Question

A geosynchronous Earth satellite is one that has an orbital period of precisely 1 day and has a radius of 42.2 km of its orbit about the Earth. For certain application, it is desirable to have a satellite that orbits the Earth with a period of precisely 2days. What should be the radius of such a (every-two-days) satellite

Answer 1

Answer:

66.98 km

Explanation:

Given :

Initial time period, $T_1$ = 1 day

Radius of initial orbit, $r_1$ = 42.2 km

Final Time period, $T_2$ = 2 days

We know that,

The time period of satellite is

$T= 2 \pi \sqrt{\frac{r^3}{GM}}$

So, for $T_2=2\pi \sqrt{\frac{r_2^3}{GM}}$    ...........(i)

For $T_1=2\pi \sqrt{\frac{r_1^3}{GM}}$  ...................(ii)

Therefore, dividing equation (i) by (ii), we get

$\frac{T_2}{T_1}=\sqrt{\frac{r_2^3}{r_1^3}}$

$\left(\frac{2}{1}\right)^2=\frac{r_2^3}{(42.2)^3}$

$r_2 = 66.98 \ km$

Therefore, the radius is 66.98 km.