I have a physics question. The planet Mercury has a radius of about 0.38 Earth radii and a mass of only 0.055 Earth masses. Estimate g on Mercury.

By Newton's second law, the gravitational force F between an object of mass m and a planet of radius r and mass M is on the surface of the planet is

F = G M m / r ² = m a

where

G = 6.67 × 10⁻¹¹ N•m²/kg², the universal gravitational constant

a = the acceleration of the object (not the planet; note that the right side is m times a, and not M times a)

The object's mass cancels on either side, leaving you with

a = G M / r ²

and this acceleration is due to gravity. On Earth, a = g.

Let M be the mass of Earth and r its radius; then

g (Earth) = G M / r ² ≈ 9.80 m/s²

To find g on Mercury, replace r with 0.38r and M with 0.055M :

g (Mercury) = G (0.055M) / (0.38r )² = 0.055/0.38² G M / r ²

g (Mercury) ≈ 0.38 g (Earth) ≈ 3.73 m/s²

not moving. pos accel,