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Transcript
JOHN FLAMSTEED
1646-1719
• BORN IN DENBY ENGLAND
• MATHEMETICIAN AND
ASTRONOMER
• ATTRACTED TO
ASTRONOMY BY
SACROBOSCO’S DE
SPHAERA MUNDI
• FIRST ASTRONOMER ROYAL
• MEMBER OF THE ROYAL
SOCIETY
• LAID THE FOUNDATION
STONE OF THE GREENWICH
OBSERVATORY
JOHN FLAMSTEED
• CALCULATED THE SOLAR ECLIPSES OF 1666 AND 1668
• OBSERVED THE PLANET URANUS AND CATALOGUED IT AS A STAR –
34 TAURI
• FEUDED WITH NEWTON AND HALLEY. HE REFUSED TO PUBLISH A
WORK (A CATALOG) COMMISSIONED BY THE KING IN 1712.
• NEWTON, THEN PRESIDENT OF THE ROYAL SOCIETY, WITH HALLEY
PUBLISHED A PRELIMINARY VERSION OF THE WORK WITHOUT
CREDITING HIM.
• HE BOUGHT A NUMBER OF COPIES AND PUBLICLY BURNED THEM
IN PROTEST IN FRONT OF THE ROYAL OBSERVATORY.
• HIS WIFE PUBLISHED IT POSTHUMOUSLY IN 1725. IT CONTAINED
OBSERVATIONS OF 2,935 STARS TO GREATER ACCURACY THAN EVER
BEFORE AND IS CONSIDERED TO BE THE FIRST SIGNIFICANT
CONTRIBUTION OF THE GREENWICH OBSERVATORY.
EDMOND HALLEY
1656-1742
• BORN IN HAGGERSTON,
ENGLAND
• CAME FROM A WEALTHY
FAMILY
• WAS COMMISSIONED BY
HOOKE TO VISIT HEVELIUS
REGARDING THE QUALITY OF
HIS OBSERVATIONS AS
HEVELIUS’ MEASUREMENTS
WERE NOT MADE WITH A
TELESCOPE.
• MEMBER OF THE ROYAL
SOCIETY
• SECOND ASTRONOMER ROYAL
HALLEY’S SCIENCE
• A GIFTED OBSERVATIONAL ASTRONOMER –
COMPARED TO TYCHO
• WHEN HE MUSED AS TO THE SOLUTION TO
KEPLER’S LAWS HE VISITED NEWTON AND
FOUND THAT NEWTON HAD SOLVED THE
PROBLEM BUT HAD NOT PUBLISHED THE
SOLUTION.
• HE CONVINCED NEWTON TO WRITE HIS
PRINCIPIA MATHEMATICA PHILOSPHIAE
NATURALIS (OR JUST “PRINCIPIA”) IN 1687 AND
PUBLISHED IT AT HIS OWN EXPENSE.
EDMOND HALLEY
• DISCOVERED THE
PROPER MOTION OF
STARS BY COMPARING
THEIR CURRENT
LOCATION WITH THAT
RECORDED VALUES IN
THE ALMAGEST
HALLEY’S COMET
• IN “SYNOPSIS ASTRONOMIA
COMETICAE” HE STATED
THAT HE BELIEVED THE
COMETS REPORTED IN
1456, 1531, 1607 AND 1682
WERE THE SAME OBJECT
AND THAT IT WOULD
REAPPEAR IN 1758
• ITS REAPPEARANCE AS
PREDICTED IS CONSIDERED
TO BE THE FIRST SCIENTIFIC
PREDICTION OF NEWTON’S
LAWS.
