91Ó°ÊÓ

Gravitational Force on the moon$F=3×{10}^{23}N$

Definition

The force attraction between every object in the universe is called gravitation force.

For example: throwing the ball in the air and the ball comes to the ground.

Gravitation force can be written as

$F=\frac{G{M}_1{M}_2}{R^2}.................................................\left(1\right)$

Where G is the universal gravitational constant, $M_1$is the mass of the moon, $M_2$is the mass of the planet, and $R$is the distance between moon and planet.

Now, $M"=3M,$

Where$M"$ is the new mass of the moon.

From equation no (1), we get,

$$\begin{gathered} F=\frac{G3M_1{M}_2}{R^2} \\ =3F \end{gathered}$$

Substituting the$3×{10}^{23}N$ for F in the above equation,

$$\begin{gathered} F\text{'}=3×3×{10}^{23}N \\ F\text{'}=9×{10}^{23}N \end{gathered}$$

Thus, if the mass of the moon were three times as large, then the magnitude of the force is$9×{10}^{23}N$.

Now for the distance between the moon and planet three times large,

$R"=3R$

From the equation no (1), we get,

$$\begin{gathered} F\text{'}=\frac{G{M}_1{M}_2}{{\left(3R\right)}^2} \\ =\frac{F}{9} \end{gathered}$$

Substituting the$3×{10}^{23}N$ for F in the above equation

$$\begin{gathered} F\text{'}=\frac{3×{10}^{23}N}{9} \\ =3.33×{10}^{22}N \end{gathered}$$

Thus, if the distance between the moon and the planet were three times as large (no change in mass), then the magnitude of the force is$3.33×{10}^{22}N.$