Question

Two objects are placed so their centers are 1.65 meters apart, and the force between them is 8.09 x 10-10 newtons. What is the mass of each object if one has twice the mass of the other? Include units in your answers.

Answer 1

Using Newton's law of universal gravitation:

$F=G\cdot\frac{m1\cdot m2}{r^2}$

Where:

$\begin{gathered} G=6.674\times10^{-11}\cdot\frac{m^3}{\operatorname{kg}\cdot s^2} \\ r=1.65m \\ F=8.09\times10^{-10}N \\ m2=2m1 \end{gathered}$

So:

$F=2G\cdot\frac{m1^2}{r^2}$

Solve for m1:

$\begin{gathered} m1=\sqrt[]{\frac{F\cdot r^2}{2G}} \\ m1=\sqrt[]{\frac{8.09\times10^{-10}\cdot(1.65)^2}{2\cdot6.674\times10^{-11}}} \\ m1=4.06\operatorname{kg} \end{gathered}$

So:

$m2=8.12\operatorname{kg}$

Answer:

4.06kg and 8.12kg