gravitational N-body problem.
The problem: A point mass is surrounded by N much smaller masses on nearly circular orbits. Is the configuration stable over very long times?”

Scott continues UH, AND BODY PROBLEM WHICH
BASICALLY SAYS IF YOU HAVE A
SINGLE MASS SURROUNDED BY SOME
ARBITRARY NUMBER SMALLER MASSES
NEARLY CIRCULAR ORBITS IS THAT
CONFIGURATION STABLE OVER VERY
LONG TIMES?
THAT IS SIMPLE ELLIPSES THAT
UH, NEWTON EXPLAINED REMAIN THE
SAME OR ARE THEY GRADUALLY
DESTROYED BY THESE WEAK
REPEATED GRAVITATIONAL FORCES
BETWEEN THE PLANETS?
UM, SO THIS IS OF COURSE
FORMULATED VERY GENERALLY AS
MATHEMATICIANS LIKE TO DO BUT
FOR THE SOLAR SYSTEM THE POINT
MASS IS THE SUN, THE NUMBER OF
PLANETS, NUMBER N IS NINE, THE
NINE PLANETS AND BY VERY LONG
TIMES I MEAN ABOUT 10 BILLION
ORBITS AND THAT'S BECAUSE THE
EARTH GOES AROUND ONCE A YEAR.
MERCURY GOES AROUND THREE OR
FOUR TIMES A YEAR, THE SOLAR
SYSTEM HAS BEEN AROUND FOR 4.5 BILLION
YEARS SINCE IT WAS FORMED
AND IT'S GOING TO LAST
FOR ANOTHER SEVEN BILLION YEARS
UNTIL THE SUN DIES, TURNS
INTO A RED GIANT AND ENGULFS
AND EVAPORATES ALL THE INNER
PLANETS.
SO WE'RE DEALING WITH TRYING TO
UNDERSTAND THIS PROBLEM OVER
SOMETHING LIKE 10 BILLION ORBITS.
WELL, WHENEVER YOU'RE TRYING TO
APPLY A WELL FORMULATED PRECISE
MATHEMATICAL PROBLEM TO A REAL
PHYSICAL SYSTEM LIKE THE SOLAR
SYSTEM YOU HAVE TO ASK HOW
ACCURATE IT IS AND YOU HAVE TO
ASK WHAT THINGS YOU'VE LEFT OUT.

A new slide reads “What have we left out? Asteroids, comets, mass loss from Sun through radiation and solar wind, drag of solar wind on planetary magnetospheres, galactic tidal forces, satellites, general relativity.”

Scott continues WELL, WE'VE LEFT OUT A LOT
THERE'S LOTS OF VERY SMALL
BODIES IN THE SOLAR SYSTEM
PARTICULAR ASTEROIDS AND
COMETS, THE SUN SLOWLY LOSES
MASS BOTH BECAUSE IT'S
RADIATING ENERGY AND BECAUSE
THERE'S A WIND OF MATERIAL
CALLED THE SOLAR WIND THAT
FLOWS OUT FROM THE SUN.
THE PLANETS SUFFER A CERTAIN
AMOUNT OF DRAG BECAUSE THE
SOLAR SYSTEM INTERACTS SAY WITH
THE EARTH'S MAGNETOSPHERE.
THE SOLAR SYSTEM ISN'T
COMPLETELY ISOLATED BECAUSE
IT'S IMBEDDED IN THE MILKY WAY
GALAXY AND THERE ARE TIDAL
FORCES FROM THE MILKY WAY.
UM, MANY OF THE PLANETS
INCLUDING OUR OWN HAVE
SATELLITES LIKE THE MOON AND
NEWTON'S LAW SAYS THAT THOSE
EXERT SOME GRAVITY ON ALL THE
PLANETS AS WELL.
WE'VE LEFT THOSE OUT.
THERE'S SMALL MODIFICATIONS
FROM EINSTEIN'S THEORY OF
GENERAL RELATIVITY AND EVERY
NOW AND THEN A PASSING STAR IN
THE GALAXY HAPPENS TO COME BY
THE SOLAR SYSTEM AND EAT THE
GRAVITY FROM THAT PASSING STAR
MIGHT HAVE A CHANGE.
CHANGE IN PLANETARY ORBITS.
BUT WHEN YOU LOOK AT ALL OF
THESE EFFECTS AND ALL OF THESE
EFFECTS THAT ANYONE HAS BEEN
ABLE TO THINK OF EITHER THEY'RE
VERY SMALL TYPICALLY AT THE
LEVEL OF A PART PER BILLION OR
A PART PER TRILLION OR THERE'S
SOMETHING THAT YOU CAN EASILY
CALCULATE AND MAKE MINOR
MODIFICATIONS IN UH, THIS
SIMPLE PROBLEM TO INCLUDE.
SO IN FACT, THE CONCLUSION IS
THAT THE LEVEL THAT A PART PER
BILLION AND PROBABLY MUCH
BETTER THIS VERY SIMPLE
MATHEMATICAL PROBLEM REALLY IS
RELEVANT TO SOLAR SYSTEM AND
THE SOLUTION TO THIS
MATHEMATICAL PROBLEM IS THE
SOLUTION THAT WILL TELL US WHAT
THE ULTIMATE FATE OF THE EARTH
AND THE EARTH'S ORBIT IS GOING
TO BE AND SO NATURALLY WE KIND
OF LIKE TO UNDERSTAND IT.
IMPORTANT FROM AN INTELLECTUAL
POINT OF VIEW TO UNDERSTAND
THIS PROBLEM I'D LIKE TO TRY TO
JUSTIFY IT A LITTLE MORE AND
THAT IS WHY DO WE CARE UH, LONG
AFTER WE'RE DEAD WHAT THE FATE
OF THE EARTH IS GOING TO BE?
WELL, FIRST I THINK MOST PEOPLE
IN THE AUDIENCE WOULD AGREE
THAT IT'S SOMETHING WE'D LIKE
TO KNOW BUT IT'S ALSO RELEVANT
FOR A NUMBER OF OTHER PROBLEMS
IN ASTRONOMY AND OTHER FIELDS.
UM, WE'D LIKE TO KNOW WHY THERE
ARE SO FEW PLANETS.
WHY ARE THERE NINE PLANETS IN
THE SOLAR SYSTEM RATHER THAN
SAY 15 OR 30 OR 100.
IS THAT JUST AN ACCIDENT OF THE
WAY THE SYSTEM WAS FORMED?
IS THERE SOMETHING SPECIAL
ABOUT THE DYNAMICS OF THE SOLAR
SYSTEM THAT FORCES YOU TO HAVE
SO FEW PLANETS?
THE SIMILAR QUESTION IS WHY IS
THE REGIONS BETWEEN THE PLANETS
SO CLEAN?
WE BELIEVE THAT THE PLANETS
WERE FORMED FROM A DIST OF DUST
AND GAS THAT GRADUALLY
ACCUMULATED INTO BIGGER AND
BETTER PARTICLES WHICH
EVENTUALLY COLLIDED AND FORMED
THE PLANETS BUT IF YOU GO AND
LOOK FOR LEFTOVER PARTICLES UH,
SAY BETWEEN EARTH AND VENUS
THERE HAVE NOW BEEN VERY DEEP
SURVEYS BETWEEN THE REGION OF
EARTH AND VENUS AND THERE ARE
NO LEFTOVER PARTICLES SAY A FEW
KILOMETRES ACROSS THAT MIGHT
HAVE BEEN LEFTOVER SO SOMEHOW
WHOEVER MADE THE SOLAR SYSTEM
CLEANED UP THE -- YOU KNOW,
SWEPT THE FLOOR AFTER IT WAS
DONE TO A LEVEL OF A PART PER
BILLION AND WE'D LIKE TO
UNDERSTAND WHY THAT'S TRUE.
WE'D LIKE TO KNOW WHERE COMETS
AND METEORS COME FROM.
THE COMETS THAT WE SEE AND THE
METEORS AND METEORITES THAT
COLLIDE WITH THE EARTH ARE ON
ORBITS THAT ARE VERY SHORT-
LIVED ON SOLAR SYSTEM TIMES
ONLY AT A TINY FRACTION OF THE
AGE OF THE SOLAR SYSTEM THERE
MUST BE SOME SOURCE THAT
THEY'RE COMING FROM THAT'S
CONTINUALLY SUPPLYING THEM.
WE'D LIKE TO KNOW WHAT THAT IS.
MOST MODELS OF THE FORMATION OF
THE SOLAR SYSTEM SAY THAT THE
SOLAR SYSTEM, THE PLANETS WERE
FORMED IN SOMETHING LIKE A
MILLION YEARS WHICH SOUNDS LONG
BUT IS LESS THAN A 10th OF A
PERCENT OF THE LIFETIME OF THE
SOLAR SYSTEM.
WE'D LIKE TO UNDERSTAND IF THE
SOLAR SYSTEM WHEN IT WAS FIRST
FORMED LOOKED THE SAME WAY IT
DOES OR IF IT'S GRADUALLY
EVOLVED SINCE THEN PERHAPS AS A
RESULT OF DYNAMICAL EFFECTS IN
THE SOLAR SYSTEM.
WE'D LIKE TO UNDERSTAND WHAT
OTHER PLANETARY SYSTEMS LOOK LIKE.
WHAT THE CONSTRAINTS ON OTHER
PLANETARY SYSTEMS WOULD BE AND
WHETHER THEY CAN BE LIKE OUR
OWN OR A MORE PROSAIC QUESTION
IS WE'D LIKE TO UNDERSTAND THE
GEOLOGICAL TIMESCALE FOR ALMOST
EVERY ASPECT OF GEOLOGY WHETHER
DATING THE DINOSAURS OR
UNDERSTANDING OF AGES OF
VARIOUS ICE AGES.
UH, THOSE AGES ARE DATED BY UH,
DRILLING AND BRINGING UP CORES
OF SEDIMENTS UM, AND OF COURSE
SINCE YOU DON'T KNOW THE
SEDIMENTATION RATE OR WHETHER
IT'S BEEN UNIFORMED YOU CAN'T
CALIBRATE THE AGE OF A PIECE OF
SEDIMENT THAT YOU DIG OUT
THAT'S 30 METRES DOWN ONE OF
THESE CORES BUT WHAT THEY DO
KNOW IS THAT THE RATIO OF SOME
ISOTOPES FOR EXAMPLE THE RATIO
OF TWO ISOTOPES OF OXYGEN
CHANGES SYSTEMATICALLY AND
PERIODICALLY IN THOSE -- IN
THOSE CORES AND THAT CHANGE IN
THE ISOTOPIC RATIO UH, REFLECTS
CHANGES IN THE AMOUNT OF WATER
ON EARTH THAT'S TIED UP IN
ICECAPS HENCE REFLECTS CHANGES
IN THE TEMPERATURE AND IT'S
BELIEVED THAT THESE PERIODIC
VARIATIONS IN THE TEMPERATURE
ARE DUE TO PERIODIC VARIATIONS
IN EARTH'S ORBIT BECAUSE THAT
AFFECTS THE AMOUNT OF SUNLIGHT
THAT THE EARTH RECEIVED --
EARTH RECEIVES.
SO IF WE CAN UNDERSTAND THE
BEHAVIOUR OF THE EARTH'S ORBIT
OVER THE LAST HUNDRED MILLION
YEARS WE CAN ACTUALLY HAVE AN
ASTRONOMICAL CLOCK THAT WE
COULD USE TO CALIBRATE ALL THE
GEOLOGICAL RECORDS UH, AND
FINALLY THIS PROBLEM, ALTHOUGH
IT'S REMAINED UNSOLVED UH, IN
THE MOST GENERAL FORM FOR THE
LAST 300 YEARS HAS INSPIRED AN
ENORMOUS AMOUNT OF WORK AND IS
KIND OF IN THE MOTHER OF ALL
PROBLEMS IN THE SUBJECTS THAT
WE NOW KNOW AS CHAOS THEORY AND
NON-LINEAR DYNAMICS.
THESE SUBJECTS UH, HAVE TURNED
OUT TO BE RELEVANT TO AN
UNEXPECTEDLY WIDE VARIETY OF
SUBJECTS INCLUDING THE FUTURE
OF THE STOCK MARKET.
THE EVOLUTION OF POPULATIONS
AND EXTINCTIONS UM, AND ONE OF THE
THE GENERAL ISSUES THAT HAS
COME UP IN TRYING TO UNDERSTAND
NON-LINEAR DYNAMICS IS WHAT THE
BEHAVIOUR OF
THESE GENERAL MORE GENERAL
DYNAMIC THE SYSTEMS ARE OVER
VERY LONG TIMES, A VERY
SPECIFIC UH, SIMILAR PROBLEM IS
TRYING TO BUILD LARGE PARTICLE
ACCELERATORS FOR HIGH ENERGY
PHYSICS EXPERIMENTS WHERE THEY
HAVE ELEMENTARY PARTICLES THAT
ORBIT UH, MILLIONS OR BILLIONS
OF TIMES AND IF WE CAN
UNDERSTAND THIS SORT OF BASIC
PROBLEM WHICH WAS THE ORIGINAL
PROBLEM IN THE SUBJECT THEN WE
HOPE IT WILL SHED SOME LIGHT ON
MANY OTHER DYNAMICAL SYSTEMS
THAT WE'VE LEARNED ARE SIMILAR
IN A SORT OF GENERAL STRUCTURE
TO THE SOLAR SYSTEM.
UH, WELL, NEWTON WAS A VERY
SMART GUY AND NEWTON THOUGHT
ABOUT THIS PROBLEM AND IT'S
INTERESTING TO ASK WHAT NEWTON
THOUGHT AND THIS IS A QUOTE
FROM ONE OF HIS BOOKS WHICH
SAYS “BLIND FATE COULD NEVER
Make ALL THE PLANETS MOVE
ONE and THE SAME WAY in orbits concentric, some inconsiderable irregularities excepted, which could have arisen from the mutual actions of planets upon one another, and which will be apt to increase, until this System wants a reformation.”
HE'S BASICALLY SAYING YOU HAVE
TO EXPLAIN WHY ALL THE PLANETS
ARE IN NEARLY CIRCULAR ORBITS
GOING AROUND THE SAME WAY.
“SOME INCONSIDERABLE
IRREGULARITIES EXCEPTED” HE'S
JUST SAYING THAT THE ORBITS ARE
ELLIPSES, THEY'RE NOT PERFECT
CIRCLES AND THEN HE SAYS “WHICH
COULD'VE ARISEN FROM THE MUTUAL
ACTIONS OF THE PLANETS UPON ONE
ANOTHER AND WHICH WOULD BE APT
TO INCREASE UNTIL THE SYSTEM
WANTS A REFORMATION.”
SO NEWTON THOUGHT THAT THESE
SMALL TUGS FROM JUPITER ON
EARTH AND MARS ON VENUS WERE
ACTUALLY GOING TO ACCUMULATE
WERE GOING TO MAKE THE ORBITS
MORE AND MORE ELLIPTICAL, MORE
AND MORE ECCENTRIC UNTIL
SOMETHING WENT WRONG AND NEWTON
UM, WANTED TO KNOW AND COULDN'T
FIGURE OUT UH, WHY THE SOLAR
SYSTEM WAS STILL SO NEARLY THE
ORBITS WERE CIRCULAR WHEN HE
BELIEVED THAT THE MUTUAL
GRAVITY WAS LIKELY TO
EVENTUALLY DESTROY THE SYSTEM
AND THERE'S A VERY INTERESTING
ARTICLE BY A HISTORIAN OF
SCIENCE HOPKINS WHO SAYS -- WHO
BASICALLY SAYS THAT NEWTON WAS
A LITTLE -- NEWTON WAS VERY
RELIGIOUS AND HE WAS UPSET
BECAUSE THE SUCCESS OF HIS LAWS
OF MOTION KIND OF BANISHED
GOD'S ROLE IN KEEPING THE
PLANETS GOING AROUND UH, THE
SUN THEY WERE NOW GOING AROUND
BY NEWTON'S LAWS RATHER THAN
BECAUSE GOD WAS PUSHING THEM.

