Question

Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a geostationary orbit?(1 point)
Responses

v=Gmp(42,164 km)−−−−−−−−√
v=Gmp(42,164 km)−−−−−−−−√

v=Gmp(7,324 km)−−−−−−−√
v=Gmp(7,324 km)−−−−−−−√

v=Gmp(48,115 km)−−−−−−−−√
v=Gmp(48,115 km)−−−−−−−−√

v=Gmp(15,522 km)−−−−−−−−√
v=Gmp(15,522 km)−−−−−−−−√
Skip to navigation

Answer 1

To find the velocity of a satellite in a geostationary orbit, we can use the formula for the centripetal motion of the satellite which is derived from Newton's law of gravitation and the definition of circular motion. The velocity \( v \) of a satellite in a circular orbit can be calculated using the following equation:

\[
v = \sqrt{\frac{G m_p}{r}}
\]

where:
- \( G \) is the gravitational constant,
- \( m_p \) is the mass of the planet,
- \( r \) is the orbital radius (the distance from the center of the planet to the satellite).

For a geostationary orbit, the satellite orbits at a height where its orbital period matches the rotation period of the Earth (approximately 24 hours). The orbital radius for geostationary orbit is approximately 42,164 km from the Earth's center.

Given this, the correct equation among the options you provided to find the velocity of a satellite placed in a geostationary orbit is:

\[
v = \sqrt{\frac{G m_p}{42,164 \text{ km}}}
\]

So the correct response is:

**v=Gmp(42,164 km)−−−−−−−−√**