Consider two planets that have the same mass but are very different in size. On which planet would the gravity be stronger on the surface?

Answer 1

The strength of gravity at the surface of a planet depends not only on its mass but also on its radius. The formula for gravitational acceleration $g$ at the surface of a planet is given by:

$$g=\frac{G\cdot M}{R^2}$$

where:

• $G$ is the gravitational constant,
• $M$ is the mass of the planet,
• $R$ is the radius of the planet.

In your case, since both planets have the same mass $M$, the only variable that affects the surface gravity is the radius $R$.

If the two planets have the same mass but one planet is smaller (having a smaller radius $R$), the gravitational acceleration $g$ on the smaller planet will be stronger because the radius appears in the denominator of the equation. Thus, for a smaller radius, the value of $g$ will be larger.

Conversely, the planet with the larger radius will have weaker gravity at its surface.

In summary, the planet with the smaller radius will have stronger surface gravity, even though both planets have the same mass.