PLANETARY ORBITSPLANETARY ORBITSPLANETARY ORBITSPLANETARY ORBITS

Chapter 2Chapter 2

CONIC SECTIONSCONIC SECTIONSCONIC SECTIONSCONIC SECTIONS

PLANETARY GEOMETRYPLANETARY GEOMETRYPLANETARY GEOMETRYPLANETARY GEOMETRY

Definition of a CircleDefinition of a CircleA Circle is a figure for which all points on it

are the same distance from the centre. Definition of an EllipseDefinition of an Ellipse

An Ellipse is a figure for which the sum of the distances from any point on the figure to two points inside the figure is always the same

HOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSE

HOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSEHOW to DRAW an ELLIPSE

Major AxisMajor Axis

FocusFocus FocusFocus

Minor AxisMinor Axis

(ellipticity e = distance between foci / major (ellipticity e = distance between foci / major axis – eaxis – eEarthEarth 0.02, e 0.02, eJupiter Jupiter 0.05, e0.05, eMercuryMercury 0.21) 0.21)

KEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWS

KEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWS

First Law:First Law: The orbit of each planet is an ellipse with The orbit of each planet is an ellipse with the Sun at one focusthe Sun at one focus

Sun

PlanetFoci

PLANETARY ORBITSPLANETARY ORBITSPLANETARY ORBITSPLANETARY ORBITS

KEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWS

First Law:First Law: The orbit of each planet is an ellipse with The orbit of each planet is an ellipse with the Sun at one focusthe Sun at one focus

Second Law:Second Law: The line joining the planet and the Sun The line joining the planet and the Sun sweeps out sweeps out equal areas in equal timesequal areas in equal times..

KEPLER’S SECOND LAWKEPLER’S SECOND LAWKEPLER’S SECOND LAWKEPLER’S SECOND LAW

SunSun

AphelionAphelionPerihelionPerihelion

AA

BB

CC

DD

Area 1 = Area 2Area 1 = Area 2

Area 1Area 1

Area 2Area 2

FLASHCARDFLASHCARDFLASHCARDFLASHCARD

WHERE DOES A PLANET MOVE FASTEST IN WHERE DOES A PLANET MOVE FASTEST IN ITS ORBIT?ITS ORBIT?

A)A) At AAt A

B)B) At perihelion At perihelion

C)C) At aphelion At aphelion

D)D) At D At D

SunSun

AphelionAphelionPerihelionPerihelion

AA

BB

CC

DD

KEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWS

First Law:First Law: The orbit of each planet is an ellipse with The orbit of each planet is an ellipse with the Sun at one focusthe Sun at one focus

Second Law:Second Law: The line joining the planet and the Sun The line joining the planet and the Sun sweeps out sweeps out equal areas in equal timesequal areas in equal times..

Third Law:Third Law: The The squares of the planets’ periodssquares of the planets’ periods of of revolution are in proportion to the revolution are in proportion to the cubes of cubes of the semimajorthe semimajor axes of their orbits axes of their orbits

SunSun

PlanetPlanet

Semimajor AxisSemimajor Axis

KEPLER’S THIRD LAWKEPLER’S THIRD LAWKEPLER’S THIRD LAWKEPLER’S THIRD LAW

(period)(period)22 = (distance) = (distance)33

Eg. Mars: p = 1.88 year, d = 1.52 AUEg. Mars: p = 1.88 year, d = 1.52 AU

(1.88)(1.88)22 = (1.52) = (1.52)33

KEPLER’S THIRD LAWKEPLER’S THIRD LAWKEPLER’S THIRD LAWKEPLER’S THIRD LAW

COMET HALLEY’S ORBITCOMET HALLEY’S ORBITCOMET HALLEY’S ORBITCOMET HALLEY’S ORBIT

FLASHCARDFLASHCARDFLASHCARDFLASHCARD

WOULD YOU EXPECT HALLEY’S COMET TO WOULD YOU EXPECT HALLEY’S COMET TO OBEY KEPLER’S LAWS?OBEY KEPLER’S LAWS?

A)A) YesYes

B)B) No No

FLASHCARDFLASHCARDFLASHCARDFLASHCARD

SPECIFICALLY, DOES HALLEY’S COMET SPECIFICALLY, DOES HALLEY’S COMET OBEY KEPLER’S THIRD LAW? PERIOD = 76 OBEY KEPLER’S THIRD LAW? PERIOD = 76

YEARS, SEMI-MAJOR AXIS = 18 AUYEARS, SEMI-MAJOR AXIS = 18 AU

A)A) YesYes

B)B) No No

ORBITAL DATAORBITAL DATAORBITAL DATAORBITAL DATA

Planet Semimaj Axis (AU)

Period (years)

d3 p2

Mercury 0.39 0.24 0.0593 0.0576

Venus 0.72 0.62 0.3732 0.3844

Erath 1.00 1.00 1.000 1.000

Mars 1.52 1.88 3.5118 3.5344

Asteroid 2.77 4.60 21.254 21.160

Jupiter 5.20 1.86 140.61 140.66

Saturn 9.54 29.4 868.25 867.89

Uranus 19.19 84.07 7,066 7,068

Neptune 30.06 164.80 27,162 27,159

Pluto 39.60 248.60 62,099 1,802

KEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWSKEPLER’S THREE LAWS

First Law:First Law: The orbit of each planet is an ellipse with The orbit of each planet is an ellipse with the Sun at one focusthe Sun at one focus

Second Law:Second Law: The line joining the planet and the Sun The line joining the planet and the Sun sweeps out sweeps out equal areas in equal timesequal areas in equal times..

Third Law:Third Law: The The squares of the planets’ periodssquares of the planets’ periods of of revolution are in proportion to the revolution are in proportion to the cubes of cubes of the semimajorthe semimajor axes of their orbits axes of their orbits

NEWTON’S THREE LAWSNEWTON’S THREE LAWSNEWTON’S THREE LAWSNEWTON’S THREE LAWS

NEWTON’S THREE LAWSNEWTON’S THREE LAWSNEWTON’S THREE LAWSNEWTON’S THREE LAWS

First Law:First Law: Every body continues what it is doing (at rest or Every body continues what it is doing (at rest or in motion in a straight line) unless acted upon by in motion in a straight line) unless acted upon by an outside force. (Note break here with tradition)an outside force. (Note break here with tradition)

Second Law:Second Law: Change in motion of a body is proportional to the Change in motion of a body is proportional to the force acting on it and is in the direction that the force acting on it and is in the direction that the force is acting.force is acting.

Third Law:Third Law: For every action there is an equal and opposite For every action there is an equal and opposite reaction.reaction.

NEWTON’S UNIVERSAL LAW NEWTON’S UNIVERSAL LAW of GRAVITATIONof GRAVITATION

NEWTON’S UNIVERSAL LAW NEWTON’S UNIVERSAL LAW of GRAVITATIONof GRAVITATION

Force = GMForce = GM11MM22/D/D22

M1 and M2 are the masses of the two objectsD is the distance between themG is a constant called the Gravitational Constant

Newton found that the orbits derived from this Newton found that the orbits derived from this force were exactly those found by Keplerforce were exactly those found by Kepler

Kepler’s 3rd Law becomes DKepler’s 3rd Law becomes D33 = (M = (M11 + M + M22) x P) x P22