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

`M_(1)` =
`(F_(g)r^(2) )/(GM_(2) )`

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)` =
`(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)` =
`(F_(g)r^(2) )/(GM_(2) )`

Therefore,
`M_(1)` can be expressed in terms of
`F_(g)`,
`r^(2)`, G,
`M_(2)` as
`(F_(g)r^(2) )/(GM_(2) )`