OLE ROEMER
1644-1710
• DANISH
• CHANGED HIS NAME FROM
CHRISTIAN PEDERSON TO OLE
ROEMER TO DISTINGUISH
HIMSELF FROM TWO OTHER
CHRISTIAN PEDERSONS
• CHIEF OF POLICE IN
COPENHAGEN
• PROFESSOR OF ASTRONOMY
AT THE UNIVERSITY OF
COPENHAGEN
• TEACHER OF THE DAUPHIN,
THE HEIR APPARENT OF LOUIS
XIV
ROEMER’S SCIENTIFIC
ACCOMPLISHMENTS
• HELPED PUBLISH TYCHO’S OBSERVATIONS
• OBSERVED AT HVEN – HIS OBSERVATIONS WERE LOST IN THE
GREAT FIRE OF COPENHAGEN IN 1728 BUT HIS STUDENT
PUBLISHED MUCH OF HIS RESEARCH FOR HIM
• HELPED BUILD THE GREAT FOUNTAINS AT VERSAILLES
• SUCCEDED IN PERSUADING THE KING TO ADOPT THE GREGORIAN
CALENDAR, SOMETHING TYCHO HAD ATTEMPTED BUT FAILED
• PROPOSED A TEMPERATURE SCALE TO FAHRENHEIT – FAHRENHEIT
IMPROVED IT TO WHAT WE NOW CALL THE FAHRENHEIT SCALE
• BY SIMULTANEOUSLY OBSERVING THE ECLIPSES OF JUPITER’S
MOON IO WITH JEAN PICARD IN PARIS HE DETERMINED THE
DIFFERENCE IN LONGITUDE BETWEEN URANIBORG AND PARIS
• MADE THE FIRST DETERMINATION OF THE VELOCITY OF LIGHT BY
OBSERVING JUPITER’S MOON IO
ROEMER’S VELOCITY OF LIGHT
MEASUREMENTS
•
•
•
•
•
FOUND THAT THE PERIOD OF JUPITER’S
MOON IO APPEARED TO CHANGE
– SHORTER WHEN THE EARTH
APPROACHED JUPITER
– LONGER WHEN THE EARTH
RECEDED FROM JUPITER
HE COLLABORATED WITH CASSINI IN
OBSERVING IO BUT CASSINI
ABANDONED HIS REASONING AND LEFT
IT TO ROEMER AND THE FRENCH
ASTRONOMER PICARD
A REPORTER ERRONEOUSLY DESCRIBED
HIS EXPERIMENT IN AN ARTICLE
CAUSING CONFUSION AMONG THE
SCIENTIFIC READERS
HE NEVER PUBLISHED HIS RESULTS
HIMSELF
HIS VALUE: c ≈ 200,000 KM/SEC
COMPARES FAVORABLY TO THE
CURRENTLY ACCEPTED VALUE OF
c = 300,000 KM/SEC.
SIR ISAAC NEWTON
1643-1727
• BORN THREE MONTHS AFTER
HIS FATHER DIED IN A SMALL
ENGLISH TOWN THE YEAR
GALILEO DIED
• HIS MOTHER REMARRIED BUT
HE WAS RAISED BY HIS
MATERNAL GRANDMOTHER
• HIS MOTHER WANTED TO
MAKE A FARMER OUT OF HIM
WHEN HIS STEPFATHER DIED
BUT HENRY STOKES, MASTER
AT THE KING’S SCHOOL
GRANTHAM, PERSUADED HER
TO SEND HIM BACK TO
SCHOOL.
ISAAC NEWTON
• AT AGE 18 HE ENTERED TRINITY COLLEGE, CAMBRIDGE
AS A SIZAR
• A SIZAR WAS KIND OF A “WORK-STUDY”
ASSISTANTSHIP FOR TALENTED STUDENTS FROM POOR
FAMILIES. THEY PAID NO TUITION BUT HAD TO
PERFORM MENIAL, SOMETIMES DEMEANING TASKS
AND WERE CONSIDERED SUBORDINATE TO TUITION
PAYING STUDENTS.
• WHILE ARISTOTILEAN PHILOSOPY WAS EMPHASIZED
THERE HE PREFERRED TO STUDY DESCARTE.
• HE ALSO IMMERSED HIMSELF IN THE STUDY OF
COPERNICUS, GALILEO AND KEPLER
ISAAC NEWTON
• WHEN HE WAS 22 HE
DISCOVERED THE
GENERALIZED BINOMIAL
THEOREM, AN EXPRESSION
DESCRIBING THE
EXPANSION OF A BINOMIAL
RAISED TO A GIVEN POWER
• FOR EXAMPLE THE
COEFFICIENTS IN THE
EXPRESSION:
(x+y)4=x4+4x3y+6x2y2+4xy3+y4
CAN BE EASILY SEEN USING
THE TRANGLE AT THE RIGHT
CALLED PASCAL’S TRIANGLE
ISAAC NEWTON
• HE GRADUATED AT AGE 22 AND, BEFORE HE COULD EMBARK ON HIS
GRADUATE STUDIES THE GREAT PLAGUE HIT IN 1665.
• HE SPENT THE NEXT TWO YEARS AT HOME WHERE HE DEVELOPED HIS
BASIC THEORIES ON CALCULUS, OPTICS, HIS LAWS OF PHYSICS AND HIS
LAW OF UNIVERSAL GRAVITATION.
• HE DEVELOPED CALCULUS (FLUXIONS AND INVERSE FLUXIONS) TO SOLVE
ONE OF THE PROBLEMS HE FACED IN DEVELOPING HIS LAW OF UNIVERSAL
GRAVITATION.
