A satellite is projected vertically upwards from an earth station. Determine the height above the earth's surface at which the force exerted on the satellite by the earth is reduced to half of its value at the earth

Question

Quantrex Academy · Accepted Answer

Correct answer: D. 2650 km

The force exerted by the earth on the satellite at the earth's surface is given by

F = \dfrac{GMm}{R^2}

.

The force at a height

h

above the surface is

F' = \dfrac{GMm}{(R+h)^2}

.

Given that

F' = \dfrac{F}{2}

, we have:

\dfrac{GMm}{(R+h)^2} = \dfrac{1}{2} \dfrac{GMm}{R^2}

(R+h)^2 = 2R^2

R+h = \sqrt{2}R

h = (\sqrt{2} - 1)R

Substituting

R = 6400 \text{ km}

and

\sqrt{2} \approx 1.414

:

h = (1.414 - 1) \times 6400

h = 0.414 \times 6400 = 2649.6 \text{ km}

This is approximately

2650 \text{ km}

.

A satellite is projected vertically upwards from an earth station....

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