Question

In 1542 Copernicus was able to calculate the sizes (we now call this the semi-major axis) of the orbits for all of the planets visible without a telescope. The results of his calculations are shown in Module 2c. In 1609 Galileo measured the positions of the four largest moons of Jupiter. A portion of these observations is also shown in Module 2c. From these observations, it is trivial to determine the period of the orbits of these moons. With a bit, more work one can also measure the (angular) distance these moons are from Jupiter. Then in 1687 Newton published his theory of gravity. There is no evidence that anyone put these three pieces of work together to estimate the mass of Jupiter, but it can be done

Determine the mass of Jupiter assuming (1) the semi-major axis of Jupiter’s orbit is 5.2 A.U.; (2) the period of Ganymede’s (the largest moon of Jupiter) orbit is 170 hours; (3) when Jupiter is at opposition Ganymede reaches a maximum of 5.9 arcminutes from Jupiter; (4) Ganymede’s orbit is a circle.

Answer 1