Transcript PLANETARY ORBITS

PLANETARY ORBITS
Chapter 2
CONIC SECTIONS
PLANETARY GEOMETRY
Definition of a Circle
A Circle is a figure for which all points on it
are the same distance from the centre.
 Definition 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 ELLIPSE
HOW to DRAW an ELLIPSE
(ellipticity
e = distance between foci / major
axis – eEarth 0.02, eJupiter 0.05, eMercury 0.21)
Major Axis
Focus
Focus
Minor Axis
KEPLER’S THREE LAWS
KEPLER’S THREE LAWS

First Law:
 The orbit of each planet is an ellipse with
the Sun at one focus
Foci
Planet
Sun
PLANETARY ORBITS
KEPLER’S THREE LAWS


First Law:
 The orbit of each planet is an ellipse with
the Sun at one focus
Second Law:
 The line joining the planet and the Sun
sweeps out equal areas in equal times.
KEPLER’S SECOND LAW
B
Area 1 = Area 2
C
A
Sun
Area 2
Perihelion
Aphelion
Area 1
D
FLASHCARD
WHERE DOES A PLANET MOVE FASTEST IN
ITS ORBIT?
A) At A
B
A
C
Sun
Aphelion
Perihelion
D
B) At perihelion
C) At aphelion
D) At D
KEPLER’S THREE LAWS



First Law:
 The orbit of each planet is an ellipse with
the Sun at one focus
Second Law:
 The line joining the planet and the Sun
sweeps out equal areas in equal times.
Third Law:
 The squares of the planets’ periods of
revolution are in proportion to the cubes of
the semimajor axes of their orbits
KEPLER’S THIRD LAW
(period)2 = (distance)3
Eg. Mars: p = 1.88 year, d = 1.52 AU
(1.88)2 = (1.52)3
Planet
Semimajor Axis
Sun
KEPLER’S THIRD LAW
COMET HALLEY’S ORBIT
FLASHCARD
WOULD YOU EXPECT HALLEY’S COMET TO
OBEY KEPLER’S LAWS?
A) Yes
B) No
FLASHCARD
SPECIFICALLY, DOES HALLEY’S COMET
OBEY KEPLER’S THIRD LAW? PERIOD = 76
YEARS, SEMI-MAJOR AXIS = 18 AU
A) Yes
B) No
ORBITAL DATA
Planet
Semimaj Period
Axis
(years)
(AU)
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
Neptune
30.06
164.80
27,162 27,159
7,068
KEPLER’S THREE LAWS



First Law:
 The orbit of each planet is an ellipse with
the Sun at one focus
Second Law:
 The line joining the planet and the Sun
sweeps out equal areas in equal times.
Third Law:
 The squares of the planets’ periods of
revolution are in proportion to the cubes of
the semimajor axes of their orbits
NEWTON’S THREE LAWS
NEWTON’S THREE LAWS



First Law:
 Every body continues what it is doing (at rest or
in motion in a straight line) unless acted upon by
an outside force. (Note break here with tradition)
Second Law:
 Change in motion of a body is proportional to the
force acting on it and is in the direction that the
force is acting.
Third Law:
 For every action there is an equal and opposite
reaction.
NEWTON’S UNIVERSAL LAW
of GRAVITATION

Force = GM1M2/D2
M1 and M2 are the masses of the two objects
D is the distance between them
G is a constant called the Gravitational Constant

Newton found that the orbits derived from this
force were exactly those found by Kepler

Kepler’s 3rd Law becomes D3 = (M1 + M2) x P2