Question

An earth satellite is moved from one stable circular orbit to another larger and stable circular orbit. Which of the following quantities increase for the satellite as a result of this change?

• A. gravitational potential energy
• B. angular velocity
• C. linear orbital velocity
• D. centripetal acceleration

Answer 1

The correct option is A gravitational potential energy

Lets see the formulae for each quantity given there,
Gravitational potential energy $=\frac{-GMm}{r}$
angular velocity $={\left(\frac{GM}{r^3}\right)}^{0.5}$
linear orbital velocity $={\left(\frac{GM}{r}\right)}^{0.5}$
centripetal acceleration $=\frac{GM}{r^2}$
We can observe that, the quantities in the options B,C,D are all indirectly proportional to $r$
i.e. $\omega ,v,a\alpha \frac{1}{r^n}$ where $n$ is distinct postive interger in each quantity.
So, with increase in $r$ all these quantities decrease.
Now, (-potential energy) $\alpha \frac{1}{r}$ i.e. negative of potential energy decreases with increase in $r$. Therefore, potential increases with increase in orbital radius.