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  • A satellite orbits around the earth in a circular orbit with a speed and orbital radius <img alt="\ma

A satellite orbits around the earth in a circular orbit with a speed \mathrm{v} and orbital radius \mathrm{r}. If it loses some energy, then \mathrm{\mathrm{v} \: and \: \mathrm{r}} changes as
 

Option: 1

\mathrm{\mathrm{v} \: \: decreases\: \: and \: \: \mathrm{r} \: \: increases}

 


Option: 2

\mathrm{both\: \: \mathrm{v} \: \: and \: \: \mathrm{r} \: \: decrease}
 


Option: 3

\mathrm{r\: \: increases\: \: and \: \: r \: \: decreases}
 


Option: 4

\mathrm{ both\: \: \mathrm{v} \: \: and\: \: \mathrm{r} \: \: increase}


Answers (1)

best_answer

Total energy of a satellite orbiting in radius \mathrm{r} is

\mathrm{ \mathrm{E}=\mathrm{KE}+\text { Pot } \mathrm{E}=\frac{1}{2} \mathrm{mv}^2-\frac{\mathrm{GMm}}{\mathrm{r}} }    

Where \mathrm{ \frac{\mathrm{GMm}}{\mathrm{r}^2}=\frac{\mathrm{mv}^2}{\mathrm{r}} }

\mathrm{ \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}} }

\mathrm{ =\frac{1}{2} \mathrm{~m} \frac{\mathrm{GM}}{\mathrm{r}}-\frac{\mathrm{GMm}}{\mathrm{r}}=-\frac{\mathrm{GMm}}{2 \mathrm{r}} }

If it loses some energy \mathrm{ r } must decrease

\mathrm{ \therefore \mathrm{v}=\sqrt{\frac{\mathrm{GM}}{\mathrm{r}}}, \mathrm{v} \text { increases } }

Hence option 3 is correct.
 

Posted by

Rishabh

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