An earth s satellite is moved from one stable circular orbit to a farther stable circular orbit. Which one of the following quantities increases?
Answer & explanation
Correct answer: option 4
Gravitational potential energy is given as
$\mathrm{U}=-\frac{\mathrm{GMm}}{\mathrm{r}}$
$\mathrm{U}_1=\frac{-\mathrm{GMm}}{\mathrm{r}_1} ; \mathrm{U}_2=\frac{-\mathrm{GMm}}{\mathrm{r}_2} ; \mathrm{r}_2>\mathrm{r}_1$
$\mathrm{U}_1-\mathrm{U}_2=\frac{-\mathrm{GMm}}{\mathrm{r}_1}+\frac{\mathrm{GMm}}{\mathrm{r}_2}$
$=\mathrm{GMm}\left[\frac{\mathrm{r}_2-\mathrm{r}_1}{\mathrm{r}_1 \mathrm{r}_2}\right]$ = positive
$\mathrm{U}_1>\mathrm{U}_2 \text { or } \mathrm{U}_2<\mathrm{U}_1$