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. we will become hotter after billions of years.
• B. Nothing will change.
• C. we will be going around but not strictly in closed orbits.
• D. after sufficiently long time we will leave the solar system

Answer 1

Answer: (C), (D)

after sufficiently long time we will leave the solar system

Gravitational force between the Earth and the Sun:

$F=\frac{G{M}_S{M}_e}{r^2}$

$F\propto \frac{1}{r^2}$

where $M_S$ is mass of the sun and $M_e$ is mass of the earth.

This provides the necessary centripetal force for the circular orbit of the earth around the sun. As G decreases with time, the gravitational force F will become weaker with time. As F is decreasing with time its radius r also increases with time and Earth will be going around the sun but not strictly in closed orbit (may be spiral).
Hence, after long time the earth will leave the solar system

Final Answer: Option (c),(d)