ORBIT OF EARTH, MARS, AND MERCURY

DISCUSSION:
    We all know that the earth goes around the sun. However, all motion is relative. Therefore, we can plot the sun's apparent path around the earth and convert this into a modern view of the solar system.
    To plot the earth we will use the apparent diameter of the sun. Since the sun appears larger when it is closer to the Earth, the inverse of the diameter of the sun is proportional to its distance from Earth. Therefore we can determine the relative orbital distance of the Earth from the sun by measuring the Sun's diameter and calculating the inverse of the diameter.
    To plot Mars we can use parallax shift by recording the longitude angle of Mars from the Earth at 2 different times, while Mars is still in its same place. (since the Earth and Mars orbit at different rates, they will be at different positions relative to each other). Using geometry, the exact location of Mars can be found.
    The third orbital plot of Mercury will use maximum elongation, the point in the sky where the planet appears furthest away from the sky where the planet appears furthest away from the sun in the sky. By measuring the maximum elongation angle and using geometry again, the location of Mercury can be located.

PROCEDURES

PART I. - EARTH
1. Make a data table for the date, diameter, scaled distance (50/D) from the sun, and direction to sun.

2. Measure and record the apparent diameter of the sun to the nearest hundredth of a centimeter. Convert scaled distance by dividing 50 by the diameter (units are still cm)
                example:  diameter  =  5.23 cm            scaled distance  = 50/5.23 = 9.56 cm

3. Tape 4 pieces of graph paper together. Make sure the lines line up. Place a dot in the center to represent Earth.

4. Plot the distance from the Earth for each date given that the following angles to the sun from the Earth were measured. (0° is to the right)
Date                      Dir. to Sun  (°)             Date                          Dir to sun (°)
Mar 21                            0                        Sep 4                                162
Apr 6                              15                       Oct 4                                191
May 6                             45                       Nov 3                               220
Jun 5                              74                        Dec 4                               250
Jul 5                              102                       Jan 4                                283
Aug 5                            132                       Feb 4                               315
                                                                  Mar 7                               346

5. Connect the plotted dots to obtain the orbit of the sun around the Earth. Label the Earth.

6. Since motion is relative, we can convert this plot to a plot of the Earth around the sun. On March 21 the sun is to the
r i g h t of the Earth. This means that the Earth is to the l e f t of the sun (that's a 180° shift) So... just flip your paper 180° and label the center dot sun and the orbit you just plotted Earth! (Yes, the center dot says Earth upside-down now and the Sun right side up)
 
 
 
 

PART II  -  MARS

7. Fill in the following data table. Use the website

http://www.cas.muohio.edu/~devriepl/phy211/copernicus/planetarydata.htm

You need to pick pairs of dates that are 687 days apart

8. Measure the longitude from your plotted Earth orbit.  0° is to your right. You must use the correct date. Find the closest date and add 1° for every day to locate the correct position of the Earth.  (360°  = 1 circle and 365 days = 1 year, so 1° is about 1 day).  Each pair of data plotted will have their lines of site cross. Where the cross is the location of Mars.

9. Connect the plotted mars location using a different color from the Earth orbit. Label it Mars.  (You need to assume a symmetrical orbit and "fill in" missing points)

PART III  - MERCURY

Plot the angle for maximum elongation from the correct Earth position like before.  East is left and West is right! You find the position of Mercury by making a right triangle with the Sun. Use the following recorded data:

Date                Elongation               Date               Elongation
Jan 4                    19°E                    Oct 6                 18°W
Feb 14                 26°E                    Dec 18               20°E
Apr 26                 20°E                    Jan 27                25°W
Jun 13                  23°W                  Apr 8                 19°E
Aug 24                 27 °E                  May 25               25°W

12. Again, connect the Mercury points plotted with a third color and label.

QUESTIONS

1. What is the average radius of Earth's orbit in meters? (use conversion factor 10 cm = 5 x 10^9 m)

2. Since you know the period of the Earth (365.25 days), and you know the radius of the Earth's orbit, calculate the speed of the Earth. (5 steps)

3. What is the acceleration of the Earth due to the sun? (5 step)

4. Since force decreases with distance, how would the acceleration of Mercury and Mars compare to Earth?

5. What are the shapes of each planet's orbit, circles or ellipses?