Change in the Orbit of Satellite
Category : JEE Main & Advanced
When the satellite is transferred to a higher orbit \[({{r}_{2}}>{{r}_{1}})\] then variation in different quantities can be shown by the following table
| Quantities | Variation | Relation with r |
| Orbital velocity | Decreases | \[v\propto \frac{1}{\sqrt{r}}\] |
| Time period | Increases | \[T\propto {{r}^{3/2}}\] |
| Linear momentum | Decreases | \[P\propto \frac{1}{\sqrt{r}}\] |
| Angular momentum | Increases | \[L\propto \sqrt{r}\] |
| Kinetic energy | Decreases | \[K\propto \frac{1}{r}\] |
| Potential energy | Increases | \[U\propto -\frac{1}{r}\] |
| Total energy | Increases | \[E\propto -\frac{1}{r}\] |
| Binding energy | Decreases | \[BE\propto \frac{1}{r}\] |
Note :
Work done in changing the orbit \[W={{E}_{2}}-{{E}_{1}}\]
\[W=\left( -\frac{GMm}{2{{r}_{2}}} \right)-\left( -\frac{GMm}{2{{r}_{1}}} \right)\]
\[W=\frac{GMm}{2}\left[ \frac{1}{{{r}_{1}}}-\frac{1}{{{r}_{2}}} \right]\]
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