To find the velocity of a satellite in a geostationary orbit, we can use the formula for orbital velocity derived from Newton's law of gravitation and centripetal force. The velocity \( v \) of a satellite in orbit can be calculated using:
\[ v = \sqrt{\frac{G m_p}{r}} \]
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, \( r \) is the distance from the center of the Earth (or the planet) to the satellite and is typically around 42,164 km (which includes the radius of the Earth plus the altitude of the geostationary orbit).
Given the options, the correct equation for the velocity of the satellite in a geostationary orbit would be:
\[ v = \sqrt{\frac{G m_p}{42,164 \text{ km}}} \]
Thus, the correct response is:
\[ v = G m_p(42,164 \text{ km})^{-\frac{1}{2}} \]
However, it looks like there might be a formatting issue with the responses as they don't correspond correctly to how the orbital velocity should be stated. But from your list, the appropriate term to match is:
v = Gmp(42,164 km)−−−−−−−−√.