• HE CALLED THIS PERIOD, "the prime of my age for invention"
• DURING THAT TIME HE WROTE A LARGE PART OF WHAT BECAME
Philosophiae Naturalis Principia Mathematica OR WHAT WE NOW SIMPLY
CALL “THE PRINCIPIA”
• HOWEVER IT WASN’T PUBLISHED UNTIL TWENTY YEARS LATER IN 1687 AT
THE INSISTANCE AND GENEROUS SUPPORT OF EDMOND HALLEY.
• ALSO, BY THE MID-60’S HE HAD ALSO INDEPENDENTLY DERIVED THE
EXPRESSION: F=mv2/r FOR THE CENTRIPITAL FORCE THAT HUYGENS HAD
DERIVED.
ISAAC NEWTON
• DURING THE INTERVENING TIME HE AND HOOKE HAD SEVERAL
DISCUSSIONS ON THE NATURE OF THE CARTESIAN FORCES
DESCRIBED BY DESCARTE.
• THEY ALSO ARGUED ABOUT WHETHER ONE SHOULD EXPECT AN
OBJECT DROPPED FROM THE TOP OF A TOWER WOULD BE
EXPECTED TO FALL STRAIGHT DOWN TO THE FOOT OF THE TOWER
OR WHETHER THE EARTH’S MOTION SHOULD MAKE IT ALIGHT
BEHIND THE OBSERVER.
• NEWTON ARGUED THAT, SINCE THE TOP OF THE TOWER IS
FARTHER FROM THE CENTER OF THE EARTH IT WOULD BE MOVING
FASTER THAN THE BASE AND, IN FACT, SHOULD FALL IN FRONT OF
THE TOWER. IN FACT HE ARGUED, CORRECTLY, THAT, IF THE EARTH
WERE NOT IN THE WAY THE OBJECT WOULD GO INTO ORBIT
AROUNG THE CENTER OF THE EARTH.
• IN FACT, IF THE SURFACE OF THE EARTH DIDN’T INTERVENE WE
WOULD FALL INTO ORBIT AROUND ITS CENTER
NEWTON’S LAWS OF MOTION
1. AN OBJECT WILL REMAIN IN UNIFORM
MOTION UNLESS ACTED ON BY AN OUTSIDE
UNBALANCED FORCE.
2. IF AN OUTSIDE UNBALANCED FORCE, F, IS
APPLIED TO A MASS , m, IT WILL PRODUCE
AN ACCELERATION , a, GIVEN BY THE
EXPRESSION, F = ma.
3. FOR EVERY FORCE OF ACTION THERE IS AN
EQUAL AND OPPOSITE FORCE OF REACTION.
NEWTON’S LAW OF UNIVERSAL
GRAVITATION
• THERE WILL BE AN ATTRACTIVE FORCE , F,
BETWEEN ANY TWO MASSES, m1 AND m2,
SEPARATED BY A DISTANCE r GIVEN BY THE
EXPRESSION: F = Gm1m2/r2 WHERE G IS THE
UNIVERSAL GRAVITATIONAL CONSTANT
ISAAC NEWTON
• ONE PROBLEM HE HAD TO OVERCOME: HE COULDN’T SEE HOW
THE GRAVITATIONAL FORCE WOULD NOT BE SHIELDED BY
INTERVENING MATTER.
• WHEN HE DID REALIZE THAT THE INTERVENING MATTER DID NOT
SHIELD THE GRAVITATIONAL FORCE HE STATED “THE ATTRACTION
LAW MUST BE IMPOSED BY GOD”.
• ANOTHER PROBLEM: HOW DO YOU CALCULATE THE
GRAVITATIONAL FORCE BETWEEN THE MILLIONS AND MILLIONS OF
MASSES THAT MAKE UP THE MOON AND THE EARTH?
• FOR THIS HE INVENTED CALCULUS AND PROVED THAT, IF THE
MASSES WERE UNIFORM AND SPHERICAL THAT ONE COULD
ASSUME THAT ALL OF THEIR MASS WAS AT THEIR CENTERS AND
TREAT THEM AS POINTS.
ISAAC NEWTON
• HALLEY HAD DISCUSSED THE DYNAMICS OF
PLANETARY ORBITS WITH HOOKE.
• HE WAS FLABBERGASTED WHEN HE ASKED
NEWTON ABOUT THE SHAPE OF A PLANET’S
ORBIT AND NEWTON REPLIED IMMEDIATELY
THAT IT WAS AN ELLIPSE.