Another quote on the slide reads “In the system of planets, Newton sees careful planning on the part of Providence that has ensured long-term stability, but the stability is not completely permanent... Providence must intervene to prevent gravitational collapse, and will thereby demonstrate a continuing concern for the welfare of mankind. In short, Providence has... a regular servicing contract with the solar system.
Hoskins, 1985.”

Scott continues UM, BUT HE WAS REASSURED
BECAUSE HE SOUGHT CAREFUL
PLANNING ON THE PART OF GOD TO
ENSURE LONG-TERM STABILITY AND
THAT NEWTON ACTUALLY BELIEVED
THAT FROM TIME TO TIME GOD HAD
TO INTERVENE IN THE SOLAR
SYSTEM, YOU KNOW, KIND OF
STRAIGHTEN THINGS UP UH, AND AS
HOPKINS PUT IT GOD HAD A
REGULAR SERVICING CONTRACT UH,
WITH THE SOLAR SYSTEM, YOU
KNOW, THAT THE MUTUAL
INTERACTIONS WOULD MAKE THINGS
MORE AND MORE REGULAR AND GOD
WOULD EVENTUALLY FIX THINGS UP
AND NEWTON WAS REASSURED
BECAUSE IT MEANT THAT THERE WAS
A CONTINUING ROLE FOR GOD WHO
HE HAD OTHERWISE BANISHED UH,
FROM THE SOLAR SYSTEM.
NEWTON WAS NOT THE ONLY PERSON
WHO THOUGHT ABOUT THIS.
LAPLACE WHO WAS ONE OF THE
GREAT CALCULATORS WHO WORKED
OUT MANY OF THE DETAILS OF
NEWTON'S MODEL POINTED OUT THAT
NEWTON'S UH, UH, MODEL --
NEWTON'S LAWS FOR THE EVOLUTION
OF THE SOLAR SYSTEM WERE SO
SUCCESSFUL IN EXPLAINING THE
POSITIONS AND THE MOTIONS OF
THE PLANETS, PREDICTING
ECLIPSES, PREDICTING THE
OCCURRENCES OF COMETS IN MODERN
TIMES, SENDING SPACECRAFT TO
OTHER PLANETS.
UH, THAT HE POINTED OUT THAT
SINCE THESE LAWS WERE SO
SUCCESSFUL THAT SIMILAR LAWS
GOVERN ALL OF NATURE then...

A new quote reads “An INTELLIGENCE knowing, AT A GIVEN INSTANT of time, ALL FORCES acting in nature, as well as the momentary positions of all things of which the universe consists, would be able to comprehend the motions of the largest bodies of the world and those of the smallest atoms in one single formula, provided it were sufficiently powerful to subject all data to analysis. To it, nothing would be uncertain; both future and past would be present before its eyes.”

Scott continues AND AS HE SAYS “NOTHING WOULD
BE UNCERTAIN.
BOTH FUTURE AND PAST WOULD BE
PRESENT BEFORE ITS EYES.”
AND THIS IS SOMEWHAT AN EXTREME
POINT OF VIEW UM, HAS HAD AN
ENORMOUS INFLUENCE ON
PHILOSOPHERS AND HAS LED TO A
SCHOOL OF THOUGHT WHICH IS NOW
CALLED LAPLACE DETERMINISM.
UM, IT'S ONLY OF THE MANY VIEWS
ABOUT THE RELATIONSHIP BETWEEN
DETERMINISM AND FREEWILL BUT
HAS BEEN ONE OF THE MOST
INFLUENTIAL BECAUSE IT SAYS
THAT WE HAVE NO FREEWILL AT ALL.
AND SO UH, THE SOLAR SYSTEM IS
NOT ONLY A PROBLEM THAT'S
INTRINSIC FOR IN ITS OWN MERITS
BUT IT'S HAD A REALLY MAJOR
EFFECT ON -- ON A BROAD RANGE
OF INTELLECTUAL THOUGHT.
UH, SO LET ME JUST REVIEW THE
CAST OF CHARACTERS SO THAT WE
ALL ARE REMINDED OF WHAT THE
PLANETS ARE.

A black and white picture shows the smooth surface of Mercury.

Scott continues THIS IS MERCURY OF COURSE NAMED
AFTER THE ROMAN GOD OF COMMERCE
AND TRAVEL.
MERCURY IS THE CLOSEST PLANET
TO THE SUN.
IT HAS THE MOST EXTREME
TEMPERATURE RANGES.
RANGE OF 600 CENTIGRADE BETWEEN
ITS HOTTEST POINT, HOTTEST
POINTS AND COLDEST POINTS.
IT'S UNLIKE THE EARTH AND IT
HAS NO PLATE TECTONICS, IT HAS
NO VOLCANOES.
IT JUST HAS A QUIESCENT HEAVILY
CRATERED SURFACE.

A new picture shows mercury in the forefront and Venus in the background.

Scott continues THIS PICTURE COMES FROM MARINER
10 WHICH VISITED UH, MERCURY 30
YEARS AGO AND REMARKABLY THAT'S
THE ONLY SPACECRAFT THAT'S EVER
VISITED MERCURY.
NOTHING HAS GONE BACK THERE
SINCE THEN.
THE SECOND PLANET OUT IS VENUS
WHICH IS THE SISTER PLANET OF
THE EARTH.
ALMOST THE SAME SIZE AND MASS.
VENUS IS -- THESE ARE AGAIN
SPACECRAFT PICTURES FROM
PIONEER 10 AND FROM MAGELLAN.
VENUS IS COVERED WITH A DENSE
LAYER OF CLOUDS SO YOU CAN SEE
ALMOST NOTHING OF THE SURFACE
FEATURES VISIBLE.
THIS MUCH MORE DETAILED PICTURE
SHOWING THE SURFACE FEATURES IS
ACTUALLY TAKEN FROM RADAR
SCANNING -- SIDE SCANNING RADAR
ON THE SPACECRAFT THAT ORBITED
THE PLANET AND FOR THE FIRST
TIME GAVE A DETAILED LOOK AT
THE TOPOGRAPHY OF VENUS.
UM, VENUS IS COVERED WITH AN
EXTREMELY DENSE ATMOSPHERE OF
CARBON DIOXIDE.
SOMETHING LIKE 100 TIMES THE
DENSITY OF THE EARTH'S
ATMOSPHERE.
UH, THE CLOUDS RAIN SULPHURIC
ACID INSTEAD OF WATER.
IT'S A VERY
UNPLEASANT ENVIRONMENT.
ITS SURFACE TEMPERATURE IS
EXTREMELY HIGH SOMETHING LIKE
500 DEGREES CENTIGRADE.
THAT'S BECAUSE OF THE EXTREME
VERSION OF THE GREENHOUSE
EFFECT UM, IN WHICH INFRARED
RADIATION CAN'T ESCAPE FROM THE
SURFACE THROUGH THE DENSE
CARBON DIOXIDE LAYER AND OF
COURSE UH, THE REALLY
UNPLEASANT NATURE OF VENUS'
SURFACE IS AN EXTREME VIEW THAT
PEOPLE WHO WORRY ABOUT THE
GREENHOUSE EFFECT ON EARTH
ALWAYS HAVE IN THE BACK OF
THEIR MINDS.

A new picture shows Earth.

Scott continues UM, EARTH I WON'T SAY MUCH
ABOUT SINCE YOU'RE FAMILIAR WITH IT.
UM, I'LL JUST MENTION THAT
EARTH ORBITS THE SUN AT 146
MILLION KILOMETRES RATHER THAN
KEEP TALKING ABOUT KILOMETRES
I'LL FOLLOW THE ASTRONOMICAL
CONVENTION AND CALL THAT
DISTANCE THE ASTRONOMICAL UNIT
AND EVERYTHING I TALK ABOUT
WILL BE MEASURED IN TERMS OF
THE EARTH'S SUN DISTANCE.

A new picture shows the smooth surface of Mars.

Scott continues MARS IS MUCH COLDER THAN THE EARTH.
AT THE WARMEST PLACES ON MARS
AND THE EQUATOR IN MID SUMMER
IT GETS UP TO ABOUT 27 DEGREES
SO IT'S QUITE BALMY BUT THE
AVERAGE TEMPERATURE OVER THE
SURFACE OF THE PLANET IS ABOUT 55.
UH, WHAT'S EVEN LESS PLEASANT
IS THAT ITS ATMOSPHERE IS FAR
THINNER THAN THE EARTH'S.
ONLY ABOUT 1 percent OF THE UH, UH,
PRESSURE ON EARTH SO IT'S QUITE
UNINHABITABLE.
UM, UH, MARS ALSO DOES NOT HAVE
PLATE TECTONICS.
IT DOES HAS EVIDENCE OF EROSION.
UH, RIVERS, UH, DRY LAKES, THE
MOST LIKELY FLUID THAT CAUSED
THAT EROSION UH, IS WATER
ALTHOUGH WE'RE NOT SURE BUT
THERE'S VERY LITTLE IF ANY
SURFACE WATER ON MARS AT THE
PRESENT TIME.

Now the huge Jupiter appears, with two of its moons.

Scott continues JUPITER IS THE FIRST AND
LARGEST OF THE GAS GIANT
PLANETS.
IT'S CALLED A GAS GIANT BECAUSE
IT DOESN'T HAVE A SOLID
SURFACE.
THIS IS JUST THE EDGE OF THE
ATMOSPHERE.
COMPOSITION IS MOSTLY HYDROGEN
AND HELIUM BECAUSE THOSE ARE
THE BASIC ELEMENTS OUT OF WHICH
THE PLANET'S FORMED AND IN
CONTRAST TO THE SMALLER PLANETS
THE GRAVITY IN THESE PLANETS IS
BIG ENOUGH TO RETAIN THE
HYDROGEN AND HELIUM.
THIS SHOWS TWO OF JUPITER'S
SATELLITES, IO WHICH IS A NICE
SORT OF UH, BRIGHT REDDISH
COLOUR BECAUSE IT HAS AN
ENORMOUS NUMBER OF VOLCANOES
THAT ARE CONSTANTLY SPEWING OUT
LAVA ON THE SURFACE AND EUROPA.
THIS OBJECT IS THE GREAT RED
SPOT UH, THE BANDS THAT YOU SEE
HERE ARE DUE TO EXTREMELY HIGH
WINDS ABOUT 600 KILOMETRES PER
HOUR AND THE GREAT RED SPOT IS
SOME SORT OF UH, SOME SORT OF
BASICALLY Jovian HURRICANE
WHICH HAS BEEN SEEN FOR AT
LEAST 300 YEARS SO IT'S A VERY
LONG LIVED STORM TO BE LIVING
THROUGH.

A new picture shows Saturn and its rings.

Scott continues UM, FURTHER OUT IS SATURN.
THE MAJOR FEATURE OF SATURN IS
THIS BEAUTIFUL RING SYSTEM.
THE BEST PICTURES WE HAVE OF
SATURN SO FAR COME FROM
VOYAGER SPACECRAFT WHICH WENT
BY IN 1980 BUT WE'RE IN FOR
DRAMATIC DISCOVERIES STARTING
THIS SUMMER BECAUSE THE CASINI
SPACECRAFT WHICH REALLY IS
ENORMOUS.
YOU SEE UH, A HUMAN DOWN HERE
HAS BEEN ON ITS WAY TO SATURN
THIS PICTURE WAS TAKEN BY
CASINI AS IT APPROACHED SATURN
AND IN ABOUT A MONTH CASINI
WILL FIRE ITS MOTORS TO GO FROM
A PASSING ORBIT TO INJECT
ITSELF INTO A SATURN ORBIT FROM
WHERE IT WILL SPEND THE NEXT
FOUR YEARS TAKING IMAGES OF
SATURN AND LAUNCHING A PROBE
INTO THE ATMOSPHERE OF ONE OF
SATURN'S UH, UH, SATELLITES.
THE RINGS LOOK SOLID BUT
THEY'RE NOT.
THEY'RE COMPOSED OF HUGE
NUMBERS OF VERY SMALL PARTICLES
PERHAPS A FEW CENTIMETRES OR A
FEW METRES ACROSS.
THE RINGS WERE ONE OF THE
THINNEST OBJECTS WE KNOW OF IN
THE UNIVERSE.
THE DIAMETER OF THE RINGS IS
ABOUT 200,000 KILOMETRES AND
THE THICKNESS IS ONLY A FEW
METRES.
A REMARKABLE SYSTEM.

Now a picture shows the perfectly smooth and faint green Uranus.

Scott continues UM, URANUS IS THE NEXT PLANET OUT.
IT LOOKS SORT OF BORING.
THAT'S BECAUSE THERE'S A HAZE
OF METHANE AND PHOTOCHEMICAL
SMOG COVERING THE SURFACE SO WE
KNOW LESS ABOUT URANUS.
THIS AGAIN IS A VOYAGER PICTURE
FROM 1986.

Now the bright blue Neptune appears.

Scott continues UM, NEXT IS NEPTUNE.
A PICTURE FROM 1989 FROM THE
SAME VOYAGER SPACECRAFT.
SOME SORT OF STORM SIMILAR TO
THE GREAT RED SPOT UH, THE
WINDS ON NEPTUNE ARE THE
STRONGEST WE KNOW IN THE SOLAR
SYSTEM REACHING UP TO 2,000
KILOMETRES PER HOUR.

Finally, a picture shows tiny Pluto and bright red Charon.

Scott continues AND THE LAST PLANET PLUTO WITH
ITS SATELLITE CHARON UH, IF I
CAN JUST GO BACK TO -- LET ME
JUST GO BACK FOR A SECOND.
I SHOULD POINT OUT THAT THE
PICTURE THAT COPERNICUS DREW OF
THE SOLAR SYSTEM DID NOT
INCLUDE URANUS, NEPTUNE OR
PLUTO UH, URANUS WAS ONLY
DISCOVERED IN THE 19th CENTURY
UH, NEPTUNE WAS ONLY DISCOVERED
AS A RESULT OF ONE OF THE REAL
TRIUMPHS OF NEWTON'S LAWS.
WHEN PEOPLE APPLIED NEWTON'S
LAWS TO TRY TO FOLLOW THE ORBIT
OF URANUS THEY FOUND SMALL,
UNEXPLAINED ERRORS RATHER THAN
REFLECTING A BREAKDOWN IN
NEWTON'S LAWS IT TURNED OUT
THAT THOSE WERE DUE TO AN EXTRA
PLANET AND MATHEMATICIANS WERE
ABLE TO ANALYZE THOSE ERRORS
USING NEWTON'S LAWS TO PREDICT
THE POSITION OF THE PLANET THAT
MUST BE NECESSARY TO EXPLAIN
THEM AND WHEN THE OBSERVERS
TURNED THEIR TELESCOPES ON IT
THEY FOUND NEPTUNE.
UH, THE DISCOVERY OF PLUTO IS
SOMEWHAT LESS OF A THEORETICAL
TRIUMPH.
PEOPLE THOUGHT THERE WERE STILL
UNEXPLAINED PROBLEMS WITH
NEPTUNE'S ORBIT.
THEY DID SIMILAR CALCULATIONS
THEY COMPUTED UH, WHERE THE
EXTRA PLANET HAD TO BE AND IN
THE 1930s AT LOWELL OBSERVATORY
IN ARIZONA UH, THEY BEGAN
SEARCHING FOR THIS PLANET.
THEY'D ONLY
SEARCHED FOR A COUPLE OF MONTHS
WHEN THEY FOUND PLUTO BUT AFTER
THEY FOUND IT AND MEASURED ITS
MASS UH, THEY FOUND THAT ITS
MASS WAS FAR TOO SMALL TO
EXPLAIN THE PROBLEMS WITH
NEPTUNE'S ORBIT AND THE PEOPLE
WHO HAD SAID
THERE WERE PROBLEMS WITH
NEPTUNE'S ORBIT WERE JUST WRONG
SO IT WAS ONLY DISCOVERED BY
COINCIDENCE.

