Worked example 12.1: Gravity on Callisto

Question: Callisto is the eighth of Jupiter's moons: its mass and radius are $M= 1.08\times 10^{23} {\rm kg}$ and $R= 2403 {\rm km}$, respectively. What is the gravitational acceleration on the surface of this moon?

Answer: The surface gravitational acceleration on a spherical body of mass $M$ and radius $R$ is simply

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

Hence,

$$g = \frac{(6.673\times 10^{-11})\times(1.08\times 10^{23})}{(2.403\times 10^6)^2} = 1.25 {\rm m/s^2}.$$