Chapter 7, Problem 79A

To determine

Whether the value of $G$ changes or not if the Earth were twice as massive but remained the same size.

Answer to Problem 79A

No change in $G$ .

Explanation of Solution

Introduction:

Gravitational force:

  $F=\frac{G{m}_1{m}_2}{r^2}$

Where, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between the masses.

  $G$ is the gravitational constant which has a value of $6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$ . This value remains constant and is independent of the mass or the radius of the planet.

Conclusion:

Hence, the value of $G$ will not change even when the mass of the Earth would double while keeping its radius same.