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