To find the orbital velocity \( v \) of a satellite in geostationary orbit, we use the formula derived from Newton's law of gravitation and the centripetal force required for circular motion:
\[ v = \sqrt{\frac{G m_p}{r}} \]
Here:
- \( G \) 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.
In the case of a geostationary orbit, the satellite's orbital radius \( r \) must be the distance from the center of the planet to the satellite, which is typically around 42,164 km (this is the radius from the center of the Earth, including the Earth's radius which is approximately 6,371 km, plus the altitude of the geostationary orbit approximately 35,786 km).
Given the options provided, the correct equation for the velocity of a satellite in a geostationary orbit is:
\[ v = \sqrt{\frac{G m_p}{42,164 \text{ km}}} \]
So, the first option is the correct answer.
Correct Response: v=Gmp(42,164 km)−−−−−−−−√
5 answers