[Laughter]

Scott continues AND THERE
ARE LOTS OF SMALL BODIES.
UH, ASTEROIDS.

A picture shows a rounded yet cratered asteroid.

Scott continues THIS IS A PICTURE OF THE
ASTEROID EROS TAKEN FROM A
SPACECRAFT ORBITING ABOUT 200
KILOMETRES ABOVE ITS SURFACE.
THIS IS ABOUT 35 KILOMETRES IN
THIS DIRECTION AND MAYBE 15 OR
20 IN THIS DIRECTION.
THE REASON IT'S SORT OF POTATO
SHAPED RATHER THAN SPHERICAL IS
BECAUSE IT'S SO SMALL, ITS
GRAVITY IS NOT ABLE TO OVERCOME
UH, THE STRENGTH OF ITS ROCKS
SO THIS REALLY IS JUST A BIG
ROCK RATHER THAN A PLANET.
AND OF COURSE COMETS.

A double picture appears that shows a comet with two tails in the night sky and a bright red nucleus of a comet.

Scott continues THIS IS A FAMOUS PICTURE TAKEN
BY THE EUROPEAN JOTTO
SPACECRAFT OF THE NUCLEUS OF
HALEY'S COMET.
IT'S A CHUNK OF ICE AND ROCK
ABOUT 10 KILOMETRES ACROSS.
YOU CAN SORT OF VAGUELY SEE ITS
SHAPE AND SEE THESE JETS OF
WHAT ARE BASICALLY STEAM AND
WATER VAPOUR BLOWING OFF AS THE
COMET APPROACHES THE SUN.
UH, THOSE JETS PRODUCE LONG
TAILS.
THIS IS COMET HAILBOP, A
DIFFERENT COMET FROM THIS ONE
BUT A TAIL PRODUCED BY A
SIMILAR MECHANISM.
HAILBOP IN FACT HAS TWO TAILS.
THIS IS DUST AND SMALL
PARTICLES UH, AND THIS IS GAS.
UH, AND HAILBOP PRESUMABLY HAS
A SIMILAR NUCLEUS WHICH IS VERY
MUCH SMALLER THAN THE SCALE OF
THIS IMAGE BURIED IN THE CONA
ASSOCIATED WITH THE TAIL.
OKAY, SO UM, WE'RE TRYING TO
UNDERSTAND THE GRAVITATIONAL
AND BODY PROBLEM.
UM, MANY FAMOUS MATHEMATICIANS
HAVE TRIED TO SOLVE IT
ANALYTICALLY AND HAVE ONLY HAD
LIMITED SUCCESS.
THAT MEANS THAT IF YOU'RE
REALLY INTERESTED IN WHAT'S
GOING TO HAPPEN TO THE SOLAR
SYSTEM YOUR ONLY OPTION IS TO
PUT THE EQUATIONS OF MOTION ON
A COMPUTER AND TRY TO JUST
SOLVE THE EQUATIONS NUMERICALLY
UM, WITH A COMPUTER.
THAT'S ONLY BECOME POSSIBLE IN
THE LAST FEW YEARS BECAUSE THE
SPEED OF COMPUTERS HAS
CONTINUED TO INCREASE RAPIDLY.
NEVERTHELESS IT'S STILL AN
EXTREMELY DIFFICULT PROBLEM AND
I'M NOT GOING TO TRY TO GIVE
YOU A LECTURE ON THE APPLIED
MATHEMATICS OF TRYING TO SOLVE
NEWTON'S EQUATIONS BUT I JUST
WANT TO GIVE YOU A LITTLE BIT
OF THE FLAVOUR OF THE PROBLEM.
THE FIRST AND MOST BASIC
PROBLEM OF COURSE IS IF YOU'RE
GOING TO DO ANYTHING A BILLION
TIMES OVER LIKE INTEGRATE --
LIKE CALCULATE AN ORBIT YOU
REALLY HAVE TO DO IT ACCURATELY
TO AVOID THE BUILD-UP OF SMALL
NUMERICAL ERRORS AND SO YOU
HAVE TO DESIGN UH, YOUR
SOFTWARE VERY CAREFULLY TO
AVOID ANY KIND OF RANDOM OR
SYSTEMATIC BUILD-UP OF ERRORS.
SECOND PROBLEM IS THAT MUCH OF
THE GROWTH OF COMPUTING
CAPACITY RECENTLY HAS BEEN
WHAT'S CALLED PARALLELIZATION
WHICH BASICALLY INVOLVES TAKING
A PROBLEM AND SPLITTING IT UP
SO THAT INSTEAD OF DOING IT ON
ONE COMPUTER YOU CAN DO IT ON
10 OR 100 OR 1,000 COMPUTERS
DIFFERENT PARTS OF THE PROBLEM
ON DIFFERENT COMPUTERS AT THE
SAME TIME AND THEN COMBINE THEM
ONCE THE DIFFERENT PARTS OF THE
PROBLEM ARE SOLVED.
THE DIFFICULTY OF COURSE IS
THAT YOU CAN DO THAT WITH THE
SOLAR SYSTEM.
YOU CAN TELL ONE COMPUTER WELL,
YOU CALCULATE THE ORBIT OF THE
EARTH BETWEEN A MILLION YEARS
AND TWO MILLION YEARS BECAUSE
YOU DON'T KNOW WHERE TO START
UNTIL YOU'VE FIGURED OUT WHAT
IT DID BETWEEN ZERO AND ONE
MILLION YEARS.
THAT IS THE PROBLEM IS
SEQUENTIAL, YOU CAN DIVIDE IT
UP INTO PARALLEL AND SO YOU CAN
NEVER USE MORE THAN ONE
COMPUTER AND SO YOU'RE LIMITED
BY UM, UM, BY THE FASTEST
SINGLE COMPUTER YOU CAN BUY.
THE GOOD NEWS IS THAT PARALYSED
COMPUTERS ARE VERY EXPENSIVE
UH, THIS PROBLEM BECAUSE YOU
CAN ONLY USE ONE YOU MAY AS
WELL GO OUT AND BUY A FAST PC
WITH THE FASTEST CHIP YOU CAN
AND THEN JUST UH, UH, RUN IT ON
SPEND A FEW THOUSAND BUCKS
ON THAT AND RUN IT ON THAT FOR
SIX MONTHS AND NOT DO ANYTHING
ELSE WITH IT.
UM, SO UH, IT'S NOT COSTLY IN
THE HARDWARE BUT YOU HAVE TO BE
VERY PATIENT.
UM, ONE OF THE SPECIFIC
PROBLEMS THAT I'LL JUST
DESCRIBE IN A LITTLE MORE
DETAIL BECAUSE IT'S A PROBLEM
THAT SHOULD BE FAMILIAR TO
EVERYBODY IS TRYING TO AVOID
ROUND OFF ERROR.
NOW I'M SURE YOU WERE ALL
TAUGHT ABOUT ROUND OFF ERROR
WHEN YOU LEARNED ARITHMETIC.
IT'S NOT TERRIBLY IMPORTANT IF
YOU'RE ADDING UP YOUR GROCERY
BILL OR TRYING TO CALCULATE
YOUR INCOME TAX, UM, BUT AS YOU
CAN IMAGINE IF YOU'RE DOING A
PROBLEM OVER AND OVER AGAIN
BILLIONS OF TIMES YOU WANT TO
BE CAREFUL THAT YOU'RE NOT
MAKING -- THAT THE ERRORS THAT
YOU MAKE FROM ROUNDING OFF
DON'T BUILD UP AND THERE ARE
ACTUALLY TWO FAMOUS REAL WORLD
EXAMPLES OF WHY YOU DON'T WANT
ROUND OFF ERROR TO BUILD UP.

A new slide reads “Roundoff error. Famous examples of problems due to roundoff error.”

Scott continues THE FIRST CAME -- COMES FROM
THE VANCOUVER STOCK EXCHANGE
WHERE IN 1982 THEY INVENTED A
NEW STOCK INDEX AND YOU KNOW AS
YOU DO WITH STOCK indices YOU
INITIALIZE IT AT A THOUSAND AND
WHAT THEY DISCOVERED THAT AFTER
ALMOST TWO YEARS THE STOCK
INDEX WAS AROUND 500 BUT YOU
KNOW FUNNY THING EVERYBODY
SEEMED TO BE MAKING LOTS OF
MONEY AND THE STOCK PRICES HAD
ALL BEEN GOING UP SO THEY
LOOKED INTO THE SOFTWARE IT
TURNED OUT THAT WHOEVER WROTE
IT UM, WHENEVER THERE WAS A
TRADE HE ROUNDED THE PRICE OF
THE STOCK DOWN AND UH, AFTER
YOU KNOW, THE STOCKS HAD BEEN
TRADED ENOUGH THE INDEX SANK
UM, THE SECOND PROBLEM WHICH
WAS MORE SERIOUS WAS IN THE
1991 GULF WAR PATRIOT MISSILE
DEFENCE SYSTEMS UM, USED A
CLOCK STEP OF A 10th OF A
SECOND AND THEY CONVERTED THAT
FROM A BINARY NUMBER WHICH IS
THE WAY THE COMPUTERS STORE
THEIR NUMBER UM, UH, STORE THE
TIMES INTO .1 SECONDS THEY HAD
22 BITS, 22 LOCATIONS IN THE
BINARY NUMBER UM, BUT WHEN THE
PATRIOTS WERE DESIGNED THEY
WERE NEVER DESIGNED TO BE
TURNED ON FOR A VERY LONG PERIOD.
AFTER 100 HOURS THE ACCUMULATED
ROUND OFF ERROR IN DOING THIS
CALCULATION OVER AND OVER AGAIN
AMOUNTED TO A THIRD OF A SECOND
AND A THIRD OF A SECOND UM, THE
PATRIOT FAILED.
IT FAILED TO INTERCEPT A SCUD
AND 28 PEOPLE WERE KILLED.
UM, AND OBVIOUSLY THIS IS THE
SORT OF PROBLEM THAT WOULD BE EASY TO
FIX IF YOU THOUGHT ABOUT IT AND
IT AROSE SIMPLY BECAUSE YOU
WERE DOING A GOOD CALCULATION
BUT MAKING THE SAME MISTAKE
OVER AND OVER AND OVER AGAIN
MILLIONS OF TIMES.
SO HOW DO YOU HOW DO HANDLE ROUND OFF
ERROR IN THESE LONG AND VERY
DIFFICULT CALCULATIONS?
WELL, ROUND OFF ERROR IS SORT
OF LIKE A CHRONIC DISEASE YOU
CAN NEVER CURE IT.
ALL YOU CAN DO IS TRY TO
MINIMIZE THE EFFECTS SO ONE IS
YOU ALWAYS USE THE HIGHEST
POSSIBLE PRECISION.
IN MOST COMPUTERS THAT'S ABOUT
16 OR 17 DECIMAL DIGITS.
UM, YOU'D LIKE TO HAVE MORE BUT
THAT'S ABOUT ALL YOU CAN DO.
ANOTHER ONE IS THAT YOU SHOULD
NEVER USE ANY NUMBER THAT'S NOT
WHAT'S CALLED REPRESENTABLE IN
THE COMPUTER SO THE WAY
COMPUTERS STORE NUMBERS, YOU
KNOW, IF YOU HAVE A ONE OR A
TWO OR A 10,000 THEY REALLY DO
STORE IT EXACTLY.
IF YOU HAVE A HALF OR A QUARTER
THEY STORE IT EXACTLY BUT A
NUMBER LIKE A THIRD THEY
APPROXIMATE BY THE NEAREST
NUMBER THAT THEY CAN STORE AND
IF YOU HAVE SOMETHING IN YOUR
UH, UH, SOFTWARE THAT HAS A ONE
THIRD IN IT THEN EVERY TIME IT
GETS USED OVER AND OVER AGAIN
IT'S ALWAYS SYSTEMATICALLY
WRONG IN EXACTLY THE SAME WAY
AND THAT CAUSES YOU BIG
PROBLEMS.
MODERN COMPUTERS, YOU MIGHT
THINK THAT ALL COMPUTERS DO
ARITHMETIC EXACTLY THE SAME WAY
THAT'S ACTUALLY NOT TRUE AND
THERE'S A STANDARD THAT WAS
PROPAGATED BY THE COMPUTER
INDUSTRY TO TRY TO MAKE
COMPUTERS DO ALL ARITHMETIC IN
THE BEST POSSIBLE WAY TO
MINIMIZE THESE PROBLEMS.
UM, LET ME JUST GIVE YOU AN
EXAMPLE OF THE SORTS OF WAYS
YOU CAN MINIMIZE THE PROBLEMS.
UM, SO WHEN I WAS SO SUPPOSE
YOU'RE TRYING TO ROUND OFF SOME
NUMBER AND THE LAST DIGIT IS
SOMEWHERE BETWEEN ZERO AND NINE
AND YOU HAVE TO ROUND IT OFF.
WELL, IT'S PERFECTLY CLEAR THAT
IF YOU HAVE A ZERO, ONE, TWO,
MODERN COMPUTERS, YOU MIGHT
THINK THAT ALL COMPUTERS DO
ARITHMETIC EXACTLY THE SAME WAY
THAT'S ACTUALLY NOT TRUE AND
THERE'S A STANDARD THAT WAS
PROPAGATED BY THE COMPUTER
INDUSTRY TO TRY TO MAKE
COMPUTERS DO ALL ARITHMETIC IN
THE BEST POSSIBLE WAY TO
MINIMIZE THESE PROBLEMS.
UM, LET ME JUST GIVE YOU AN
EXAMPLE OF THE SORTS OF WAYS
YOU CAN MINIMIZE THE PROBLEMS.
UM, SO WHEN I WAS SO SUPPOSE
YOU'RE TRYING TO ROUND OFF SOME
NUMBER AND THE LAST DIGIT IS
SOMEWHERE BETWEEN ZERO AND NINE
AND YOU HAVE TO ROUND IT OFF.
WELL, IT'S PERFECTLY CLEAR THAT
IF YOU HAVE A ZERO, ONE, TWO,
THREE OR FOUR YOU ROUND IT DOWN
TO ZERO AND IF YOU HAVE A SIX,
SEVEN, EIGHT OR NINE YOU ROUND
IT UP TO ONE BUT THE QUESTION
IS WHAT DO YOU DO WITH THE FIVE?
UH, NOW WHEN I TOOK ARITHMETIC
AT THORNHILL PUBLIC SCHOOL Mrs.
McBRIDE TOLD ME THAT YOU SHOULD
ALWAYS ROUND IT UP AND I JUST
WANT TO CHECK.
I LIKE TO CHECK.
IF YOU WERE TAUGHT TO ROUND
YOUR FIVES UP, COULD YOU RAISE
YOUR HAND?
OKAY, AND HOW MANY PEOPLE WERE
TAUGHT TO DO SOMETHING OTHER
THAN ROUND YOUR FIVES UP.
OKAY, WELL, YOU WERE THE ONES
WHO WERE TAUGHT RIGHT.
IT'S WRONG TO ROUND FIVES UP
AND THE REASON IS THAT IF YOU
THINK ABOUT IT UM, THE NUMBERS
YOU'RE ROUNDING DOWN ARE ONE,
TWO, THREE, FOUR, THE NUMBERS
YOU'RE ROUNDING UP ARE FIVE,
SIX, SEVEN, EIGHT, NINE, THAT
MEANS YOU ROUND UP FIVE TIMES
FOR EVERY FOUR TIMES YOU ROUND
DOWN AND THAT GIVES YOU A
SYSTEMATIC ERROR AND THE RIGHT
WAY TO DO IT JUST SO YOU'LL
KNOW FOR THE FUTURE WHICH I
ASSUME IS THE WAY EVERYBODY
ELSE WAS TAUGHT IS THAT YOU
SOMETIMES ROUND FIVES UP, YOU
SOMETIMES ROUND THEM DOWN.
YOUR HAND?
OKAY, AND HOW MANY PEOPLE WERE
TAUGHT TO DO SOMETHING OTHER
THAN ROUND YOUR FIVES UP.
OKAY, WELL, YOU WERE THE ONES
WHO WERE TAUGHT RIGHT.
IT'S WRONG TO ROUND FIVES UP
AND THE REASON IS THAT IF YOU
THINK ABOUT IT UM, THE NUMBERS
YOU'RE ROUNDING DOWN ARE ONE,
TWO, THREE, FOUR, THE NUMBERS
YOU'RE ROUNDING UP ARE FIVE,
SIX, SEVEN, EIGHT, NINE, THAT
MEANS YOU ROUND UP FIVE TIMES
FOR EVERY FOUR TIMES YOU ROUND
DOWN AND THAT GIVES YOU A
SYSTEMATIC ERROR AND THE RIGHT
WAY TO DO IT JUST SO YOU'LL
KNOW FOR THE FUTURE WHICH I
ASSUME IS THE WAY EVERYBODY
ELSE WAS TAUGHT IS THAT YOU
SOMETIMES ROUND FIVES UP, YOU
SOMETIMES ROUND THEM DOWN.
THE WAY YOU PICK IS JUST TO
ROUND SO THAT THE DIGIT THAT'S
THE LAST DIGIT THAT YOU KEEP IS
ALWAYS EVEN AND THAT JUST SORT
OF GIVES YOU A RANDOM UH, UP
AND DOWN THAT EVENS OUT
SYSTEMATIC ERRORS.
AND MODERN COMPUTERS ARE
SUPPOSED TO ALWAYS DO EXACTLY
THAT WITH THEIR ROUNDING.
IF YOU AREN'T REALLY SURE AND
YOU WANT TO CHECK THERE'S A
PROGRAM WITH THE WONDERFUL NAME
OF PARANOIA UH, THAT'S
AVAILABLE ON THE WEB AT THAT
WEB ADDRESS.
YOU CAN RUN IT ON YOUR COMPUTER
AND IT WILL TELL YOU EVERYTHING
THAT'S WRONG WITH THE WAY YOUR
COMPUTER DOES ARITHMETIC.

