Question

Is it ok to assume the following statements in order to determine the mass of Jupiter? Why?

Statements: 1.The orbits of the moons are all perfectly circular with unchanging radii

2. The orbits do not speed up or slow down from one period to the next

3. The moons all orbit Jupiter at zero inclination

4. Jupiter is much more massive than its moons

5.Every 12 hours we are able to take a picture of Jupiter

Answer 1

The all above statements are correct for Jupiter and it's satellites. The orbits of satellites are circular and in zero inclined plane. Jupiter has rotation period about 9hr 56 min. And Jupiter is 5000 massive than the satellites. For the determining the mass of the Jupiter, we can use the formula of Kepler third law which is modified by the Newton. As follows

M= a³/ P²

^{here, M is mass of primary body. a is semi major axis of the satellite and P is the orbital period of the satellites.}

^{so we can now say that, the orbital periods of satellites and the semi major axes of their orbit have effect on the mass of planet. As the moons of Jupiter has circular orbits and their period are not speed up or slows down, they directly add some mass into the mass of Jupiter. But this mass is very less as compare to Jupiter own mass. So we neglect it. Finally according to Kepler's third law, the effects of orbital characteristics determines the actual mass of Jupiter .}