To find the velocity of a satellite in a geostationary orbit, we can use the following formula derived from the gravitational force and centripetal force concepts:
\[ v = \sqrt{\frac{G m_p}{r}} \]
where:
- \(v\) is the orbital velocity of the satellite,
- \(G\) is the universal gravitational constant,
- \(m_p\) is the mass of the planet (or the central body),
- \(r\) is the distance from the center of the planet to the satellite.
In the case of a geostationary orbit, the satellite orbits at a specific radius (from the center of the planet) where it has the same rotational period as the planet, which is about 24 hours. The radius for a geostationary orbit around Earth is approximately 42,164 km from the Earth's center.
From the options given, the correct formula to find 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 = Gmp(42,164 km)−−−−−−−−√
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