[Laughter]

Scott continues OKAY, WELL,
LET'S ASSUME THAT WE NOW KNOW
HOW TO SOLVE THE PROBLEM.
THE INTERESTING QUESTION IS
WHAT'S THE ANSWER.
WELL, I'M PLEASED TO SAY THAT
AFTER FIVE BILLION YEARS UH,
THE EARTH IS STILL THERE THAT'S
THE PUNCH LINE OF THE TALK AND
YOU CAN GO HOME IF YOU WANT.
UM, ALL THE PLANETS ARE STILL
THERE AND ALL THEIR ORBITS LOOK
PRETTY MUCH UH, THE WAY THEY DO NOW.

Four charts pop up showing slightly different orbits.

Scott continues SO THIS IS AN EXAMPLE AND WHAT
THEY'VE DONE HERE IS JUST TAKEN
AN INTERVAL OF 50 MILLION YEARS.
THE INNERMOST FOUR PLANETS
MERCURY, VENUS, EARTH, MARS,
THEY'VE UH, AND THEY'VE JUST
PLOTTED A THOUSAND OR SO POINTS
TAKEN RANDOMLY FROM THIS PERIOD
AND THE POINTS SORT OF MAP OUT
BASICALLY WHERE THE ORBIT IS
AND HOW FAR IT DEVIATES FROM
CIRCULAR AND THIS IS WHAT IT
LOOKS LIKE OVER THE NEAREST 55
MILLION YEARS.
SORRY, THE NEXT 55 MILLION
YEARS.
THAT'S THE LAST 55 MILLION
YEARS.
THIS IS A SIMILAR INTERVAL OF
FOUR AND A HALF BILLION YEARS
IN THE FUTURE AND FOUR AND A
HALF BILLION YEARS IN THE PAST.
REMEMBER THEY JUST PICKED THIS
BECAUSE THAT'S THE AGE OF THE
UH, UH, OF THE SOLAR SYSTEM AND
YOU CAN SEE THERE ARE SOME
MINOR DIFFERENCES BUT BASICALLY
ALL FOUR PLANETS ARE STILL
THERE AND THE ORBITS STILL LOOK
PRETTY MUCH THE SAME.
NEVERTHELESS THIS IS NOT A
BORING PROBLEM.
THERE REALLY ARE A LOT OF
INTERESTING FEATURES UH, IN
WHAT GOES ON IN THIS SYSTEM AND
LET ME MENTION A COUPLE OF THE
INTERESTING FEATURES.
THE FIRST HAS TO DO WITH PLUTO
WHICH YOU REMEMBER IS UH, THE
MOST DISTANT PLANET.
IT ALSO HAS BY FAR THE MOST
UNUSUAL ORBIT WHEREAS MOST OF
THE ORBITS OF THE PLANETS ARE
PRETTY MUCH CIRCULAR, PLUTO HAS
AN EXTREMELY ELLIPTICAL ORBIT
UM, ITS ECCENTRICITY WHICH
WOULD BE ZERO IF IT WERE
CIRCULAR IS AROUND 25 percent.
IT ALSO IS THE HIGHEST
INCLINATION OF ANY PLANET.
ITS ORBIT IS TIPPED AT 17
DEGREES UM, COMPARED TO THE
PLANE FORM OF ALL THE OTHER
PLANETS.

A new slate reads “Pluto’s peculiar orbit.” It shows a drawing of all the orbits, and Pluto’s is much larger and mucho more inclined than the rest.

Scott continues WHAT'S MOST CURIOUS ABOUT ITS
ORBIT IS THAT ITS CLOSEST
APPROACH TO THE SUN BECAUSE
IT'S SO ELLIPTICAL IS ONLY 29.6
ASTRONOMICAL UNITS WHEREAS
NEPTUNE IS ON A CIRCULAR ORBIT
OF 30.1 ASTRONOMICAL UNITS.
SO IF PLUTO
IS CROSSING NEPTUNE'S ORBIT ALL
THE TIME THE ACTUAL QUESTION IS
IF IT'S DONE THIS 100 MILLION
TIMES WHY HAVEN'T THEY
COLLIDED?
WHY HAVEN'T THEY HIT?
UM, AND THE ANSWER ONLY REALLY
BECAME CLEAR
ONCE WE WERE ABLE TO DO THESE
LONG CALCULATIONS OF THE ORBITS
AND THE ANSWER REALLY IS
REMARKABLY ELEGANT.

A new slide shows a drawing of the mutual influence between two planets’ orbits.

Scott continues THE ORBITAL PERIOD OF PLUTO THE
TIME IT TAKES TO GO ONCE AROUND
THE SUN IS 247.7 YEARS.
THE ORBITAL PERIOD OF NEPTUNE
IS 164.8 YEARS.
IF YOU DIVIDE ONE BY THE OTHER
YOU GET 1.5 TO THREE
SIGNIFICANT FIGURES WHICH IS
ALMOST EXACTLY THREE OVER TWO
AND THAT GIVES YOU A CLUE THAT
THERE'S SOME SORT OF FUNNY
RESONANCE UH, GOING ON BETWEEN
THE TWO PLANETS AND THAT CLUE
WAS VERIFIED.
IT TURNS OUT THAT THE TWO
PLANETS ARE EXACTLY IN THIS
RESONANCE THAT IS IF I -- NO
MATTER HOW MANY MORE DIGITS I
WOULD PUT ON THIS UH, THESE TWO
ORBITAL PERIODS I GET 1.50000
UH, THE PHYSICAL NATURE OF THE
RESONANCE IS EASIEST TO SEE BY
IMAGING THAT YOU'RE SITTING ON
NEPTUNE SO THIS IS A FRAME
THAT'S KIND OF ROTATING AROUND
THE SUN WITH NEPTUNE.
AND YOU CAN SEE THAT WITHIN
THAT FRAME THE ORBIT OF PLUTO
TAKES THIS FUNNY UH, ROSETTE
SHAPE SO THERE'S JUPITER,
SATURN AND URANUS.
THEY STILL LOOK CIRCULAR BUT
PLUTO HAS THIS FUNNY ROSETTE
AND YOU CAN SEE THAT WHENEVER
PLUTO IS CLOSEST TO THE SUN
IT'S ALWAYS PRETTY CLOSE TO 90
DEGREES AWAY FROM NEPTUNE MAYBE
GETS AS CLOSE AS 60 DEGREES BUT
THIS RESONANCE ARRANGES THE
ORBIT SO THAT PLUTO ONLY
CROSSES NEPTUNE'S ORBIT WHEN
IT'S A LONG WAY AWAY FROM
NEPTUNE.
SO THEY NEVER COLLIDE.
YOU CAN CALCULATE THESE ORBITS AS FAR
AS YOU WANT INTO THE FUTURE AND
THE PAST AND EVEN THOUGH THE
ORBITS CROSS THEY'LL NEVER
COLLIDE.
THIS IS REALLY A BEAUTIFUL
RESULT AND THE NEXT OBVIOUS
QUESTION IS HOW DID THIS
HAPPEN?
WHY SHOULD
UH, THE FORMATION OF THE SOLAR
SYSTEM HAVE ARRANGED FOR THIS
STRANGE -- FOR PLUTO TO SHOW UP
IN THIS STRANGE ORBIT?
UM, AND THE EXPLANATION WHICH
IS AGAIN ALMOST EQUALLY ELEGANT
UH, CAME FROM RENE MALHUTRA
ABOUT 10 YEARS AGO.

A new slide shows a chart with lines that appear to stabilize in time.

Scott continues SHE POINTED OUT VERY EARLY IN
THE HISTORY OF THE SOLAR SYSTEM
THERE WAS PLENTY OF DEBRIS
LEFTOVER BETWEEN THE PLANETS,
THE MATERIAL THAT HADN'T YET
BEEN INCORPORATED IN THE PLANETS.
UH, THIS DEBRIS WOULD
GRAVITATIONALLY INTERACT WITH
NEPTUNE AND NEPTUNE WOULD TEND
TO EJECT IT FROM THE SOLAR
SYSTEM AND IN THE PROCESS OF
DOING SO THE BACK REACTION
WOULD CAUSE NEPTUNE'S ORBIT TO
SLOWLY DRIFT OUTWARDS.
NOW IF YOU IMAGINE THAT PLUTO
STARTED OFF IN A CIRCULAR ORBIT
LIKE ALL THE OTHER PLANETS DID
OUTSIDE NEPTUNE AS NEPTUNE
DRIFTS OUT WOULD EVENTUALLY
CROSS THIS -- NEPTUNE'S ORBITAL
PERIOD WOULD INCREASE AND
EVENTUALLY THERE'D COME A POINT
WHEN PLUTO'S ORBITAL PERIOD WAS
JUST 1.50000 TIMES THE ORBITAL
PERIOD OF NEPTUNE AT THAT POINT
IT TURNS OUT IF YOU FOLLOW WHAT
HAPPENS USING NEWTON'S LAWS
PLUTO GETS CAPTURED INTO THE
RESONANCE AND FROM THEREAFTER
EVEN AS NEPTUNE CONTINUES TO
MOVE OUT, IT STAYS IN EXACTLY
THAT THREE TO TWO RATIO.
UM, HOWEVER AS NEPTUNE MOVES
OUT ALTHOUGH IT STAYS IN THAT
THREE TO TWO RATIO THE ORBIT
STARTS TO CHANGE.
IT BECOMES MORE -- IT BECOMES
LESS CIRCULAR AND MORE
ECCENTRIC AND STARTS TO BUILD-
UP AN INCLINATION AND IN FACT,
ALL THE OF FUNNY FEATURES OF
NEPTUNE OF PLUTO'S ORBITS, THE
HIGH ECCENTRICITY, THE HIGH
INCLINATION AND THE FACT THAT
IT'S EXACTLY IN THIS RESONANCE
OR NATURAL CONSEQUENCE OF THE
SINGLE HYPOTHESIS UH, THAT
NEPTUNE DRIFTED OUT AND
CAPTURED PLUTO FROM A CIRCULAR
ORBIT.
UM, MOREOVER THIS HYPOTHESIS
MAKES A PREDICTION SINCE PLUTO
WASN'T NECESSARILY THE ONLY
OBJECT OUT THERE OTHER OBJECTS
MIGHT BE CAPTURED IN THIS
RESONANCE AS WELL SO PLUTO
MIGHT NOT BE ALONE.
UM, AND THAT PREDICTION TURNS
OUT HAS BEEN VERIFIED UM, THIS
IS A SNAPSHOT AS OF OCTOBER
20th OF LAST YEAR THE POSITIONS
OF ALL THE SMALL BODIES UH,
ASTEROIDS, COMETS AND OTHER
BODIES KNOWN IN THE SOLAR
SYSTEM...

A picture chart shows concentric circles with bright blue dots in the middle, few yellow dots in the nearest circles, and hundreds of red dots spread out in the farther curcles.

