planetary orbits chapter 2. conic sections planetary geometry l definition of a circle äa circle is...
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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