Consider two planets that have the same mass but are very different in size. Which statement on the surface on each planet?

The objects would experience the same gravitational pull on each planet.

The objects would experience a greater gravitational pull on the smaller planet.

The objects would experience only a slightly greater gravitational pull on the larger planet.

The objects would experience a much greater gravitational pull on the larger planet.

1 answer

To analyze the gravitational pull on the surfaces of two planets with the same mass but different sizes, we need to consider the formula for gravitational acceleration at the surface of a planet, which is given by:

\[ g = \frac{GM}{R^2} \]

where:

  • \( g \) is the gravitational acceleration,
  • \( G \) is the universal gravitational constant,
  • \( M \) is the mass of the planet,
  • \( R \) is the radius of the planet.

Since both planets have the same mass \( M \), the key factor influencing the gravitational pull is the radius \( R \).

  • For the smaller planet (which has a smaller radius), the value of \( R \) in the denominator will be smaller, resulting in a larger value of \( g \).
  • For the larger planet (which has a larger radius), the value of \( R \) in the denominator will be larger, resulting in a smaller value of \( g \).

Thus, the objects would experience a greater gravitational pull on the smaller planet because the gravitational acceleration is inversely proportional to the square of the radius.

Therefore, the correct statement is:

The objects would experience a greater gravitational pull on the smaller planet.