Question

Two satellite s P and Q orbit around the earth The radius of orbit P is four times that of Q.If the period of orbit for Q is T,what is the period for P?

Answer 1

We can find the period for satellite P from the Third Kepler's Law:

$$\dfrac{r_P^3}{T_P^2}=\dfrac{r_Q^3}{T_Q^2},$$ $$T_P=\sqrt{\dfrac{T_Q^2r_P^3}{r_Q^3}},$$ $$T_P=\sqrt{\dfrac{T_Q^2(4r_Q)^3}{r_Q^3}}=8T_Q.$$