The centres of the Earth and the Moon are separated by

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

3.84\times10^{8}\,\text{m}

. The Earth has mass

M_E=6.0\times10^{24}\,\text{kg}

and the Moon has mass

M_M=7.4\times10^{22}\,\text{kg}

. A spacecraft of mass

500\,\text{kg}

is to be positioned at a point on the line joining the two centres where the net gravitational force on it is zero. (i) Derive an expression for the distance

x

of this point from the centre of the Earth in terms of

M_E

M_M

and the separation

D

of the two bodies. (ii) Using the given data, calculate the value of

x

. (iii) If the spacecraft is displaced by

1.0\times10^{3}\,\text{m}

towards the Moon from the point found in part (ii), determine the magnitude and direction of the net gravitational force acting on it at the new position. State clearly any approximations made.

Related theory

Universal Law of Gravitation
Gravitation
Gravitation & Weight

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