1. Tychonic Model  Tycho Brahe - late 1500’s  Combination Copernican &
Ptolemaic Models
 Introduced as Tycho
could not measure parallax
 Strong biblical influence
 Accepted by many clerics
as Copernican system banned

2. PLANETARY ORBITS
Chapter 2

3. CONIC SECTIONS Circles and Ellipses are Conic
Sections - plane cutting a cone
produces a circle (plane cuts
parallel to the base) or an
ellipse (plane cuts at an angle
to the base)

4. 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

5. HOW to DRAW an ELLIPSE

6. Major parts of an ellipse
Ellipses
How to draw an ellipse
ellipticity e = distance
between foci / major axis
Major parts of an ellipse

7. HOW to DRAW an ELLIPSE
(ellipticity e = distance between foci / major axis – eEarth 0.02, eJupiter 0.05, eMercury 0.21)
Major Axis
Focus
Minor Axis

8. German mathematician, astronomer His 3 laws led the way to Newtonian
KEPLER’S THREE LAWS
Johannes Kepler
German mathematician, astronomer
and astrologer
His 3 laws led the way to Newtonian
physics

9. KEPLER’S THREE LAWS First Law:
The orbit of each planet is an ellipse with the Sun at one focus
Foci
Planet
Sun

10. PLANETARY ORBITS

11. 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.

12. KEPLER’S SECOND LAW Sun Aphelion Perihelion A B C D Area 1 = Area 2
If Area 1 = Area 2 time to go from A to B is same as time to go from C to D

13. WHERE DOES A PLANET MOVE FASTEST IN ITS ORBIT?
FLASHCARD
WHERE DOES A PLANET MOVE FASTEST IN ITS ORBIT?
A) At A
B) At perihelion
C) At aphelion
D) At D
Sun
Aphelion
Perihelion A B C D

14. 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

15. Period must be in years and distance in AU
KEPLER’S THIRD LAW
(period)2 = (distance)3
Eg. Mars: p = 1.88 year, d = 1.52 AU
(1.88)2 = (1.52)3
Sun
Planet
Semimajor Axis
Period must be in years and distance in AU

16. Flashcard If perihelion of a comet is 2 AU and aphelion is 4 AU,
what is the comet’s orbital period around the Sun?
(A) 2.1 years
(B) 3.2 years
(C) 5.2 years
(D) 8.0 years

17. KEPLER’S THIRD LAW

18. When was comet last at perihelion? Three comments about the orbit?
COMET HALLEY’S ORBIT
When was comet last at perihelion?
Where is the comet now?
Three comments about the orbit?

19. WOULD YOU EXPECT HALLEY’S COMET TO OBEY KEPLER’S LAWS?
FLASHCARD
WOULD YOU EXPECT HALLEY’S COMET TO OBEY KEPLER’S LAWS?
A) Yes
B) No

20. FLASHCARD
SPECIFICALLY, DOES HALLEY’S COMET OBEY KEPLER’S THIRD LAW? PERIOD = 76 YEARS, SEMI-MAJOR AXIS = 18 AU
A) Yes
B) No

21. ORBITAL 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
1.000
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

22. 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

23. NEWTON’S THREE LAWS 1643 - 1727 perhaps greatest scientist of all time
Described theory gravitation
which removed last doubts about
heliocentric model
Showed Kepler’s Laws could be
derived from his theory
Invented reflecting telescope
and theory colour
Invented calculus (with Leibniz)
In 2005 voted person with greatest
influence on science
(beat out Einstein).

24. 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.

25. It is Newton’s third law that allows jets to fly and rockets
to be flown to the
Moon and beyond.

26. 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

27. Flashcard Force = GM1M2/D2
If the distance between two masses increases
by 3 times and one mass decreases by 2 times,
how will the gravitational force between the masses
change?
(A) Decreases by 2/3
(B) Decreases by 18 times
(C) Increases by 1.5 times
(D) Increases by 6 times