Scott continues THAT IS THE SMALL BODIES
OUTSIDE THE PLANETS UM, THE
BLUE OBJECTS ARE COMETS WHICH
YOU ONLY SEE WHEN THEY'RE VERY
CLOSE TO THE SUN.
UH, THIS IS THE ORBIT OF
NEPTUNE, URANUS, SATURN, UH,
JUPITER, THE EARTH'S ORBIT IS
TOO SMALL TO SEE ON THIS.
UM, MOST OF THESE RED AND WHITE
OBJECTS ARE OBJECTS CALLED
Kuiper belt OBJECTS.
THEY'RE IN AN EXTENDED BELT
SOMEWHAT LIKE THE ASTEROID BELT
OF SMALL BODIES THAT ORBITS
OUTSIDE UH, NEPTUNE.
THESE WERE MOSTLY DISCOVERED IN
THE LAST UH, DECADE.
THERE ARE NOW ROUGHLY A
THOUSAND NOW AND AS PEOPLE
DISCOVERED MORE AND MORE OF
THEM AND STARTED TO CALCULATE
THEIR ORBITS AND WORK OUT
EXACTLY WHAT THEIR ORBITS WERE
LIKE THEY DISCOVERED A
REMARKABLE THING WHICH IS A
VERY LARGE FRACTION OF THEM ARE
EXACTLY IN THE SAME THREE TO
TWO RESONANCE THAT PLUTO IS IN
SO THE ONES IN THIS RESONANCE
HAVE STARTED TO BE CALLED
PLUTINOS FOR LITTLE PLUTOS UM,
AND ALMOST CERTAINLY WHAT
HAPPENED IS THAT THESE WERE
SMALLER BODIES THAT PLUTO THAT
LIKE PLUTO WERE CAPTURED IN THE
RESONANCE AND NEPTUNE MIGRATED
OUTWARDS.
UM, AND THAT -- THE FACT THAT
PLUTO'S ORBIT SHARES THIS
PROPERTY WITH SO MANY OF THESE
SMALLER BODIES DO IS ONE OF THE
REASONS THAT MOST ASTRONOMERS
NOWADAYS DON'T THINK OF PLUTO
AS A PLANET, THEY THINK OF IT
AS JUST THE LARGEST MEMBER OF
THIS VAST KUIPER BELT OF SMALL
BODIES OUTSIDE OF NEPTUNE.
UM, BUT THERE ARE MORE
INTERESTING THINGS ABOUT THE
BEHAVIOUR OF THE SOLAR SYSTEM
ON VERY LONG TIMES.
ONE OF THE THINGS WE'VE LEARNED
FROM STUDYING THIS PROBLEM AND
MANY OTHER DYNAMICAL SYSTEMS IS
THAT ROUGHLY SPEAKING YOU CAN
DIVIDE DYNAMICAL SYSTEMS INTO
TWO KINDS UM, WHAT ARE CALLED
REGULAR DYNAMICAL SYSTEMS WHICH
ARE HIGHLY PREDICTABLE AND WELL
BEHAVED.

A new slide reads “Two kinds of dynamical system.”

Scott continues MATHEMATICALLY WHAT THAT SAYS
IS IF YOU TAKE THE SYSTEM AND
YOU CHANGE IT A LITTLE BIT AND
FOLLOW THE NEW SYSTEM AND THE
OLD SYSTEM THE DIFFERENCE
BETWEEN THEM WILL GROW BUT
IT'LL ONLY GROW LINEARLY WITH
THE TIMES.
SO IF YOU SAY THROW A BASEBALL
AND THEN YOU IMAGINE THROWING
ANOTHER BASEBALL FROM A
POSITION A MILLIMETRE DIFFERENT
AFTER ONE SECOND THE DIFFERENCE
MIGHT BE TWO MILLIMETRES, AFTER
TWO SECONDS IT MAY BE THREE.
AFTER THREE SECONDS IT MIGHT BE
FOUR AND SO FORTH AND SO THE
DIFFERENCE GROWS SLOWLY.
IN CONTRAST TO THIS THERE ARE
CHAOTIC SYSTEMS WHICH ARE
DIFFICULT TO PREDICT AND
ERRATIC IN THOSE CASES SMALL
DIFFERENCES GROW EXPONENTIALLY
SO THAT MEANS THE DIFFERENCES
OF A MILLIMETRE AFTER ONE
SECOND, AFTER TWO SECONDS IT'S
TWO MILLIMETRES, AFTER THREE
SECONDS IT MIGHT BE FOUR.
THEN EIGHT, THEN 16.
THE DIFFERENCE BLOWS UP.
UH, AND THERE ARE MANY EXAMPLES
SO THE FIRST EXAMPLE A TYPICAL
CHAOTIC SYSTEM WOULD BE A
ROULETTE WHEEL AND THAT'S
BECAUSE A ROULETTE WHEEL IS
DESIGNED TO MAKE THE MOTION OF
THE BALL AS UNPREDICTABLE AS
POSSIBLE.
DICE OR PINBALL ARE OTHER
EXAMPLES.
MORE IMPORTANT EXAMPLE IS THE
WEATHER.
THE REASON THAT WEATHER
PREDICTIONS ONLY WORK WELL OVER
THE SPACE OF A FEW DAYS IS
BECAUSE THE SYSTEM -- THE
ATMOSPHERIC SYSTEM IS BASICALLY
CHAOTIC UM, REGULAR SYSTEMS --
THE WHOLE
IDEA OF GOLF IS THAT THE MOTION
OF THE GOLF BALL IS VERY
REGULAR AND THEREFORE
PREDICTABLE.
IF YOU HAVE A VERY ROUGH GREEN
THAT MAKES THE MOTION CHAOTIC
AND SORT OF DESTROYS ALL THE
FUN OF GOLF.
THE IMPORTANCE OF CHAOTIC SYSTEMS
WASN'T RECOGNIZED REALLY UNTIL
COMPUTERS CAME ALONG BECAUSE IT
TURNS OUT THAT THE ONLY
PROBLEMS YOU CAN WRITE DOWN THE
ANSWER TO WITH A PENCIL AND
PAPER ARE REGULAR PROBLEMS SO
ALL OF THE PROBLEMS THAT YOU
EVER DID IN A PHYSICS COURSE
ARE REGULAR SYSTEMS UM, AND I
HAVE A LITTLE DEMONSTRATION
WHICH I HOPE SOME OF YOU CAN
SEE THE DIFFERENCE BETWEEN A
REGULAR AND A CHAOTIC SYSTEM.

He walks up to a metal and wood device on the stage and continues
UM, THIS IS JUST A VERY SIMPLE PENDULUM.
PENDULUMS ARE EXTREMELY REGULAR
THAT'S WHY THEY WERE THE BASIS
OF CLOCK MECHANISMS FOR
HUNDREDS OF YEARS.

He starts the pendulum and says
IF YOU START THIS IT JUST GOES
BACK AND FORTH UH, COMPLETELY
PREDICTABLE YOU KNOW EXACTLY
WHAT THE PERIOD IS, YOU KNOW
EXACTLY WHAT IT'S GOING TO DO
UNTIL IT GRADUALLY DAMPS OUT
FROM FRICTION IN THE BEARING.

He unfolds the pendulum, turning it into a double pendulum.

Scott continues UM, BUT YOU CAN MODIFY THIS AND
THE MODIFICATION IS SIMPLY TO
MAKE IT INTO A DOUBLE PENDULUM
SO WHAT I'VE GOT IS THE FIRST
PENDULUM HERE, SECOND ONE HERE
WITH THE SECOND HUB UM, AND IF
I START IT NEAR THE BOTTOM AND
I JUST LET IT GO BACK AND FORTH
YOU CAN SEE IT BEHAVES PRETTY
MUCH LIKE A SINGLE PENDULUM
THAT IS IT'S STILL REGULAR.
IT'S NOT DOING ANYTHING VERY
INTERESTING BUT IF YOU START UP
SAY UP HERE YOU'VE GOT A
SOMEWHAT DIFFERENT BEHAVIOUR.

He starts the pendulum from the very top, and as it unfolds the second pendulum begins to spin and move erratically.

[Laughter]

Scott continues AND YOU CAN
SEE THAT JUST ADDING THIS ONE
EXTRA COMPLICATION TO THE UM...

[Laughter]

Scott continues TO THE
MECHANICAL SYSTEM MAKES THE
BEHAVIOUR COMPLETELY DIFFERENT
AND THIS IS THE SORT OF
PROTOTYPICAL CHAOTIC SYSTEM UM,
OKAY, IT REALLY IS -- I'LL
START IT AGAIN WHILE I KEEP
TALKING.
IT'S REALLY DIFFICULT.

He starts it again and continues
OKAY, WELL,
OF COURSE THE WHOLE SUCCESS OF
NEWTON'S LAWS IN EXPLAINING THE
MOTION OF THE SOLAR SYSTEM
ARISES FROM THE FACT THAT ON
RELATIVELY SHORT TIMESCALES
TENS OF YEARS OR HUNDREDS OF
YEARS OR TENS OF THOUSANDS OF
YEARS THE SOLAR SYSTEM IS
COMPLETELY REGULAR AND
EXTREMELY WELL BEHAVED HOWEVER
WHEN PEOPLE STARTED TO DO THESE
VERY LONG CALCULATIONS OF THE
PLANETS THEY GOT A SURPRISE,
UM, THEY WERE DOING THE CLASSIC
TESTS TO SEE WHETHER A SYSTEM
WAS REGULAR OR CHAOTIC BUT AS
THEY STARTED ALL THE PLANETS
OFF AND THEN THEY STARTED OFF A
SLIGHTLY DIFFERENT SYSTEM SO
FOR INSTANCE HERE THIS IS
DISTANCE BETWEEN JUPITER AND
THE FIRST CALCULATION AND THE
SECOND CALCULATION WHICH THEY
KEPT EVERYTHING THE SAME EXCEPT
THEY MOVED THE POSITION OF
JUPITER BY ONE MILLIMETRE OUT
OF 300 MILLION KILOMETRES AND
WHAT HAPPENED IS THAT OVER VERY
LONG TIMES, OVER A FEW HUNDRED
MILLION YEARS UM, THE
DIFFERENCE STARTED TO GROW
EXPONENTIALLY.

A new slide pops up with two charts, for Pluto and Jupiter, showing the growing distance between orbits.

Scott continues SO THIS IS A GRAPH IN WHICH UH,
THIS DISTANCE IS THE FACTOR OF
A THOUSAND AND YOU CAN SEE THAT
ABOUT EVERY HUNDRED MILLION
YEARS UH, THE DIFFERENCE
BETWEEN THE TWO GROWS BY ABOUT
A FACT OF A THOUSAND.
IT STOPS OUT HERE AND THAT'S
SOMETHING BECAUSE AFTER THIS
AMOUNT OF TIME THE ORIGINAL
JUPITER AND THE SECOND ONE THAT
YOU STARTED ARE ON OPPOSITE
SIDES OF THE SOLAR SYSTEM.
THEY CAN'T GET ANY FURTHER APART.
UH, SO THE DIFFERENCE BETWEEN
THEM GREW FROM ONE MILLIMETRE
TO UH, UH, SEVERAL HUNDRED
MILLION KILOMETRES OVER 300
MILLION YEARS.
THE SAME THING IS TRUE FOR
PLUTO.
HERE YOU CAN SEE THE DIFFERENCE
BETWEEN PLUTO AND A FAKE PLUTO
IN TWO DIFFERENT TESTS GROWING
BY A FACTOR OF 10,000 ABOUT
EVERY 100 MILLION YEARS.
WHEN YOU LOOK AT THIS FOR THE
PLANETS YOU FIND THAT EVERY
PLANET IN THE SOLAR SYSTEM IS
CHAOTIC INCLUDING THE EARTH.
THE CHAOS IS SUFFICIENTLY
STRONG AT THE SEPARATION OF AN
ORIGINAL PLANET AND UH, A
SECOND PLANET WILL TEND TO
DOUBLE ON A TIMESCALE OF ABOUT
10 MILLION YEARS.
UM, SO WHAT ARE THE
CONSEQUENCES OF THIS?
UM, ALL THE ORBITS OF THE
PLANETS ARE CHAOTIC.
THAT DOESN'T MEAN THAT THE
PLANETS ARE ALL WANDERING ALL
OVER THE SOLAR SYSTEM, IT TURNS
OUT THE CHAOS, THEY'RE --
THEY'RE LIMITED TO RELATIVELY
SMALL RINGS AROUND THEIR
CURRENT ORBITS SO THE ORBITS --
THAT'S WHY THE ORBITS LOOK THE
SAME IN THAT PICTURE I SHOWED
YOU EARLIER.
NEVERTHELESS IT MEANS THAT
SMALL CHANGES IN THE POSITIONS
OF THE PLANETS ARE AMPLIFIED BY
A FACTOR THAT'S 10 WITH 150
ZEROS AFTER IT OVER THE
LIFETIME OF THE SOLAR SYSTEM.
SO FOR EXAMPLE WHAT THAT MEANS
THAT IF NASA LAUNCHES AN
INTERPLANETARY SPACECRAFT IN
ONE DIRECTION UM, NEXT WEEK THE
BACK REACTION ON THAT CHANGES
THE ORBIT OF THE EARTH A LITTLE
AND THAT CHANGE WILL GRADUALLY
GROW ENOUGH SO THAT AFTER 100
MILLION YEARS THE EARTH WILL BE
ON THE OPPOSITE SIDE OF THE SUN
FROM WHERE IT WOULD'VE BEEN
BEFORE THE SPACECRAFT WAS
LAUNCHED.
WHAT IT ALSO MEANS THAT IF YOU
FOLLOW THE PLANETS FOR A VERY
LONG TIME YOU DO EVENTUALLY
START TO SEE SOME CHANGES IN
THE ORBITS.
THIS IS THE LONGEST CALCULATION
THAT'S BEEN DONE.

A chart pops up showing three lines that behave very differently.

Scott continues THE TIME HERE IS MEASURED IN
BILLIONS OF YEARS.
IT'S KIND OF A FAKE CALCULATION
BECAUSE AS I SAID THE SUN WILL
TURN INTO A RED GIANT HERE BUT
OF COURSE YOU CAN DO THE
CALCULATION IGNORING THE DEATH
OF THE SUN AND JUST KEEP GOING
AND WHAT YOU SEE IS THAT THE
ECCENTRICITY OF MERCURY'S ORBIT
BASICALLY UNDERGOES A SORT OF
RANDOM WALK IT LOOKS KIND OF
LIKE THE STOCK MARKET OVER A
VERY LONG PERIOD OF UH, 10 TO
15 BILLION YEARS.
THE EARTH ON THE OTHER HAND
DOESN'T SEEM TO VARY VERY MUCH.
MARS IS SOMEWHAT INTERMEDIATE.
UM, WHAT ARE THE CONSEQUENCES
OF THAT?
WELL, IF MERCURY IS WANDERING
ALL OVER THE PLACE LIKE THAT
EVENTUALLY UM, MERCURY IS GOING
TO COLLIDE WITH ONE OF THE
OTHER PLANETS OR FALL INTO THE
SUN OR GET EJECTED FROM THE
SOLAR SYSTEM.
UM, SO THAT MEANS THAT IN A
CERTAIN SENSE THAT THE SOLAR
SYSTEM REALLY IS UNSTABLE.
IF YOU WAIT LONG ENOUGH ONE OF
THE PLANETS PROBABLY MERCURY
UM, IS LIKELY TO GET EJECTED SO
THE MATHEMATICAL QUESTION OF
WHETHER THE SOLAR SYSTEM IS
STABLE THE ANSWER IS NO.
THE PRACTICAL QUESTION IS IS
THE EARTH STILL GONNA BE HERE
WHEN THE SUN DIES THE ANSWER IS
PROBABLY YES.
UH, IT ALSO, ONE OF THE IRONIES OF THIS OF
COURSE SOLAR SYSTEM WAS THE
INSPIRATION FOR UH, LAPLACE
DETERMINISM UM, IT'S THE MODEL
THAT'S ALWAYS HELD UP AS THE
DETERMINISTIC UNIVERSE AND IN
FACT IT TURNS OUT TO BE UNPREDICTABLE
ON VERY LONG TIMESCALES BUT
THERE ARE OTHER VERY
INTERESTING CONSEQUENCES AS WELL.
IF MERCURY IS LIKELY TO BE
EJECTED SOMETIME IN THE FUTURE,
WHAT'S TO SAY THAT HASN'T
ALREADY HAPPENED IN THE PAST?
WHAT'S TO SAY THAT WE DIDN'T
START OUT WITH 10 OR 15 PLANETS
AND SEVERAL OF THEM HAVE BEEN
EJECTED IN THE PAST.
OBVIOUSLY WE CAN'T TELL.
THE PLANETS ARE GONE.
WE HAVE NO WAY OF KNOWING
WHETHER THEY WERE THERE OR NOT
BUT THERE IS A REALLY
SIGNIFICANT CLUE THAT THIS
MIGHT HAVE HAPPENED.
THIS PLOT IS A LITTLE BIT
COMPLICATED BUT UH, THE CONCEPT
IS EASY TO EXPLAIN.