• IN FACT HE WOULD LATER SHOW THAT, MORE
GENERALLY, IF ONE SOLVED THE SIMULTANEOUS
EQUATIONS OF NEWTON’S 2ND LAW AND HIS LAW
OF UNIVERSAL GRAVITATION THAT THE ORBITS
WOULD BE CONIC SECTIONS.
CONIC SECTIONS
ECCENTRICITIES OF CONIC SECTIONS
• FOR BOUND ORBITS
– FOR A CIRCLE: e = 0
– FOR A NONCIRCULAR ELLIPSE: 0<e<1
• FOR UNBOUND ORBITS
– FOR A PARABOLA: e=1 (v = ESCAPE VELOCITY)
– FOR A HYPERBOLA: e>1 (v > ESCAPE VELOCITY)
THE SUCCESSES OF NEWTON’S LAWS
• THE MOON’S ORBIT WAS CORRECTLY
DESCRIBED
• THE TIDES WERE EXPLAINED
• THE EARTH’S BULGE WAS CORRECTLY
PREDICTED
• PRECESSION OF THE EQUINOXES (CAUSED BY
THE MOON’S ATTRACTION ON THE EARTH’S
EQUATORIAL BULGE)
KEPLER’S LAWS RESTATED
1. PLANETS MOVE IN ELLIPTICAL ORBITS, THE
CENTER OF MASS AT THE FOCUS.
2. THE RADIUS VECTOR SWEEPS OUT EQUAL
AREAS IN EQUAL TIMES (UNCHANGED
EXCEPT THE RADIUS VECTOR HAS TWO
SECTORS, NOT ONE)
3. P2(MS+MP) = a3 WHERE THE MASSES ARE
GIVEN IN SOLAR MASSES , P IN EARTH YEARS
AND a IN ASTRONOMICAL UNITS.
ISAAC NEWTON
• CENTER OF MASS (BARYCENTER)
• MR = mr WHERE M AND m ARE THE MASSES
AND R AND r ARE THEIR RESPECTIVE
DISTANCES FROM THE CENTER OF MASS
• GO TO
http://www.youtube.com/watch?v=_IHXj8k2jqc
TO SEE HOW THE SUN MOVES DUE TO ALL OF THE
OBJECTS IN THE SOLAR SYSTEM REVOLVING AROUND
IT.
THE IMPACT OF THE PRINCIPIA
• MATHEMATICALLY VERY CHALLENGING, PERHAPS IN SOME
RESPECT, DUE TO NEWTON’S DISLIKE FOR HOOKE WITH WHOM HE
WAS FEUDING SO HE WROTE IT AT SUCH A HIGH LEVEL THAT
HOOKE COULD NOT UNDERSTAND IT.
• IN FACT, THE LEVEL OF THE MATHEMATICS IN IT WERE SO
CHALLENGING THAT FEW COULD UNDERSTAND IT, SO IT FAILED TO
GAIN MUCH TRACTION.
• ALEXANDER POPE WROTE: “NATURE AND NATURE’S LAWS LAY HID
IN NIGHT. GOD SAID, ‘LET NEWTON BE’, AND ALL WAS LIGHT”.
• IN A SURVEY OF THE ROYAL SOCIETY IN 2005 MEMBERS SAID THAT
NEWTON HAD A GREATER CONTRIBUTION BOTH TO THE HISTORY
OF SCIENCE AND TO HUMAN KIND THAN DID ALBERT EINSTEIN.
• MICHAEL HART, AN OXFORD FELLOW IN POLITICS, RANKS NEWTON
2ND ONLY TO MOHAMMED AS THE MOST INFLUENTIAL PERSON IN
HISTORY.
MORE ACCOLADES
• French mathematician Joseph-Louis Lagrange often
said that Newton was the greatest genius who ever
lived, and once added that Newton was also "the most
fortunate, for we cannot find more than once a system
of the world to establish.”
• NEWTON, IN A LETTER TO HOOKE SAID, “If I have seen
further it is by standing on the shoulders of Giants”.
• SOME SAY THIS WAS A STAB AT HOOKE WHO WAS
RATHER STOOPED, OTHERS SAY IT WAS AN HONEST
SENITMENT.
NEWTON’S OTHER CONTRIBUTIONS
• DEVELOPED THE NEWTONIAN TELESCOPE
• WROTE A LARGE VOLUME ON OPTICS –
STATED THAT WHITE LIGHT WAS SIMPLY A MIX
OF ALL COLORS
• DESCRIBED THE PHENOMENON KNOWN AS
CHROMATIC ABERRATION
• POSITED (INCORRECTLY) THE EXISTENCE OF A
SUPERLUMINIFEROUS EITHER
TIDES
• THE TIDE FORCE IS A
DIFFERENTIAL FORCE
• FT = const/r3
• THEREFORE: THE MOON
RAISES GREATER TIDES
ON THE EARTH THAN THE
SUN DOES BY ALMOST A
FACTOR OF 2.
