Callisto is a moon of Jupiter. It takes 16.6890184 Earth days to orbit Jupiter. Ganymede is another moon of Jupiter. It takes Ganymede 7.15455296 Earth days to orbit Jupiter. Ganymede is measured to be 1,070,000,000 m from Jupiter's center. How far away is Callisto from the center of Jupiter.

Callisto is a moon of Jupiter. It takes 16.6890184 Earth days to orbit Jupiter. Ganymede is another moon of Jupiter. It takes Ganymede 7.15455296 Earth days to orbit Jupiter. Ganymede is measured to be 1,070,000,000 m from Jupiter's center. How far away is Callisto from the center of Jupiter.

Hint
This is a great example of when to use Kepler's third law to solve a problem. When you are given to satelites orbiting the same body and you're given 3 out of four of distances from the center of the body to the satelites and the period you can use Kepler's third law. These bodies all have the same Kepler constant because they revolve around the same body.

Since both of these setellites are orbiting the same body, Jupiter, and therefore have the same Kepler's constant. Therefore

This is the typical set up for solving problems using Kepler's third law. Because everything is set up as a ratio, you do not need to convert units to any known standard. But you do need to make sure they all have matching units.

Callisto is a moon of Jupiter. It takes 16.6890184 Earth days to orbit Jupiter. Ganymede is another moon of Jupiter. It takes Ganymede 7.15455296 Earth days to orbit Jupiter. Ganymede is measured to be 1,070,000,000 m from Jupiter'e center. How far away is Callisto from the center of Jupiter. |

Hint (scroll down for the solution)
This is a great example of when to use Kepler's third law to solve a problem. When you are given to satelites orbiting the same body and you're given 3 out of four of distances from the center of the body to the satelites and the period you can use Kepler's third law. These bodies all have the same Kepler constant because they revolve around the same body.

Since both of these setellites are orbiting the same body, Jupiter, and therefore have the same Kepler's constant. Therefore

This is the typical set up for solving problems using Kepler's third law. Because everything is set up as a ratio, you do not need to convert units to any known standard. But you do need to make sure they all have matching units.

Solution

Unless otherwise stated all distances are between the center's of the satellite and the body it is orbiting for planetary motion problems.

Use Kepler's 3rd law of planetary motion to set up a ratio problem comparing the period and radii of the two moons.