ANSWER
[tex]M=\frac{rv^2^{}}{2G}[/tex]
EXPLANATION
Solve for the object's mass M means that we have to clear M from the equation:
[tex]v^2=\frac{2GM}{r}[/tex]
First multiply both sides by r:
[tex]\begin{gathered} rv^2=\frac{2GM}{r}\cdot r \\ rv^2=2GM \end{gathered}[/tex]
And then divide both sides by 2G:
[tex]\begin{gathered} \frac{rv^2}{2G}=\frac{2GM}{2G} \\ \frac{rv^2}{2G}=M \end{gathered}[/tex]
So M is:
[tex]M=\frac{rv^2}{2G}[/tex]
