## Question

If the period of revolution of an artificial satellite just above the earth be *T*and the density of earth be then prove that ρT^{2} is a universal constant. Also calculate the value of this constant.

### Solution

If the period of revolution of a satellite about the earth be *T*. then

Where *h* is the height of the satellite from earth’s surface.

The satellite is revolving just above the earth, hence *h* is negligible compared to *R _{e}*.

where ρ is the density of the earth. Thus

Which is a universal constant. To determine its value,

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