Question

Two artificial satellites A and B are at distance rA and rB above the earth surface if the radius of earth is R then the ratio of there speed will be

Answer 1

Answer: $\frac{v_A}{v_B}=\sqrt{\frac{r_B+R}{r_A+R}$

Explanation:

The orbital speed of a satellite at a distance of r is given by:

$v=\sqrt{\frac{2G}{r}$

where, G is the gravitational constant,

$G= 6.67 \times 10^-11 m^3/kgs^2$

It is given that $v_A$ and $v_B$ are the speeds of satellites A and B at $r_A$ and $r_B$ above the Earth's surface respectively.

Thus,

$\frac{v_A}{v_B}=\frac{\sqrt{\frac{2G}{r_A+R}}}{\sqrt{\frac{2G}{r_B+R}}}\\ \Rightarrow \frac{v_A}{v_B}=\sqrt{\frac{r_B+R}{r_A+R}$

Hence, the ratio of there speed will be:

$\frac{v_A}{v_B}=\sqrt{\frac{r_B+R}{r_A+R}$