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

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

Gravitation

Solution:

We know that, gravitational force between the earth and the sun is
$F_{G}=\frac{G M m}{r^{2}}$
where, $M$ is mass of the sun and $m$ is mass of the earth. When $G$ decreases with time, the gravitational force $F_{G}$ will become weaker with time. As, $F_{G}$ is changing with time, so the earth will not be revolving around the sun in a closed orbit strictly. Also, the radius may increase, since the attraction force is becoming weaker. Hence, after long time period, the earth will leave the solar system.