Question

For 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 36,000 km
• D. Its period of rotation must be > 2$\pi \sqrt{R/g}$ where R is radius of earth

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$\pi \sqrt{R/g}$ where R is radius of earth

For any body orbiting around the earth, it must have center of earth in its orbiting plane. So, it should cross equator atleast once in its revolution.
The time period for a satellite $=2\pi {\left(\frac{r}{g}\right)}^{0.5}$
Here $r$ is radius of orbit$,g$ is acceleration due to gravity. So $r=R+h,$ where $R$ is radius of earth and $h$ is height above earth's surface.
Therefore, for satellite $T=2\pi {\left(\frac{R+h}{g}\right)}^{0.5}>2\pi {\left(\frac{R}{g}\right)}^{0.5}$.
Both A, D are true.