The centres of Earth and Moon are separated by

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

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

. The masses are

M_{\oplus}=6.0\times10^{24}\,\text{kg}

and

M_{\text{M}}=7.4\times10^{22}\,\text{kg}

respectively. A spacecraft is to be parked at a point on the straight line joining the centres such that it remains in gravitational equilibrium under the attraction of Earth and Moon only. (i) Obtain a general symbolic expression for the distance

r

from the centre of the Moon at which the net gravitational field on the spacecraft is zero. Express your result in terms of

M_{\oplus},\,M_{\text{M}},

and the Earth–Moon separation

D

. (ii) Using the values given, calculate

r

in kilometres. Also state the corresponding distance of the point from the Earth’s centre. (iii) Determine the gravitational potential (with zero at infinity) at the equilibrium point due to Earth and Moon together. Give the answer in J\,kg

^{-1}

and comment, in one or two sentences, on whether this point represents a maximum or minimum of potential along the line.

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