Question

The ratio of value of gravitational constant G between Earth and the Moon system and Earth and Sun system is:
A.) > 1
B.) < 1
C.) 1
D.) Can’t be calculated

Answer 1

Hint: Gravitational constant is a universal constant which means it has the same value at every place in the universe and does not depend on the fact that which astronomical bodies we are talking about.

Detailed step by step solution:
Newton’s law of gravitation says that two bodies which have mass exert an attractive force on each other. This force is called gravitational force or gravity. According the Newton, mathematically this force is

Directly proportional to the masses of the two bodies under consideration

$F\propto m_1{m}_2...\text{(i)}$

where $m_1$and $m_2$ are the masses of the two bodies.

Inversely proportional to the square of the distance by which they are separated from each other

$F\propto {\displaystyle \frac{1}{r^2}}...\text{(ii)}$

where r signifies the separation distance between the two bodies.

This means that greater the mass of the bodies, greater is the gravitational force between the two bodies and if we increase the distance between the two bodies, then the gravitational force between them will also decrease and vice-versa.

Combining equation (i) and (ii), we get

$$\begin{gathered} F\propto {\displaystyle \frac{m_1{m}_2}{r^2}} \\ \Rightarrow F=G{\displaystyle \frac{m_1{m}_2}{r^2}} \end{gathered}$$
where G is the constant of proportionality called the universal gravitational constant. Its value is given as

$G=6.67\times {10}^{-11}{m}^{3}k{g}^{-1}{s}^{-2}$

The value of the gravitational constant remains the same for all astronomical systems including the earth-moon system and sun-earth system.
Therefore, the correct answer is option C.

Note:
1. The gravitational force follows the inverse square law which means that it reduces or increases with the square of the distance between two bodies.
2. Moon revolves around the earth under the influence of the gravity of earth while earth revolves around the sun under the influence of the gravity of the sun. The bigger mass dominates the gravitational force between two bodies.