Question

A satellite is revolving round the earth in circular orbit

• A. if mass of earth is made four times, keeping other factors constant, orbital speed of satellite will become two times
• B. corresponding to change in part $\left(a\right)$, times period of satellite will remain half
• C. when value of $G$ is made two times orbital speed increases and time period decreases
• D. $G$ has no effect on orbital speed and time period

Answer 1

Answer: (A), (B), (C)

The correct options are
A if mass of earth is made four times, keeping other factors constant, orbital speed of satellite will become two times
B corresponding to change in part $\left(a\right)$, times period of satellite will remain half
C when value of $G$ is made two times orbital speed increases and time period decreases

Let $m$ be the mass of the satellite and $M$ be the mass of the planet it is revolving around.

Therefore, we have:

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}\Rightarrow v=\sqrt{\frac{GM}{r}}\Rightarrow T=\frac{2\pi r}{v}=2\pi \sqrt{\frac{r^3}{GM}}$

Therefore, if $M$ is quadrupled then velocity is doubled and time period is halved. Similarly, if G is increased then v increases and T decreases.

Hence, options A, B and C are correct.