This lab is adapted from a Project Physics lab in the early 1980's. I am not sure if the acetates and photographs are still available.
The purpose of this lab will be to use the data from the Mars photographs to verify Kepler's three laws. Directions 1. Obtain a large piece of graph paper from Mrs. Colwell. Carefully, determining the center of the paper. Place a large pencil dot in its position. 2. On this graph paper, draw a 10 cm radius circle as close to the center of the grid as possible using your compass. Label the center of this circle with a large "S" for the Sun. This circle represents the orbit of the Earth around the Sun. 3. From "S" draw a line to the right until it intersects with the circle. This represents the positive xaxis. Neatly label this intersection point as 0º  Sept. 23. Now draw a line from "S" to the left. This will represent the negative xaxis. Label this intersection point as 180º  March 21. 4. Since the Earth travels once (360º) around the Sun in 365 days, use the rough estimate that the Earth moves approximating 1 degree/day, to locate and neatly label each of the positions listed as A through P below on the circle drawn in Step #3.
Jan 4, 103.2º 
April 6, 195.7º 
July 5, 282.5º 
Oct 4, 11.3º 
Feb 4, 134.7º 
May 6, 225º 
Aug 5, 312.1º 
Nov 3, 40º 
March 7, 166º 
June 5, 253.9º 
Sept 4, 342º 
Dec 4, 70.9º 
Photograph 
Date 
Location on Earth's Orbit in Degrees 
A 
March 21 

B 
February 5 

C 
April 2O 

D 
March 8 

E 
May 26 

F 
April 12 

G 
September 16 

H 
August 4 

I 
November 22 

J 
October 11 

K 
January 21 

L 
December 9 

M 
March 19 

N 
February 3 

O 
April 4 

P 
February 21 

5. After obtaining a booklet of star photographs and transparencies, locate Mars on each picture and use a short ruler to interpolate the planet's position. Record your results in the chart provided below. After checking with your instructor, share them with the rest of the class by placing them in the appropriate blanks on the board. Notice that the dates on which each of the pictures was taken coincides with the dates already placed on your Earth Orbit.
Photograph 
Date 
Location of Mars' Longitude in Degrees 
A 
March 21, 1931 

B 
February 5, 1933 

C 
April 2O, 1933 

D 
March 8, 1935 

E 
May 26, 1935 

F 
April 12, 1937 

G 
September 16, 1939 

H 
August 4, 1941 

I 
November 22, 1941 

J 
October 11, 1943 

K 
January 21, 1944 

L 
December 9, 1945 

M 
March 19, 1946 

N 
February 3, 1948 

O 
April 4, 1948 

P 
February 21, 1950 

6. Through each Earth position, lightly sketch in a new "Oº axis" parallel to your original xaxis which passed through the Sun. Then using a protractor, locate the "line of sight" for Mars. Each set of overlays (AB), (CD), etc. represents one Martian year and will allow you to triangulate one Martian position  you will have a total of "8 spikes". Place a neat circle around each intersection and label them appropriately as M_{AB}, M_{CD}, M_{EF}, M_{GH}, M_{IJ}, M_{KL}, M_{MN}, and M_{OP}.
7. Use a ruler to draw in a straight line between two adjacent Mars positions. Then use a compass to bisect the line and a ruler to draw in the perpendicular bisector. Perform this operation up to four times for more accurate results. Extend the bisectors as long as necessary to insure that they intersect. According to a theorem from geometry, the perpendicular bisectors of any two chords of a circle will intersect in the center of the circle. You should now be able to draw a circle that represents Mars' orbit. Note that the center of this circle will not pass through the Sun. 