Question

Two identical probes, each of mass 2.00 x 10^22 kg, are "parked" close to each other in outer space. If they are separated initially by 1.00km, how long
(in hours) will it take for the distance between them to decrease by 1.00m , due to gravitational attraction? Assume that the probes behave as point particles and that gravitational force remains constant as the probes move closer to each other.

Answer 1

calculate the 'g'
\[ g = \frac{Gm}{r^2} \]
and use
\[ d = \frac{1}{2}gt^2 \]
then, because both probe have same mass, we get
\[ d_1 + d_2 = 2d = 1 \]
or
\[ t = \left( \frac{r^2}{Gm} \right)^{\frac{1}{2}} \]