The average radius of Earth is and the acceleration due to gravity at the surface is

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

The average radius of Earth is 6.37×106 m6.37\times10^{6}\,\text{m} and the acceleration due to gravity at the surface is 9.80 m s−29.80\,\text{m\,s}^{-2}. (a) Derive an expression for Earth’s mass in terms of the gravitational constant GG, the surface value of gg, and Earth’s radius RR. (b) A communication satellite is in a circular orbit of radius 4.22×107 m4.22\times10^{7}\,\text{m} around Earth. Using the value of G=6.67×10−11 N m2kg−2G = 6.67\times10^{-11}\,\text{N\,m}^{2}\text{kg}^{-2}, calculate Earth’s mass from the satellite’s orbital radius and a period of exactly 24 h24\,\text{h}. (c) Compare the mass obtained in part (b) with the theoretical mass from part (a) and comment on the degree of agreement, expressing any percentage difference you find.

Related theory

Browse the problem library