Question

Europa, a satellite of Jupiter, has an orbital diameter of 1.34 × 109m and a period of 3.55 days. What is the mass of Jupiter?

Answer 1

Given,

The orbital diameter is

`d=1.34*10^9m`

The radius is

`r=(d)/(2)=(1.34*10^9)/(2)=0.67*10^9m`

The time period is T=3.55 days=3.55x86400 sec.

We know,

`\begin{gathered} T=\frac{2\pi r^{(3)/(2)}}{\sqrt[\square]{GM}}^{}^{} \\ \Rightarrow3.55*86400=\frac{2\pi\text{ (0.67}*10^9)^{(3)/(2)}}{\sqrt[]{6.67*10^(-11)* M}} \\ \Rightarrow9.4*10^(10)=(1.18*10^(28))/(6.67*10^(-11)M) \\ \Rightarrow M=1.89*10^(27)kg \end{gathered}`

The answer is

`1.89*10^(27)kg`