Orbits of Satellites Quick Check
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Question
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)
Responses
v=Gmp(7,324 km)−−−−−−−√v=Gmp(7,324 km)−−−−−−−√
v=Gmp(15,522 km)−−−−−−−−√v=Gmp(15,522 km)−−−−−−−−√
v=Gmp(42,164 km)−−−−−−−−√v=Gmp(42,164 km)−−−−−−−−√
v=Gmp(48,115 km)−−−−−−−−√
The correct equation to find the velocity of the satellite in a geostationary orbit is v=Gmp(42,164 km)−−−−−−−−√.
The equation that could be used to find the velocity of the satellite if it is placed in a geostationary orbit is:
v = Gmp(42,164 km)^(1/2)
To find the equation that could be used to find the velocity of a satellite in a geostationary orbit, we need to understand what a geostationary orbit is. A geostationary orbit is a circular orbit around a planet where the satellite's orbital period matches the planet's rotation period, causing the satellite to remain fixed in the same position above the planet's surface.
In a circular orbit, the velocity of the satellite is determined by the gravitational force between the satellite and the planet. The equation for the velocity of a satellite in a circular orbit is given by:
v = √(G * mp / r)
where v is the velocity of the satellite, G is the universal gravitational constant, mp is the mass of the planet, and r is the orbital radius of the satellite.
Now, we need to choose the equation that corresponds to the correct orbital radius for a geostationary orbit. A geostationary orbit is typically located at an altitude of 35,786 kilometers above the Earth's surface.
Let's check which equation matches the correct orbital radius:
1. v = Gmp(7,324 km)^1/2
2. v = Gmp(15,522 km)^1/2
3. v = Gmp(42,164 km)^1/2
4. v = Gmp(48,115 km)^1/2
Out of these options, the equation that matches the correct orbital radius of a geostationary orbit is:
v = Gmp(42,164 km)^1/2
Therefore, the correct answer is:
v = Gmp(42,164 km)^1/2