Answer to Question #157724 in Physics for Andu

Question

Calculate the period of the Jupiter satellite Europa, when it is known that the radius of its orbit is about 600,000 km and the mass of Jupiter is M = 2 × 10²⁷kg.

Answer 1

$mv^2/r=GMm/r^2\to v^2=GM/r$

$T=2\pi r/v\to v=2\pi r/T$

$(2\pi r/T)^2=GM/r\to$

$T=\sqrt{\frac{4\pi^2r^3}{GM}}=\sqrt{\frac{4\cdot 3.14^2\cdot 600000000^3}{6.67\cdot10^{-11}\cdot2\cdot10^{27}}}=252702(s)=70.2(h)$ .Answer