For a satellite to orbit around earth, which of following must be true ?

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7.Gravitation

hard

For a satellite to orbit around the earth, which of the following must be true ?

It must be above the equator at some time

Its period of rotation must be $> 2\pi \sqrt{R/g} $ where $R$ is radius of earth

Its height above the surface cannot exceed $36,000 \,km$

$(A)$ and $(B)$ both

Solution

For any object (satellite) to revolve another body(earth), it must have the center of body in its orbital plane. As equator being one of the planes with center of earth, satellite's orbital plane must intersect with it atleast once. So, a satellite must be over equator at some time.

The time period of satellite is given by $T=2 \pi \sqrt{\frac{r}{g}}$

Here, $r=R+h$ where $R=$ radiusofearth, $h=$height from surface of earth.

So, $T=2 \pi \sqrt{\frac{R+h}{g}}>2 \pi \sqrt{\frac{R}{g}}$

Standard 11

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