Question

rearrange the following equation (gravitational force between two objects) to make r the subject: $f_{g}=\frac{g\times m_{1}\times m_{2}}{r^{2}}$ $r = \frac{f_{g}\times g\times m_{1}\times m_{2}}{2}$ $r=\frac{g\times m_{1}\times m_{2}}{2f_{g}}$ $r=sqrt{g\times m_{1}\times m_{2}\times f_{g}}$ $r=sqrt{\frac{g\times m_{1}\times m_{2}}{f_{g}}}$

Explanation:

Step1: Cross - multiply

$F_g\times r^{2}=G\times m_1\times m_2$

Step2: Isolate $r^{2}$

$r^{2}=\frac{G\times m_1\times m_2}{F_g}$

Step3: Take square - root of both sides

$r = \pm\sqrt{\frac{G\times m_1\times m_2}{F_g}}$
Since $r$ represents a distance (a non - negative quantity in this context), we consider the positive value. So $r=\sqrt{\frac{G\times m_1\times m_2}{F_g}}$

Answer:

$r=\sqrt{\frac{G\times m_1\times m_2}{F_g}}$