Question
Download Solution PDFThe satellite of mass ‘m’ is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
- For a satellite of mass ‘m’ moving in a circular orbit of radius ‘r’,
- The Kinetic energy is given by,
\(\Rightarrow K.E = \frac{{GMm}}{{2r}}\)
- Potential energy is given by,
\(\Rightarrow P.E = - \frac{{GMm}}{r}\)
- Orbital speed is given by,
\(\Rightarrow v = \sqrt {\frac{{GM}}{r}} \)
CALCULATION:
Given: Satellite mass = m, Orbital speed = v;
- From the above relations, the total energy is given by,
\(\Rightarrow E = \frac{{GMm}}{{2r}} + \left( { - \frac{{GMm}}{r}} \right) \)
\( \Rightarrow E = - \frac{{GMm}}{{2r}}\)
- In terms of orbital speed,
\(\Rightarrow E = \; - \frac{1}{2}m\left( {\frac{{GM}}{r}} \right) = - \frac{1}{2}m{v^2} \)
Last updated on May 26, 2025
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