A new chart shows the behaviour of particles throughout time.

Scott continues IN THIS PARTICULAR CASE UM,
INSTEAD OF JUST CALCULATING THE
MOTION OF ALL OF THE PLANETS
UH, WHAT MATT HOLMAN DID WAS HE
ADDED A WHOLE BUNCH OF SMALL
PARTICLES IN BETWEEN THE
PLANETS.
HE ADDED ABOUT 5,000 SMALL
PARTICLES SPREAD OUT BETWEEN
JUPITER WHICH IS AT A RADIUS
HERE AND NEPTUNE AT A RADIUS
HERE AND THEN HE JUST FOLLOWED
WHAT HAPPENED TO THEM ALONG
WITH THE PLANETS AND THE GREEN
DOTS REPRESENT THE POINT AT
WHICH ONE OF THESE SMALL
PARTICLES GOT EJECTED SO FOR
INSTANCE THIS PARTICLE GOT
EJECTED AFTER A MILLION YEARS,
THIS ONE AFTER A HUNDRED
MILLION YEARS, THIS ONE UH,
HERE AFTER ABOUT A BILLION
YEARS AND THE RED ONES MARK THE
PARTICLES THAT SURVIVED UNTIL
THE AGE OF THE SOLAR SYSTEM AT
ABOUT FIVE BILLION YEARS AND
YOU CAN SEE THAT PRACTICALLY
NONE OF THE PARTICLES SURVIVE.
THESE UM, ARE ACTUALLY
PARTICLES ON THE SAME ORBIT AS
JUPITER BUT LEADING OR LAGGING
IT BY 60 DEGREES.
WE KNOW THAT PARTICLES THERE
SHOULD SURVIVE BECAUSE A SET OF
FAMILY OF ASTEROIDS CALLED THE
TROJAN ASTEROIDS ARE THERE BUT
ALL OF THE SMALL BODIES IN
BETWEEN UM, THE PLANETS DIDN'T
SURVIVE.
THE ONES OUT HERE SURVIVED AND
THAT'S GOOD BECAUSE THAT'S
WHERE WE SEE THE OBJECTS IN THE
KUIPER BELT SO IT'S A GOOD
THING THAT THOSE ORBITS ARE
STABLE.
WHAT THAT SAYS IS IF THERE WAS
EVER WAS A PLANET ANYWHERE
BETWEEN JUPITER AND NEPTUNE IT
WOULD'VE GOTTEN KICKED OUT OF
THE SOLAR SYSTEM LONG BEFORE
UH, THE CURRENT TIME.
WHAT THAT MEANS IN A SENSE IS
THIS REGION OF THE GIANT
PLANETS IS FULL EVEN IF YOU
WANTED TO STUFF ANOTHER PLANET
IN THERE UH, YOU COULDN'T DO
THAT AND THE MOST NATURAL
REASON TO SUSPECT THAT IT'S
FULL IS THAT IT ONCE HAD MORE
PLANETS.
AND SOME OF THE PLANETS LIKE
SOME OF THESE SMALL BODIES GOT
EJECTED WHEN THE SOLAR SYSTEM
WAS MUCH YOUNGER.
OKAY, SO LET ME JUST
RECAPITULATE UM, THESE ARE SOME
OF THE QUESTIONS THAT I ASKED
RIGHT AT THE START AND WE CAN
NOW GIVE SOME BUT NOT ALL OF
THE ANSWERS.

A slide pops up that reads “Why do we care?”

Scott continues WHAT'S THE FATE OF THE EARTH AS
FAR AS WE KNOW?
THE EARTH WILL SURVIVE SEVEN
BILLION YEARS UNTIL THE SUN
DIES AND TURNS INTO A RED GIANT.
WHETHER IT WILL SWALLOW THE
EARTH OR NOT IS A LITTLE HARD
TO SAY.
MOST LIKELY THE EARTH WILL
SURVIVE BUT MERCURY AND VENUS
WILL NOT.
WHY ARE THERE SO FEW PLANETS?
BASICALLY BECAUSE THE SOLAR
SYSTEM IS FULL.
WE COULDN'T PUT ANYMORE IN EVEN
IF WE WANTED TO.
UH, WHY ARE THE REGIONS BETWEEN
THE PLANETS SO CLEAN?
THAT'S THE SAME REASON.
YOU DON'T SEE SMALL BODIES
BETWEEN EARTH AND VENUS OR
BETWEEN JUPITER AND SATURN
BECAUSE THEY COULDN'T SURVIVE.
THE ONLY REGION WHERE THEY
COULD SURVIVE IS THE ASTEROID
BELT BETWEEN MARS AND JUPITER
AND THE KUIPER BELT OUTSIDE
NEPTUNE.
WAS THE PRESENT STATE OF THE
SOLAR SYSTEM DETERMINED IN THE
FIRST MILLION YEARS?
WE DON'T KNOW BUT THE ANSWER IS
PROBABLY NOT.
UH, PEOPLE WHO FOCUS ON THE
FORMATION OF THE SOLAR SYSTEM
UM, UH, ARE TRYING TO SOLVE AN
IMPORTANT PROBLEM BUT THERE'S
ALMOST CERTAINLY A SECOND MUCH
SLOWER EVOLUTIONARY STAGE
THAT'S DETERMINED MANY OF THE
PROPERTIES OF THE CURRENT
SYSTEM.
CAN WE CALIBRATE THE GEOLOGICAL
TIMESCALE OF THE LAST HUNDRED
MILLION YEARS?
THE ANSWER IS YES, WE CAN'T DO
IT MUCH FURTHER THAN THAT
BECAUSE OF THIS CHAOTIC NATURE
OF THE SOLAR SYSTEM UH, STARTS
TO AFFECT THE ACCURACY OF THE
CALCULATION.
UM, BUT ASTRONOMERS ARE NOW
PROVIDING THE GEOLOGISTS WITH
EXTREMELY ACCURATE UH, UH, WITH
EXTREMELY ACCURATE MODELS.
A VARIATION OF THAT ON SUNLIGHT
ON THE EARTH OVER THE LAST
HUNDRED MILLION YEARS.
THE FINAL AND PERHAPS THE MOST
INTERESTING QUESTION IS WHAT
WILL OTHER PLANETARY SYSTEMS
LOOK LIKE?
UM, I DON'T HAVE A THEORETICAL
ANSWER FOR THAT BUT WHAT I WILL
DO IN THE LAST FEW MINUTES OF
THE TALK IS TELL YOU WHAT THE
CURRENT OBSERVATIONAL STATUS IS
OF OTHER PLANETARY SYSTEMS.
FOR HUNDREDS OF YEARS
ASTRONOMERS HAVE BEEN LOOKING
FOR UH, PLANETARY SYSTEMS
AROUND OTHER STARS UH, BUT IT'S
AN EXTREMELY DIFFICULT PROBLEM.
THE PROBLEM IS NOT THAT THE
PLANETS ARE SO FAINT IT'S THAT
THE STARS ARE SO BRIGHT.
THE PROBLEM IS NOT THAT YOU CAN
SEE THE PLANETS, IF THEY WERE
ISOLATED BUT THEY'RE
OVERWHELMED BY THE LIGHT OF THE
STAR, THE ANALOGY THAT
SOMETIMES DRAWN IS LIKE TRYING
TO UH, LOOK AT A -- LOOKING AT
A SEARCHLIGHT WITH A BIG
TELESCOPE FROM 10 MILES AWAY
AND TRYING TO FIND A FIRE FLY
FLYING AROUND THE SEARCHLIGHT
SO YOU HAVE TO USE INDIRECT
METHODS.

A diagram titled “Doppler shift due to Stellar wobble” shows a telescope looking at two positions of a star as a small planet moves below with the caption “unseen planet.”

Scott continues AND BY FAR THE MOST SUCCESSFUL
OF THESE HAS BEEN THE
RECOGNITION THAT IF YOU HAVE AN
UNSEEN PLANET ORBITING A STAR
BOTH THE PLANET AND THE STAR --
THE PLANET DOESN'T JUST ORBIT
AROUND THE STAR BUT BOTH THE
STAR AND PLANET ORBIT AROUND
THEIR COMMON CENTRE OF GRAVITY
AND THAT MEANS THAT AS THE
PLANET ORBITS THE STAR UH,
COMES TOWARDS YOU AND THEN AWAY
FROM YOU AT SPEEDS OF MAYBE 100
KILOMETRES PER HOUR UM, AND UH,
THE DOPPLER SHIFT, THE SAME
SHIFT THAT CAUSES UH, UH, THE
SOUND OF A TRAIN COMING TOWARDS
YOU COULD BE DIFFERENT FROM A
TRAIN GOING AWAY SHIFTS THE
SPECTRUM OF THE STAR AND THOSE
SHIFTS CAN BE DETECTED WITH VERY ACCURATE
MEASUREMENTS.
THIS TECHNIQUE WAS ACTUALLY
PIONEERED BY GORDON WALKER AT
THE UNIVERSITY OF BRITISH
COLUMBIA WHO HAD A LONG
PROGRAM TO MONITOR A DOZEN NEARBY STARS TO
LOOK FOR PLANETS.
IT TURNED OUT THAT HE WAS
UNLUCKY.
HE PICKED THE WRONG STARS AND
THE FIRST GROUP WHO WERE LUCKY
WERE CENTRED AT THE UNIVERSITY
OF GENEVA AND THEY FOUND A STAR
WHOSE VELOCITY TOWARDS A STAR
LIKE THIS THAT'S AN
UNMISTAKABLE SIGNATURE OF A
PLANET WITH A PERIOD OF A
LITTLE OVER FOUR DAYS.

A blue and yellow chart shows the velocity and time of a star in its orbit.

Scott continues A NEARLY CIRCULAR ORBIT AND
IT'S JUST UNDER JUPITER'S MASS.
BY NOW WE KNOW OF OVER 100
PLANETS...

A new diagram shows hundreds of items ordered by growing distance.

Scott continues UH, THIS IS A DIAGRAM
THAT USED TO MAKE A LOT MORE
SENSE WHEN THERE WERE FEWER
PLANETS BUT NOW IT'S SQUASHED
SO MUCH YOU CAN HARDLY READ IT
BUT BASICALLY I'VE RANKED THE
PLANETS IN TERMS OF DISTANCE
FROM THEIR PARENT STAR.
THERE'S ONE ASTRONOMICAL UNIT
SO THE EARTH WOULD BE ABOUT HERE.
THERE ARE A FEW CASES WHERE
THERE ARE MULTIPLE PLANETS
WHERE THEY SEE MORE THAN ONE
PLANET IN A GIVEN SYSTEM.
ALL OF THE PLANET MASSES ARE
TYPICALLY A FEW JUPITER MASSES.
UM, AND MAYBE OCCASIONALLY AS
SMALL AS A SATURN MASS.
THAT'S SIMPLY BECAUSE CURRENT
TECHNIQUES AREN'T SENSITIVE
ENOUGH TO DETECT PLANETS THAT
ARE ANY SMALLER NOT BECAUSE
THERE'S ANY REASON TO SUPPOSE
THAT THEY'RE NOT THERE.
UH, NOW ONE OF THE -- SINCE
THESE ARE DETECTED BY AN
INDIRECT METHOD JUST BY LOOKING
AT CHANGES IN THE STAR OF
COURSE YOU DON'T KNOW FOR SURE
THAT THEY'RE PLANETS AND THERE
WAS A TREMENDOUS AMOUNT OF
SCEPTICISM UH, THAT THESE MIGHT
BE DUE TO SOME FUNNY EFFECT IN
THE ATMOSPHERE OF THE STAR OR
SOME MISTAKE THAT UH, UH,
PEOPLE WERE MAKING THE ANALYSIS
SO IT'S EXTREMELY IMPORTANT TO
HAVE SOME KIND OF CONFIRMATION.
UH, ONE POSSIBLE WAY OF
CONFIRMATION IS TO RECOGNIZE
THAT ALTHOUGH THESE PLANETARY
ORBITS ARE GOING TO BE ORIENTED
AT RANDOM.
IF YOU HAVE ENOUGH STARS
THERE'S LIKELY TO BE A SMALL
FRACTION OF THEM WHERE THE
PLANETARY ORBIT IS EXACTLY EDGE
ON THAT MEANS THAT ONCE PER
ORBIT THE PLANET WILL PASS
DIRECTLY IN FRONT OF THE STAR.

A drawing titled “transit method” shows a planet passing in front of a star. Below, a chart shows the change in the brightness of the star caused by the passing planet.”

Scott continues WHEN IT PASSES DIRECTLY IN
FRONT OF THE STAR IT WILL BLOCK
OUT SOME OF THE STARLIGHT AND
YIELD TO A VERY SMALL BUT
PERHAPS DETECTABLE PERIODIC DIP
UH, IN THE LIGHT FROM THE STAR.
UH, THIS IS A PHENOMENA THAT
ACTUALLY ALSO OCCURS UH, IN THE
SOLAR SYSTEM MOST PROMINENTLY
IN THE TRANSIT OF VENUS.
THIS IS A RELATIVELY RARE EVENT
IN OUR SOLAR SYSTEM.
NO ONE LIVING HAS SEEN THIS
EVENT BECAUSE THE LAST ONE
OCCURRED UH, IN 1882 BUT I'M
PLEASED TO REPORT THAT THE NEXT
ONE IS NEXT TUESDAY.

[Laughter]

A picture shows a small black circle on the surface of a bright celestial body.

Scott continues THIS IS AN
IMAGE FROM THE 1882 UH, EVENT
UH, THESE WERE EXTREMELY
IMPORTANT HISTORICALLY AND IN
FACT UH, CAPTAIN COOKE'S VOYAGE
OF DISCOVERY TO THE SOUTH SEAS
IN WHICH HE DISCOVERED TAHITI
WAS MOTIVATED BY THE FACT THAT
THERE WAS A TRANSIT OF VENUS
THAT WAS OBSERVABLE FROM THE
SOUTH PACIFIC AND IT WAS USED
IN THE 18th AND 19th CENTURY TO
TRY TO MEASURE ACTUALLY THE
SIZE OF THE ASTRONOMICAL UNIT.
BY NOW IT'S MORE OF A CURIOSITY
THAN ANYTHING ELSE.
UM, THIS PARTICULAR TRANSIT,
ENTIRE TRANSIT IS VISIBLE FOR
EUROPE.
IT'S NOT VISIBLE FROM THE WEST
COAST.
IT'S ONLY MARGINALLY VISIBLE
FROM HERE, FROM WATERLOO.
IT'S ONLY VISIBLE UH, FROM
AFTER THE SUN RISES UNTIL ABOUT
7:25 NEXT TUESDAY MORNING.
UH, I WOULD CAUTION YOU THAT IF
YOU WANT TO LOOK FOR THIS UM,
YOU DON'T LOOK AT THE SUN
DIRECTLY BECAUSE YOU CAN CAUSE
PERMANENT DAMAGE TO YOUR EYES.
UM, THE SAFEST WAY IS TO USE A
PINHOLE CAMERA UM, JUST TO PUT
A SMALL PINHOLE, SMALL HOLE IN
A PIECE OF PAPER AND HOLD IT UP
IN FRONT OF A FLAT SCREEN BUT
IF YOU JUST LOOK FOR -- IF YOU
JUST GOOGLE TRANSIT OF VENUS
YOU'LL FIND LOTS OF ADVICE ON
UH, UH, HOW TO LOOK FOR IT IF
THE SKIES ARE CLEAR ON TUESDAY
MORNING.
WELL, TO GO BACK TO OTHER
PLANETARY SYSTEMS UM, PEOPLE
THAT WENT OUT, ONCE THEY
RECOGNIZED THE POSSIBILITY OF A
TRANSIT THEY WENT OUT AND
LOOKED WITH 100 UH, STARS WITH
KNOWN PLANETS AROUND THEM.
THE CHANCES WERE THAT ONE OR
MAYBE TWO UH, MIGHT SHOW A
TRANSIT AND WE WERE LUCKY AND
ONE OF THEM DID.

