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Kepler's third law holds for the moons of a planet too, with another constant.
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Kepler's third law holds for the moons of a planet too, with another constant. For three moons of Jupiter, the distance from the planet in km and the period in days are: Io 421 700 and 1.769, Europa 671 100 and 3.551, Ganymede 1 070 400 and 7.155. Fit a straight line to the logarithms, and find the power. Then predict the period of Callisto, at 1 882 700 km, and compare it with the true period, 16.689 days.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Fit the line to the logarithms of the three moons. Use the fitted law to predict the period of the fourth, which was not in the fit.
Check. The power is 1.500, the same as for the planets: the law is general. The predicted period of Callisto is 16.69 days, and the true period is 16.689 days. The prediction is correct to 0.01 percent.
Answer: the power is 1.50, and the predicted period of Callisto is 16.69 days (true: 16.689 days).
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