Energy Required for Satellite Orbit Transfer – Rankers Physics

Planet and Satellite: Practice Problem & Solution

A satellite of mass \(m\) is in a circular orbit of radius \(2R\) about the earth. How much energy is required to transfer it to a circular orbit of radius \(4R\) :  (\(R =\) Radius of earth)
\(\frac{mgR}{8}\)
\(\frac{mgR}{4}\)
\(\frac{mgR}{2}\)
None of these

Solution Explained:

To solve this problem, we apply the core principles of Planet and Satellite. Understanding the underlying formula is key to arriving at the correct answer below:

The total energy of a satellite is \(E = -\frac{GMm}{2r}\). The required energy is \(\Delta E = E_f - E_i = -\frac{GMm}{8R} - \left(-\frac{GMm}{4R}\right) = \frac{GMm}{8R}\). Since \(g = \frac{GM}{R^2}\), we get \(\Delta E = \frac{mgR}{8}\).

Leave a Reply

Your email address will not be published. Required fields are marked *

Similar Practice Questions

Explore conceptually related problems to test your knowledge.

1. At certain height \(h\) from surface of earth the value of \(g\) become \(6.25%\) of its value at earth surface. The ratio of \(\frac{h}{R}\) is. (\(R\) is radius of earth)
2. Two satellites A and B go around a planet P in circular orbits having radius 4R and R respectively. If the speed of satellite A is 3 v, then the speed of satellite B will be :
3. Assertion (A): Gravitational field of a uniform spherical shell outside it is same as that of particle of same mass placed at its centre of mass. Reason (R): For the calculation of gravitational force between any two uniform spherical shells, they can always be replaced by particles of same mass placed at respective centres.  
4. The height at which the weight of a body becomes $1/16^{\text{th}}$, its weight on the surface of earth (radius R), is: (2012 Pre)
5. A satellite of mass $m$ is orbiting the earth (of radius $R$) at a height $h$ from its surface. The total energy of the satellite in terms of $g_0$, the value of acceleration due to gravity at the earth's surface, is: (2016 - II)