Question 280: Gravitation

Question

The total energy of a circularly orbiting satellite is

Accepted Answer

First, recall the NCERT results for a satellite of mass $m$ orbiting a planet of mass $M$ at radius $r$:
Gravitational potential energy:
$$   U = -\frac{GMm}{r}   $$
Kinetic energy:
$$   K = \frac{GMm}{2r}   $$
The total energy $E$ is the sum of kinetic and potential energy:
$$ E = K + U $$
Substitute the values:
$$ E = \frac{GMm}{2r} + \left(-\frac{GMm}{r}\right) $$
$$ E = \frac{GMm}{2r} - \frac{GMm}{r} $$
$$ E = -\frac{GMm}{2r} $$
Now compare $E$ with $K$ and $U$:
$E = -\frac{GMm}{2r} = -K$
$U = -\frac{GMm}{r} = 2E$
Therefore, the total energy is
half the potential energy
of the satellite.
Correct answer:
Option B: half the potential energy of the satellite.

Answer

half the kinetic energy of the satellite.

Answer

half the potential energy of the satellite.

Answer

twice the kinetic energy of the satellite.

Answer

twice the potential energy of the satellite.

Gravitation

The total energy of a circularly orbiting satellite is

Choose the correct answer: