The masses of distant celestial bodies are measured by measuring the gravitational pull of those bodies on each other. We weigh planets and moons relative to their pull on other planets and moons. The speed of a planets orbit is the only thing keeping it from colliding into the largest object near it. This experiment gives us insight on the affect gravity has on orbiting planets.
This “experiment” is done using nothing but computer simulation. After the Astronomy program is loaded and the time and date values entered, the simulation begins. Choose one of the 4 moons of Jupiter (Io, Europa, Ganymede, and Callisto) to follow its path of orbit. Next, follow the orbit using the simulation recording its position at several intervals (at least ten) and also recording the “cloudy” days when readings could not be made. The data should be recorded until the satellite makes a complete revolution around Jupiter and gets back to the position it began in. Exit the program.
Time (in hours)
Day (in days)
The amplitude of the curve in Jovian diameters is 3 giving the radius of the orbit.
3 JD/1050= 0.00285 AU
The period of the orbit is roughly 1.7 days (40 hours).
1.7 days/365.25= 0.00465 years
M (jupiter) =0.00107060354 solar masses
The mass of the sun is 1.992×10^33 grams.
0.00107060354(1.992×10^33 grams.)=2.133×10^30 grams
The mass of the Earth is 5.975×10^27 grams
2.133×10^30 grams/5.975×10^27 grams=356.987
Jupiter is 356.987 times more massive than Earth.
There was not very many places for error in this lab because it was almost all computer based, but I had error in plotting one of my points on my graph because I forgot to skip an interval to take into account the cloudy day. The graph still made a correct sinusoidal curve, but there was still an error in it. Also, the relationship between hours and days on the data table is off because of using significant figures on the data table causes the amount of days to be rounded up.
Determining gravity through a satellite’s orbit is an easy point to begin at to determine its mass. We weigh planets and moons relative to their pull on other planets and moons. “Because we, as observers, are nearly in the plane of the satellite orbits, we see each moon oscillating from one side of Jupiter to the other, almost in a straight line. The apparent distance R of the moon from the center of Jupiter follows a Sinusoidal curve.” Astronomers use computers and the data readouts they provide to perform observations and “experiments” just like we did in the lab. We chose our own satellite to track, plotted its sinusoidal curve, and determined its mass as a result.