A satellite is in a circular orbit around Earth at an altitude where the orbital radius is exactly \(4\) times the radius of another satellite's orbit. If the first satellite has a time period of \(2\) hours, what is the time period of the second satellite (in hours)?
Show Hint
Kepler's Third Law:
\[
\boxed{
T^2\propto r^3
}
\]
or equivalently,
\[
\boxed{
\frac{T_2}{T_1}
=
\left(\frac{r_2}{r_1}\right)^{3/2}.
}
\]
Always determine carefully which orbit has the larger radius before substituting.