Question

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,

• A. nothing will change
• B. it will become hotter after billions of years
• C. it will be going around strictly in closed orbits
• D. after sufficiently long time it will leave the solar system

Answer 1

Answer: (D)

We know that, gravitational force between the earth and the sun is
$F_G=\frac{GMm}{r^2}$
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.