To determine the velocity of a satellite in a geostationary orbit, we use the formula for orbital velocity \( v \):
\[ v = \sqrt{\frac{G m_p}{r}} \]
where:
- \( G \) 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.
For a geostationary orbit, the satellite orbits at a specific altitude above the planet's surface, which for Earth is approximately 42,164 km from the center of the Earth. Therefore, the correct equation to find the orbital velocity of a satellite in a geostationary orbit would be:
\[ v = \sqrt{\frac{G m_p}{42,164 \text{ km}}} \]
Thus, the appropriate response from the given options is:
v = Gmp(42,164 km)−−−−−−−−√