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)

Question

Responses

v=Gmp/(42,164 km)−−−−−−−−√

v=Gmp/(48,115 km)−−−−−−−−√

v=Gmp/(7,324 km)−−−−−−−√

v=Gmp/(15,522 km)−−−−−−−−√

Answer 1

To find the velocity of a satellite in a geostationary orbit, you can use the formula for circular orbital velocity:

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

where:

• \( v \) is the orbital velocity of the satellite,
• \( G \) is the universal gravitational constant,
• \( m_p \) is the mass of the planet,
• \( r \) is the distance from the center of the planet to the satellite.

A geostationary orbit is one where the satellite orbits the planet at the same rotational period as the planet (24 hours), and for Earth, this orbit occurs at approximately 42,164 km from the center of the Earth.

Therefore, the correct equation for the velocity of a satellite in a geostationary orbit around the Earth would be:

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

Thus, the correct response is:

v = Gmp/(42,164 km)−−−−−−−−√