Satellite Motion Laboratory
In our study of projectile motion, we could go to the laboratory and take strobe photographs in order to see how projectiles behaved. Obtaining experimental data for the study of satellite motion is somewhat more difficult. What we will do is to use the Orbit 1 program or slight modification of it to stimulate satellite motion, using it as our laboratory for the study of the behavior of satellites.
But first we wish to check that the Orbit 1 program makes predictions that are in agreement with experiment. The program is based on Newton's laws of gravity, F _g = GMm/r² , Newton's law of motion , and the procedures we developed earlier for predicting the motion of an object whose acceleration is known. Thus a verification of the results of the Orbit 1 program can be considered a verification of these laws and procedures.
Some tests of the Orbit 1 program can be made using the results of your own experience. Anyone who has listened to the launch of a low orbit satellite should be aware that the satellite takes about 90 minutes to go around the earth once. The Orbit 1 program should give the same result, which you can check in Exercise 11. Another obvious test is the prediction of the period of the moon in its orbit around the earth. It is about 4 weeks from full moon to full moon, thus the period should be approximately 4 weeks or 28 days. The fact that the apparent diameter of the moon does not change much during this time indicates that the moon is traveling in a nearly circular orbit about the earth. If you accept the astronomer's measurements that the moon orbit radius is about 60 earth radii away, then you can check the Orbit 1 program to see if it predicts a 4 week period for an earth satellite in a circular orbit of that radius.
(An easy way to measure the distance to the moon was provided by the first moon landing. Because of a problem with Neil Armstrong's helmet, radio signals sent to Neil from Houston were retransmitted by Neil’s microphone, giving an apparent echo. The echo was particularly noticeable while Neil was setting up a TV camera. On a tape of the mission supplied by NASA, you can hear the statement "That's good there, Neil". A short while later you hear the clear echo "That's good there, Neil". The time delay from the original statement and the echo is the time it takes a radio wave, traveling at the speed of light, to go to the moon and back. Using an inexpensive stop watch, one can easily measure the time delay as being about 2 2/5 seconds. Thus the oneway trip to the moon is 1 1/5 seconds. Since light travels 1 ft
anosecond, or 1 billion feet per second, from this one determines that the moon is about 1.2 billion feet away. You can convert this distance to earth radii to check the astronomer's value of 60 earth radii as the average distance to the moon.)