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

66.98 km

Step-by-step 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

`$T= 2 \pi \sqrt{(r^3)/(GM)}$`

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

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

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

`$(T_2)/(T_1)=\sqrt{(r_2^3)/(r_1^3)}$`

`$\left((2)/(1)\right)^2=(r_2^3)/((42.2)^3)$`

`$r_2 = 66.98 \ km$`

Therefore, the radius is 66.98 km.