Ncert Exercises & Solutions

There have been suggestions that the value of the gravitational constant $G$ becomes smaller when considered over a very large time period (in billions of years) in the future. If that happens, for our earth,

(a)	nothing will change
(b)	we will become hotter after billions of years
(c)	we will be going around but not strictly in closed orbits
(d)	after a sufficiently long time, we will leave the solar system

Choose the correct alternatives:

1.	(a), (c)	2.	(a), (d)
3.	(c), (d)	4.	(a), (b)

Hint: The motion of the Earth is dependent on the gravitational force of the sun.

Step: Find the effect on the gravitational force between the earth and the sun.
We know the gravitational force between the earth and the sun, $F_{G} = \frac{G M m}{r^{2}}$ , where M is the mass of the sun and m is the mass of the earth.

When G decreases with time, the gravitational force $F_{G}$ will become weaker with time. Due to it, the earth will be going around the sun not strictly in closed orbit and the radius also increases, Hence, after a long since the attraction force is getting weaker with time, the earth will leave the solar system.

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