Exercise 5

The gravitational force, $F$, between two objects in space with masses $m_1$ and $m_2$ is given by the formula $F=\frac{Gm_1m_2}{r^2}$ where $r$ is the distance between the objects' centers of mass and $G$ is the universal gravitational constant.

Two pieces of space junk, one with mass 500 kg and the other with mass 3000 kg, were drifting directly toward one another. When the objects' centers of mass were 250 km apart the lighter piece was moving at a rate of 0.5 km/h and the heavier piece was moving at a rate of 0.9 km/h. Leaving $G$ as a constant, determine the rate at which the gravitational force between the two objects was changing at that instant. Make sure that each stated and calculated rate value has the correct sign. Make sure that your conclusion sentence clearly communicates whether the force was increasing or decreasing at that given time. The unit for $F$ is Newtons (N).