Question

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

• A. It must be above the equator at some time.
• B. It cannot pass over the poles at any time.
• C. Its height above the surface cannot exceed $36,000km$.
• D. Its period of rotation must be $>2\pi \sqrt{\frac{R}{g}}$.

Answer 1

Answer: (A), (D)

The correct options are
A It must be above the equator at some time.
D Its period of rotation must be $>2\pi \sqrt{\frac{R}{g}}$.

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