• THERE ARE 2 HIGH TIDES
AND 2 LOW TIDES PER
DAY.
TIDES
• SPRING TIDES – THE SUN
AND THE MOON WORK
TOGETHER TO RAISE
EXTRAORDINARY HIGH AND
LOW TIDES – NEW AND
FULL MOON
• NEAP TIDES – THE SUN AND
THE MOON RAISE
OPPOSING TIDES TO RAISE
EXTRAORDINARILY LOW
HIGH TIDES AND
EXTRAORDINARILY HIGH
LOW TIDES – 1ST AND 3RD
QUARTER MOON
TIDES
• THE HEIGHT OF A TIDE IS
DETERMINED BY THE
TOPOGRAPHY OF THE
OCEAN BOTTOM AND THE
SHORELINE
• HIGHEST TIDES OCCUR IF
YOU HAVE A GENTLY
SLOPING BOTTOM INTO AN
INLET OR BAY
• THE HIGHEST TIDES ON THE
EARTH ARE AT THE BAY OF
FUNDY IN NOVA SCOTIA –
AS HIGH AS 50 FEET
TIDES
• IF THE EARTH WERE COVERED BY DEEP WATER THE TIDE
WOULD BE ABOUT 1.2 METERS
• THE EARTH’S BODY TIDE IS ABOUT 15 INCHES AT THE
EQUATOR
• THE FRICTION CAUSED BY THE TIDAL MOTION SLOWS THE
EARTH’S ROTATIONAL RATE DOWN BY ABOUT 1.5
MSEC/CENTURY
• CONSERVATION OF ANGULAR MOMENTUM CAUSES A
SHIFT IN ANGULAR MOMENTUM TO THE MOON
• THE MOON IS MOVING AWAY FROM THE EARTH AND THE
LENGTH OF THE MONTH IS INCREASING
• IN THE FAR FUTURE THE EARTH’S ROTATION WILL SLOW TO
47 DAYS, THE MONTH WILL LAST 47 DAYS AND THE EARTH
AND MOON WILL KEEP THE SAME FACE TOWARD EACH
OTHER
JAMES BRADLEY
1693-1762
• BRITISH
• THIRD ASTRONOMER
ROYAL
• MEMBER OF THE ROYAL
SOCIETY
BRADLEY’S CONTRIBUTIONS TO
ASTRONOMY
• MEASURED THE DIAMETER OF VENUS
• DISCOVERED THE ABERRATION OF STARLIGHT
• THAT, ALONG WITH THE LATER OBSERVED
STELLAR PARALLAX, DISTINGUISHED BETWEEN
TYCHO’S COSMOLOGY AND A HELIOCENTRIC
COSMOLOGY, I.E., IT PROVED THAT THE EARTH
WAS ACTUALLY IN MOTION.
• DISCOVERED NUTATION
JAMES BRADLEY
• DISCOVERED THE EARTH’S
NUTATION
• NUTATION IS A VARIATION IN THE
EARTH’S PRECESSION CAUSED
PRIMARILY BY THE FACT THAT THE
SUN AND THE MOON PULL ON
THE EARTH FROM DIFFERENT
POSITIONS AS TIME PASSES.
• IT HAS SEVERAL PERIODS – THE
PRIMARY ONE IS A8.6 YEARS –
THE PERIOD OF THE
“REGRESSION OF THE MOON’S
NODES”.
• THE VARIATION REACHES 17” IN
LONGITUDE AND 9” IN
OBLIQUITY.
SHAPE OF THE EARTH
• IN 1735 BOUGUER AND LA CONDAMINE, FRENCH
ASTRONOMERS, TRAVELED TO PERU TO
MEASURE THE SHAPE OF THE EARTH
• PIERRE LOUIS MAUPERTUIS, A FRENCH SCIENTIST,
MADE A TRIP TO LAPLAND IN 1736 TO MEASURE
THE EARTH’S SHAPE
• THEIR DATA SHOWED THAT THE EARTH’S RADIUS
WAS 33.5 KM LARGER AT THE EQUATOR THAN AT
THE POLES
• THE CURRENT VALUE IS 21.4 KM. THEY WERE
OFF BY ABOUT 50%.
THE SHAPE OF THE EARTH
MAUPERTUIS’ OPINION
OBLATE SPHEROID (ELLIPSOID)
CASSINI’S OPINION
PROLATE SPHEROID (ELLIPSOID)