1. Chatfield Senior High Physics Department
Mars Orbit Lab
Chatfield Senior High
Physics Department

2. Elliptical Orbits
All planets sweep out elliptical orbits around the Sun
For the Earth….
the perihelion (closest distance) is on Jan. 5
the aphelion (furthest distance) is on July 5

3. Earth rotation
The Earth sweeps out 1 o counter-clockwise ellipse per day
Mar. 21 Vernal Equinox
June 21 Summer Solstice
Sept 21 Autumnal Equinox
Dec 21 Winter Solstice

4. Cause of seasons
Seasons are not caused by the closeness of the Earth to the Sun but by the 23.5 o tilt of the Earth

5. Earth Orbit

6. Mars Orbit Lab Stellar Template

7. Mars Orbit Stellar Template
Overlay template over stellar map

8. Determining Longitude of Mars from Earth
Using a stellar map for 8 pairs of points that are exactly one Martian year apart (687 days) you can create the following data table

9. Earth position at each point

10. To plot Earth points 3/21 A directly left 10/11 J 14+11=25o
4/4 O 10+4=14o 11/22 I 20+22=42o
4/12 F 8o 12/9 L o
4/20 C 8o 1/21 K =43o
5/26 E 10+26=36o 2/3 N = 13o
8/4 H =70o 2/5 B 2o
9/16 G 27+16=43o 2/21 P 16o
3/8 D 7+8 = 15o

11. Plot each pair of Mars longitudes

12. Finished Mars points

13. Kepler’s 1st Law Applications
The left hand side shows that Mars is at aphelion because the points are farther from the Sun
The sun is at one focal point, and the other focal point must be somewhere along that side
Two pins and a string can be used to plot the ellipse as shown.

14. Mars Orbit best-fit curve

15. Mars Orbit Statistics The radius of Mars orbit is 1.525 AU
The eccentricity of the Mars’ orbit is
0.08

16. Kepler’s 2nd Law
A line can be drawn from Mars to the Sun to sweep out the following areas…
Area 1 (2/5/33-4/20/33) 74 days
Area 2 (8/4/41-11/22/41) 110 days

17. Kepler’s 2nd Law

18. Kepler’s 2nd Law
You can use the area of a sector of a circle to approximate Area 1 and Area 2
Area = (n / 360) p R 2
If you divide the areas by the Earth day’s swept out, you will find that the
Area/day is equal

19. Kepler’s 3rd Law
You can use the fact that Mars has a period of 687 Earth days (1.88 yrs)
Mars R av is AU
K (or Kepler’s constant) can be found by….
k = (1.88)2 = 1 yr 2 / AU 3
(1.525)3

20. Kepler’s Quote
“…a fullness of agreement between my seventeen years of labor on the observations of Brahe and his present study of mine that at first I believed I was dreaming”