A planet has two satellite moons. Moon X has an orbital period of 2.27 days. Moon Y has an orbital period of about 3.40 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 1.60 1027 kg.

Question

A planet has two satellite moons. Moon X has an orbital period of 2.27 days. Moon Y has an orbital period of about 3.40 days. Both moons have nearly circular orbits. Use Kepler's third law to find the distance of each satellite from the planet's center. The planet's mass is 1.60  1027 kg.
distance from Moon X to the planet's center__  km
distance from Moon Y to planet's center	___  km

For the first problem (Moon X), I keep getting 8.09but that answer is wrong.  What am I doing wrong? I get K= 3.69x10^-16. Then 1.96x10^5s for the planets orbital and plug it into the cubed root equation. Any suggestions?

drwls · Answer

Use Kepler's Third Law, in Newton's modified frm. You can find the formula at http://easycalculation.com/physics/classical-physics/learn-keplers-law.php