Question

The formula to calculate the gravitational force between two objects is F_g=GM_1M_2/r^2, where M_1 and M_2 are the masses of the objects, G is the gravitational constant and r is the distance between the objects. Solve for M_1 in terms of F_g, G, M_2 and r.

Answer 1

Answer:

$M_{1}$ = $\frac{F_{g}r^{2} }{GM_{2} }$

Step-by-step explanation:

From Newton's law of universal gravitation, the force of attraction between two objects of masses $M_{1}$ and $M_{2}$ is given as:

$F_{g}$ = $\frac{GM_{1} M_{2} }{r^{2} }$

Thus, cross multiply to have;

$F_{g}$$r^{2}$ = G$M_{1}$$M_{2}$

then divide through by G$M_{2}$ to have,

$M_{1}$ = $\frac{F_{g}r^{2} }{GM_{2} }$

Therefore, $M_{1}$ can be expressed in terms of $F_{g}$, $r^{2}$, G, $M_{2}$ as $\frac{F_{g}r^{2} }{GM_{2} }$