A new chart shows a significant dip in the light of a star.

Scott continues UM, YOU CAN SEE THIS IS ONE
EXAMPLE OF THE TRANSIT CAUSED
BY THE PLANET IN THIS
PARTICULAR SYSTEM THE LIGHT
FROM THE STAR DROPS BY ABOUT
ONE AND A HALF PERCENT.
THE SHAPE OF THIS CURVE IS
ENORMOUSLY INFORMATIVE ON
TELLING YOU ABOUT PROPERTIES OF
THE PLANETS IN THIS CASE WE
KNOW MORE ABOUT THIS BECAUSE
THE -- BECAUSE OF THIS WE KNOW
MORE ABOUT THIS THAN ANY OTHER
SOLAR PLANET.
THE MASSES JUST UNDER 70 percent OF
JUPITER MASS.
THE RADIUS IS SOMEWHAT BIGGER
THAN JUPITER'S AND THAT'S
SIMPLY BECAUSE IT'S SO CLOSE TO
THE PARENT STAR.
ITS ORBITAL RADIUS UH, IS ONLY
A 20th OF AN ASTRONOMICAL UNIT
FAR CLOSER THAN MERCURY IS TO
THE SUN UM, THE PLANET IS GOING
TO BE HEATED UP.
IT'S HEATED UP IT EXPANDS AND
SO THIS 1.35 JUPITER RADII IS
JUST ABOUT WHAT YOU WOULD
EXPECT AND THERE'S EVEN
EVIDENCE THAT THEY'VE DETECTED
UH, UH, ABSORPTION LINE IN THE
PLANETARY ATMOSPHERE WHICH
SUGGESTS THAT IT'S A GAS GIANT
PLANET LIKE JUPITER.
UM, YOU CAN ALWAYS DO
MEASUREMENTS OF TRANSITS BETTER
FROM SPACE THAN FROM THE GROUND
FOR TWO REASONS YOU DON'T HAVE
TO WORRY ABOUT FLUCTUATIONS AND
THE BRIGHTNESS OF THE STARS DUE
TO THE ATMOSPHERE AND YOU CAN
WATCH THE STAR 24 SEVEN WITHOUT
WORRYING ABOUT CLOUDS OR DAYTIME.
THE EUROPEAN SPACE AGENCY AND
NASA ARE THEREFORE LAUNCHING AN
ARMADA OF SATELLITES THAT WILL
DO NOTHING BUT LOOK AT TRANSITS
AROUND NEARBY STARS, LOOK FOR
TRANSITS AROUND NEARBY STARS
BUT ACTUALLY THE FIRST
SATELLITE TO DO THIS IS A
CANADIAN SATELLITE CALLED MOST
WHICH WAS DESIGNED MOSTLY FOR
OTHER PURPOSES LAUNCHED LAST
SUMMER...

A picture of a square satellite pops up with the caption “MOST: Microgravity and Oscillations of STars. Launched June 30, 2003.”

Scott continues AND HAS A LIMITED
CAPABILITY TO LOOK FOR TRANSITS
AND IS NOW MONITORING TRANSITS
AROUND SEVERAL STARS AND IN
PARTICULAR THE ONE THAT I JUST
SHOWED YOU.
UH, THEY HAVEN'T RELEASED ANY RESULTS YET.
WE'RE ALL EAGERLY WAITING TO
SEE WHAT THE RESULTS WILL BE
AND THEY OUGHT TO BE RELEASED
SOMETIME IN THE NEXT FEW WEEKS.
THE THIRD METHOD TO LOOK FOR
PLANETS IS ASTROMETRY IT'S THE COMPLIMENT
OF LOOKING AT VELOCITIES IN
THIS CASE UM, AS THE PLANET AND
THE STAR MOVE AROUND THEIR
MUTUAL CENTRE OF GRAVITY YOU
SEE A LITTLE BIT OF WOBBLE UH,
IN THE POSITION OF THE STAR.

A chart titled “astrometry” shows the motion of the Sun as viewed from 30 light years away.

Scott continues THIS IS WHAT THE WOBBLE OF THE
SUN WOULD LOOK LIKE IF WE WERE
LOOKING AT IT FROM 30 LIGHT
YEARS AWAY.
UM, THE CHALLENGE HERE IS THAT
THE WOBBLE IS VERY SMALL.
THIS DISTANCE IS A THOUSANDTH
OF A SECOND OF OUR UM, THAT'S
ABOUT THE DISTANCE SUBTENDED BY
MY THUMB IF I WERE STANDING IN
VANCOUVER AND YOU WERE LOOKING
AT IT FROM HERE.
THAT'S ACTUALLY NOT SO BAD.
ASTRONOMERS CAN DO THAT FROM
SPACE.
THE PROBLEM IS THAT YOU HAVE TO
GET MUCH BETTER THAN THAT TO
SEE UH, UH, TO DO AN ACCURATE
MEASUREMENT OF THE PLANET.
A MISSION PLANNED BY NASA FOR
LAUNCH IN 2009 CALLED THE SPACE
INTERFEROMETER MISSION IS
AIMING FOR A MICRO ARK SECOND,
THAT'S A FACTOR OF A THOUSAND
BETTER AND IT'S GOING TO BE A
REAL TECHNICAL CHALLENGE TO SEE
IF THEY CAN DO IT.
FINALLY THE MOST EXOTIC METHOD
OF DETECTING PLANETS UH, IS A
METHOD CALLED GRAVITATIONAL LENSING.

A drawing shows a telescope on Earth looking at a distant star as a planet passes in front of it. A caption reads “Gravitational microlensing: Light from a distant star is bent and focused by gravity as a planet passes between the star and Earth.”

Scott continues UM, IF A STAR PASSES BETWEEN --
IF AN INTERVENING BODY OF ANY
KIND PASSES BETWEEN A DISTANT
STAR AND THE EARTH ACCORDING TO
EINSTEIN IT BENDS THE LIGHT OF
THE STAR, THAT BENDING OF THE
LIGHT MEANS THAT THIS
INTERVENING BODY ACTS SORT OF
LIKE A LENS AND IT MEANS THAT
TEMPORARILY WHEN THAT BODY IS
LINED UP JUST RIGHT IT'LL MAKE
THE STAR BRIGHTEN IN A VERY
PREDICTABLE WAY.
THE TROUBLE IS THAT YOU HAVE BE
VERY ACCURATELY ALIGNED TO BE
AN EFFECTIVE LENS BUT THAT
MEANS YOU HAVE TO MONITOR A
LARGE NUMBER OF STARS AND JUST
HOPE THAT EVERY NOW AND AGAIN
ONE WILL SHOW THIS BRIGHTENING
AND THAT HAS NOW BEEN DONE.
THIS IS AN EXAMPLE OF A
GRAVITATIONAL LENSING EVENT
CAUSED BY AN INTERVENING STAR
NOT A PLANET.

A new chart shows a peak in the brightness of a star.

Scott continues YOU CAN SEE THAT THE BRIGHTNESS
OF THE STAR INCREASED BY A
LARGE FACTOR DURING THIS EVENT
WHICH LASTED SEVERAL YEARS.
AND CAN BEFIT EXTREMELY WELL BY
SIMPLE THEORETICAL MODELS
BECAUSE THE LIGHT CURVE FROM
THE STAR CAN BEFIT SO WELL BY
THIS VERY SIMPLE MODEL IF THIS
STAR HAS A PLANET AROUND IT
WHAT YOU EXPECT TO SEE IS SOME
SORT OF BUMP OR DEVIATION FROM
THIS SIMPLE CURVE WHEN THE
PLANET ITSELF ACTS LIKE AN EVEN
SMALLER LENS.

Another chart shows a similar change in brightness.

Scott continues PEOPLE HAVE BEEN SEARCHING FOR
THIS FOR SEVERAL YEARS AND JUST
A FEW WEEKS AGO THEY ANNOUNCED
THE FIRST SECURE EVENT UM, THIS
IS UH, UH, SOMEWHAT NOISIER YOU
CAN SEE HOW TOUGH THE PROBLEM IS.
THERE'S WHAT THE STAR LOOKS
LIKE BEFORE IT BRIGHTENS AND
THERE'S WHAT IT LOOKS LIKE AT
THE PEAK OF THE BRIGHTNESS.
AND OF COURSE THE TECHNICAL
CHALLENGES SEPARATING THIS FROM
ALL THE STUFF AROUND IT BUT YOU
CAN SEE THAT THIS
STRAIGHTFORWARD LIKE CURVE HAS
TWO SPIKES ON IT IN PARTICULAR
THIS VERY SHARP SPIKE HERE
MODELLING THAT TELLS YOU THAT
THIS PLANET HAS A PLANET --
THIS STAR HAS A PLANET OF ABOUT
A JUPITER MASS AROUND IT
ORBITING AT ABOUT THREE
ASTRONOMICAL UNITS FROM THE
STAR.
SO THIS IS THE FIRST DETECTION
OF THE PLANET BY MICROLENSING.
IT'S BY FAR THE MOST DISTANT
PLANET KNOWN.
IT'S ABOUT HALFWAY TO THE
CENTRE OF THE GALAXY AND WITH
LARGER AND LARGER DETECTORS AND
MORE PROGRAMS WE'RE GOING TO BE
DISCOVERING A LOT MORE PLANETS
THAT WAY.
OKAY, WELL, LET ME SUMMARIZE.
WHAT WE'VE LEARNED IS THAT
PLANET FORMATION IS COMMON.
10 YEARS AGO IF YOU'D SAID ONLY
ONE STAR IN A MILLION HAVE
PLANETS UH, YOU MIGHT VERY WELL
HAVE BEEN CORRECT.
WE NOW KNOW AT LEAST 10 percent OF
NEARBY STARS HOST GIANT PLANETS
HOWEVER THESE PLANETARY SYSTEMS
ARE VERY DIFFERENT FROM OUR OWN.
IN OUR SYSTEM WE HAVE
TERRESTRIAL PLANETS LIKE THE
EARTH CLOSE BY AND GIANT
PLANETS OUT MUCH LARGER
DISTANCES AND IN THESE SYSTEMS
THE GIANTS -- GIANT PLANETS ARE
SOMETHING LIKE 100 TIMES CLOSER
TO THE SUN TO THEIR STAR THAN
JUPITER UH, IS TO THE SUN.
WHAT WE DON'T KNOW IS WHY
THEY'RE SO DIFFERENT UH, FROM
OUR SOLAR SYSTEM.
IS OUR SOLAR SYSTEM THE
EXCEPTION OR THE RULE.
WE DON'T KNOW IF YOU CAN HAVE
EARTH MASS PLANETS IN THESE
SYSTEMS.
WE DON'T KNOW HOW COMMON EARTH
MASS PLANETS ARE IN GENERAL.
WE KNOW OF NO EARTH MASS
PLANETS OUTSIDE OUR OWN SOLAR
SYSTEM UM, AND OF COURSE WHAT
WE'D REALLY LIKE TO KNOW IS HOW
COMMON ARE HABITABLE PLANETS
AND WE HAVE NO INFORMATION ON
THAT EITHER.
SO TO CLOSE UH, I WANTED TO
CLOSE BY SUMMARIZING OUR
CURRENT UH, THE CURRENT STATUS
OF OUR UNDERSTANDING OF
PLANETS.
THE BEST I CAN DO IS A SORT OF
ANALOGY WHICH IS TO IMAGINE
THAT DARWIN WAS TRYING TO WRITE
HIS THEORY OF EVOLUTION BUT ALL
HE HAD OBSERVATIONAL DATA ON
PRIMATES, MONKEYS, and man,
HE MIGHT STILL HAVE BEEN A CLEVER
GUY AND COME UP WITH THE THEORY
OF EVOLUTION.
YOU MIGHT UNDERSTAND THAT
PRIMATES AND MEN UH, DESCENDED
FROM A COMMON ANCESTOR AND HE
PROBABLY WOULD'VE GOTTEN THE
BASIC IDEAS CORRECT BUT HE
NEVER WOULD'VE UH, UH, HE NEVER
WOULD'VE UH, BEEN ABLE TO
IMAGINE THE TREMENDOUS RICH
DIVERSITY THAT THERE ARE IN
LIVING ORGANISMS.
HE WOULD NEVER BEEN ABLE EVEN
IF HE UNDERSTOOD EVOLUTION HE
WOULD NEVER BEEN ABLE TO INVENT
THE IDEA OF A WHALE OR A
BUTTERFLY OR AN ALLIGATOR AND I
THINK RIGHT NOW PLANETARY
SCIENTISTS AND ASTRONOMERS ARE
IN SOMEWHAT THE SAME POSITION.
UM, WE UNDERSTAND A LOT ABOUT
PLANETS.
WE UNDERSTAND A LOT ABOUT HOW
THE PLANETS IN OUR OWN SOLAR
SYSTEM WERE FORMED UM, BUT MY
HOPE WOULD BE THAT OVER THE
COMING YEARS AND DECADES WE'LL
DISCOVER A RICHNESS IN UH,
OTHER PLANETARY SYSTEMS THAT'S
COMPARABLE TO THE RICHNESS THAT
YOU SEE UH, IN BIOLOGICAL
SPECIES ON THE EARTH.
THANK YOU.

[Long applause]

Now a man says
WE WILL TAKE QUESTIONS
FROM THE AUDIENCE.
WE HAVE ONE PERSON OVER THERE.

A male member of the audience says
UH, DOES THE
RESEARCH THAT THIS IS LEADING
TO PROVIDE BETTER INFORMATION
ON INTERCEPTION PATHS BETWEEN
THINGS LIKE ASTEROIDS AND
THINGS LIKE PLANETS?

