Practicing Success
An earth s satellite is moved from one stable circular orbit to a farther stable circular orbit. Which one of the following quantities increases? |
Linear orbital speed Gravitation force Centripetal acceleration Gravitational potential |
Gravitational potential |
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 $\mathrm{U}_1>\mathrm{U}_2 \text { or } \mathrm{U}_2<\mathrm{U}_1$ |