Question

If a planet is twice as far from the sun at aphelion than at perihelion, then the strength of the gravitational force at aphelion will be how many times the force at perihelion?

Answer 1

The gravitational force at aphelion will be `1/4` of that at perihelion.

Explanation:

According to Newton's laws of gravity the force between the sun and a planet is given by:

`F=(GMm)/r^2`

Where `G` is the gravitational constant, `M` is the mass of the sun, `m` is the mass of the planet and `r` is the distance between the sun and the planet.

So, the force is inversely proportional to the square of the distance between the sun and the planet. If the aphelion distance is twice the perihelion distance then the force at aphelion is a quarter of the force at perihelion.

In actual fact there is no such thing as a gravitational force. Newton's laws are a good approximation. Gravity is not a force it is the curvature of spacetime as described by General Relativity. A planet in orbit is following a geodesic which is the equivalent of a straight line in 4 dimensional spacetime.