Scott says NOT DIRECTLY.
OBVIOUSLY ONE OF THE CONCERNS
UM, IF YOU LIKE TO WORRY ABOUT
THINGS ON A TIMESCALE LONGER
THAN YOUR
MORTGAGE SORT OF INTERMEDIATE
TO WORRYING ABOUT WHETHER THE
EARTH IS GOING TO BE AROUND IN
FIVE MILLION YEARS AND WORRYING
ABOUT YOUR MORTGAGE IS WHETHER
THERE'S GOING TO BE A
CATASTROPHIC IMPACT 100 MILLION
YEARS FROM NOW THAT WIPES OUT
UH, WIPES OUT CIVILIZATION.
THIS INFORMATION DOES NOT UH,
HELP US -- I MEAN, SEARCHING
FOR SUCH OBJECTS IS VERY
IMPORTANT UM, BUT THIS KIND OF
RESEARCH DOESN'T REALLY HELP
WITH THAT BECAUSE ON THE SCALES
WE'RE TALKING ABOUT HERE YOU
KNOW FIGURING OUT WHETHER AN
ASTEROID IS GOING TO UH,
COLLIDE WITH THE EARTH IN 100
OR A COUPLE OF HUNDRED YEARS OR
NEXT WEEK IS IN THE SORT OF
SHORT-TERM REGIME WHERE
NEWTON'S EQUATIONS GIVE VERY
PREDICTABLE, VERY WELL BEHAVED
ANSWERS AND UH, UH, IT'S EASY
THE PROBLEM THERE IS NOT
CALCULATING THE FUTURE COURSE
OF THE ASTEROID AND WHETHER
IT'S GOING TO HIT.
THE PROBLEM IS DOING A LARGE
ENOUGH OBSERVATIONAL SURVEY
THAT'S ACCURATE ENOUGH AND
REACHES OBJECTS FAINT ENOUGH TO
BE ABLE TO DETECT ALL OF THE
POTENTIALLY HAZARDOUS OBJECTS.

A second member of the audience rises. He’s in his late thirties, with short black hair.

He says I WAS WONDERING ABOUT BODES
LAW IT'S COMPELLING BECAUSE
IT'S VERY SIMPLE EMPIRICAL
SUCCESSION OF PLANETARY RADII
UM, HAS YOUR MODEL -- SORRY,
YOUR CALCULATIONS SHOW THAT UH,
THE CONFIGURATION OF THE SOLAR
SYSTEM LOOKS PRETTY STEADY OVER
PERIODS OF BILLIONS OF YEARS,
UH, AND YOU WOULD THINK THAT
THIS WOULD SHOW THAT BODES LAW
SHOWS AN UNDERLYING SYSTEM OF
RESONANCE'S OR STABLE
RESONANCE'S UH, YET UH, IT
LOOKS LIKE YOU HAVE A WHOLE
VARIETY OF SYSTEMS OUT THERE,
UM, DO YOU HAVE ANY COMMENT ON
THAT WHETHER BODES LAW MIGHT BE
A NATURAL PROGRESSION OF
SYSTEM LOOKS PRETTY STEADY OVER
PERIODS OF BILLIONS OF YEARS,
UH, AND YOU WOULD THINK THAT
THIS WOULD SHOW THAT BODES LAW
SHOWS AN UNDERLYING SYSTEM OF
RESONANCE'S OR STABLE
RESONANCE'S UH, YET UH, IT
LOOKS LIKE YOU HAVE A WHOLE
VARIETY OF SYSTEMS OUT THERE,
UM, DO YOU HAVE ANY COMMENT ON
THAT WHETHER BODES LAW MIGHT BE
A NATURAL PROGRESSION OF
PLANETARY POSITIONS?

Scott says SURE, UH,
JUST LET ME GIVE A LITTLE BIT
OF THE BACKGROUND OF BODES LAW
IS AN EMPIRICAL LAW THE
DESCRIBES THE POSITIONS OF THE
PLANETS UM, AS A GEOMETRIC
PROGRESSION.
IT WAS INVENTED UH, UH, BY BODE
BACK I THINK IN THE 18th OR
17th CENTURY, UM, AND IT HAD
TWO GREAT SUCCESSES.
IT WAS UH, HE INVENTED THE LAW
BEFORE THE DISCOVERY OF URANUS
AND THE POSITION OF URANUS FIT
EXTREMELY WELL INTO THE
PREDICTION OF BODES LAW.
IT ALSO PREDICTED THAT THERE
WAS A MISSING PLANET BETWEEN
MARS AND JUPITER AND ITS
PREDICTED POSITION FOR THE
MISSING PLANET TURNED OUT TO BE
VERY CLOSE IN THE POSITION OF
THE LARGEST ASTEROID SO THOSE
TWO SUCCESSES GAVE BODES LAW A
GREAT DEAL OF CREDITABILITY
HOWEVER IT DOES HAVE SOME
PROBLEMS.
I MEAN, FIRST PROBLEM IS THAT
ASTEROIDS REALLY AREN'T
PLANETS, THEY'RE A LOT SMALLER.
THE SECOND IS THAT IT FAILED
BADLY TO PREDICT THE LOCATION
OF NEPTUNE UM, AND IF YOU LOOK
IN DETAIL AT THE LAW HE HAD TO
KIND OF CHEAT TO GET MERCURY TO
FIT SO YOU'VE GOT EIGHT PLANETS
AND THREE EXCEPTION AND SO IT
PROBABLY SHOULDN'T BE TAKEN TOO
SERIOUSLY.
UM, WHAT IT PROBABLY DOES SAY
IS THAT IF YOU'RE TRYING TO
BUILD A SOLAR SYSTEM YOU CAN'T
JUST DUMP THE PLANETS DOWN IN
RANDOM LOCATIONS UH, BECAUSE
IT'S LIKELY TO BE UNSTABLE.
THE MOST STABLE SYSTEMS ARE
LIKELY TO BE ONES IN WHICH THE
BADLY TO PREDICT THE LOCATION
OF NEPTUNE UM, AND IF YOU LOOK
IN DETAIL AT THE LAW HE HAD TO
KIND OF CHEAT TO GET MERCURY TO
FIT SO YOU'VE GOT EIGHT PLANETS
AND THREE EXCEPTION AND SO IT
PROBABLY SHOULDN'T BE TAKEN TOO
SERIOUSLY.
UM, WHAT IT PROBABLY DOES SAY
IS THAT IF YOU'RE TRYING TO
BUILD A SOLAR SYSTEM YOU CAN'T
JUST DUMP THE PLANETS DOWN IN
RANDOM LOCATIONS UH, BECAUSE
IT'S LIKELY TO BE UNSTABLE.
THE MOST STABLE SYSTEMS ARE
LIKELY TO BE ONES IN WHICH THE
PLANETS ARE SOMEWHAT REGULARLY
SPACED AND IF YOU PUT IN SOME
SORT OF APPROXIMATE REGULAR
SPACING UM, AND YOU TRY A BUNCH
OF DIFFERENT LAWS YOU'RE LIKELY
TO FIND ONE THAT WORKS AS WELL
AS BODES LAW.

Another man rises. He’s in his early twenties, with long curly hair.

He says
UM, YOU DIDN'T MENTION
ANYTHING ABOUT SATURN AND ITS
RINGS AND UM, IF IT'S UM, IF
IT'S STABLE, IF THE RINGS ARE
STABLE OR IF THEY'RE IN THE
PROGRESS OR IF THEY'RE IN THE
PROGRESS OF CHANGING INTO
SOMETHING DIFFERENT OR HOW IT
HOW IT BECAME THE ONLY
PLANETARY SOLAR SYSTEM THAT HAS RINGS.

Scott says WELL, OF
COURSE ONE REASON IS THE
RESULTS FROM CASINI ARE GOING
TO REVOLUTIONIZE EVERYTHING WE
UNDERSTAND ABOUT THE RINGS OVER
WELL, OF
COURSE ONE REASON IS THE
RESULTS FROM CASINI ARE GOING
TO REVOLUTIONIZE EVERYTHING WE
UNDERSTAND ABOUT THE RINGS OVER
THE NEXT TWO OR THREE YEARS SO
I DIDN'T WANT TO SAY ANYTHING
WRONG.

[Laughter]

Scott continues BUT UM, I
THINK THAT'S A VERY INTERESTING
QUESTION AND A VERY DIFFICULT
QUESTION.
THE BASIC ISSUE IS HOW LONG
LIVED ARE THE RINGS?
HAS SATURN ALWAYS HAD THIS
BEAUTIFUL RING SYSTEM OR IS IT
SOMETHING THAT UM, WAS FORMED
RELATIVELY RECENTLY AND DOESN'T
LAST FOR VERY LONG?
TRADITIONALLY ASTRONOMERS HAVE
ALWAYS BELIEVED THAT THE RING
SYSTEM WAS PERMANENT AND IT'S
ALWAYS BEEN THERE AND WAS SOME
SORT OF RELIC FROM THE
FORMATION PROCESS OF SATURN UM,
BUT UH, THE RESULTS THAT CAME
BACK FROM VOYAGER INDICATED
THAT UM, THE DYNAMICAL
PROCESSES WITHIN THE RINGS AND
THE INTERACTIONS BETWEEN THE
RINGS AND THE SATELLITES WERE
SUGGESTING THAT THE CONFIGURATION OF THE
RINGS WOULD CHANGE ON
TIMESCALES OF MAYBE 10 TO 100
MILLION YEARS IF THAT'S TRUE
IT'S LIKELY THAT THE RINGS ARE
RATHER SHORT-LIVED.
THEY MAY
HAVE FORMED BECAUSE A PASSING
BODY OF KUIPER BELT OBJECT
PASSED SO CLOSE TO SATURN THAT
IT WAS TIDALLY DISRUPTED AND
THEN THE TIDALLY DISRUPTED
PIECES GROUND ONE ANOTHER DOWN
TO FORM THE RINGS BUT AT THIS
STAGE WE REALLY DON'T KNOW SO
IT'S ENTIRELY AN OPEN QUESTION.

Another man rises. He’s in his thirties, with short curly hair and a beard.

He says IS THE FACT THAT THE SYSTEMS
THAT WE'VE DISCOVERED UM, HAVE
MOSTLY VERY LARGE PLANETS MUCH
CLOSER IN THAN OUR SOLAR SYSTEM
DUE TO THE FACT THAT THAT'S ALL
WE CAN DETECT RIGHT NOW?
ANOTHER WAY TO PHRASE THAT IS
IF OUR SOLAR SYSTEM WERE 100 OR
200 MILLION YEARS AWAY -- TWO
MILLION LIGHT YEARS AWAY, WOULD
WE BE ABLE TO DETECT IT FROM HERE?

Scott says RIGHT SO
THAT'S A VERY GOOD QUESTION THE
ANSWER IS YES.
THE REASON THAT WE'RE ONLY
SEEING UM, LARGE PLANETS THAT
ARE CLOSE IN IS BECAUSE THAT'S
ALL WE CAN DETECT.
UM, THE CAPABILITIES OF THE
OBSERVERS ARE STEADILY
INCREASING PARTLY BECAUSE
THEY'RE GETTING BETTER
TECHNIQUES AND PARTLY BECAUSE
THEY'VE JUST BEEN WATCHING
THESE THINGS FOR A LONGER TIME.
THE ORBITAL PERIOD OF JUPITER
IS OVER 10 YEARS AND SO YOU'D
HAVE TO WATCH THE EARTH FOR 15
YEARS OR SO BEFORE YOU WERE
CONVINCED THAT YOU'D SEEN THE
SORT OF OSCILLATORY MOTION
ASSOCIATED WITH THE PLANET.
WE'RE JUST NOW GETTING TO THE
POINT WHERE THEY'RE STARTING TO
REPORT PLANETS THAT ARE ALMOST
JUPITER'S PERIOD AND ALMOST
JUPITER'S MASS.
SO IF THEY WERE LOOKING AT THE
SOLAR SYSTEM FROM 100 LIGHT
YEARS AWAY YOU MIGHT EXPECT AN
ANNOUNCEMENT SOME TIME IN THE
NEXT FEW OF YEARS SO THEY'RE
CLOSE BUT UM, UH, ONLY JUST CLOSE.

A man in his early thirties rises. He has short black hair and wears round glasses.

He says UM, YES, IN YOUR TALK YOU
ELUDED TO URANUS AND NEPTUNE
SORT OF MIGRATING FURTHER OUT
AND I'VE HEARD THAT IN THE
FORMATION OF THE SOLAR SYSTEM
IT'S LIKELY THAT URANUS AND
NEPTUNE FORMED MUCH LATER AND
I'M WONDERING IF THE OUTWARD
MIGRATION COULD STILL BE GOING
ON AND IF SO IS THAT GOING TO
GIVE MORE SPACE FOR THE INNER
PLANETS TO ALSO SORT OF -- TO
SORT OF MIGRATE?

Scott says THE BEST
GUESS THAT WE HAVE IS THAT THE
MIGRATION IS NOT GOING ON
ANYMORE AND THE REASON IS
SIMPLY THAT THE MIGRATION --
THE ONLY THING THAT WE KNOW OF
THAT WOULD DRIVE THE MIGRATION
IS KIND OF CLEANING UP THE
DEBRIS LEFT FROM THE FORMATION
THAT IS UH, GRAVITATIONAL
INTERACTIONS WITH LEFTOVER
BODIES THAT WERE BEING EJECTED
AND THAT EJECTION BACK REACTION
FROM THAT EJECTION WAS DRIVING
THE PLANETS OUTWARD.
THE ONLY UM, DEBRIS THAT'S
LEFTOVER IN THE SOLAR SYSTEM
THAT WE KNOW OF ARE THE
ASTEROIDS AND THE KUIPER BELT
UM, THE MASSES OF THOSE ARE
ONLY SOMEWHERE BETWEEN A
MILLIONTH AND A BILLIONTH OF
THE MASS OF THE SUN.
THEY'RE FAR TOO SMALL TO HAVE
ANY SIGNIFICANT AFFECT ON THE
ORBITS OF URANUS AND NEPTUNE AT
THIS POINT.

Another man rises and says
SOME OF THE extra SOLAR
PLANETS RECENTLY DISCOVERED
EXHIBIT A NOTICEABLE DEGREE OF
PROCESSION AND IF SO WOULD YOU
BE ABLE TO GET SOME INFORMATION
OF THE FORCE LAWS THAT GIVE
rise PROCESSION.

Scott says UM...
IF YOU'RE TALKING ABOUT
PROCESSION OF THE ELLIPTICAL
ORBITS OF THE PLANETS UM, UH,
YOU WOULD –
YOU CAN GET SOME INFORMATION ON THAT.
AS THE ORBITS THAT WE SEE RIGHT
NOW ARE PERFECTLY WELL FIT BY
NEWTON'S LAWS.
THEY LOOK JUST LIKE THE ORBITS
IN THE SOLAR SYSTEM.
IF THERE WERE SOME SORT OF DEVIATION
FROM NEWTON'S LAWS PERHAPS
CAUSED BY OTHER PLANETS THOSE
WOULD CAUSE THE ORBITS TO
PROCESS THAT IS THE ORIENTATION
OF CHANGE BUT TYPICALLY THAT
CHANGE IS RATHER SLOW.
THAT MEANS THAT YOU HAVE TO
LOOK FOR MANY, MANY ORBITAL
PERIODS TO UH, TO DETECT SUCH
PROCESSION AND SO YOU KNOW IT'S
GOING TO BE SOMETHING THAT WE
CAN'T -- THAT THE OBSERVERS CAN
INVESTIGATE BUT IT KIND OF
DEPENDS ON HOW PATIENT THEY ARE
AND WHETHER THEY'RE REALLY
WILLING TO LOOK AT THESE THINGS
SYSTEMATICALLY AND STEADILY FOR
DECADES TO FIND THESE SMALL EFFECTS.

The presenter speaks again and says
GREAT.
AT THIS POINT I WOULD VERY MUCH
LIKE TO THANK PROFESSOR
TREMAINE FOR A VERY CLEAR AND
STIMULATING AND INFORMATIVE
LECTURE.
THANK YOU VERY MUCH.

[Long applause]

Watch: Scott Tremaine on The Stability of the Solar System