The acceleration due to gravity at the Earth’s surface is

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

Problem

g = 9.80\,\text{m s}^{-2}

. Assume the Earth to be a uniform sphere of radius

R = 6.4\times10^{6}\,\text{m}

. (i) Derive an expression for the mass of the Earth

M

in terms of

g

R

and the universal gravitational constant

G

. (ii) Using

G = 6.67\times10^{-11}\,\text{N m}^{2}\,\text{kg}^{-2}

, calculate the numerical value of

M

. (iii) A satellite of mass

1000\,\text{kg}

is placed in a circular orbit

2.0\times10^{6}\,\text{m}

above the Earth’s surface. Treating both Earth and satellite as point masses, determine the gravitational force acting on the satellite.