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(48,115 km)−−−−−−−−√
v=Gmp(48,115 km)−−−−−−−−√
v=Gmp(42,164 km)−−−−−−−−√
v=Gmp(42,164 km)−−−−−−−−√
v=Gmp(7,324 km)−−−−−−−√
v=Gmp(7,324 km)−−−−−−−√
v=Gmp(15,522 km)−−−−−−−−√
The equation that could be used to find the velocity of the satellite in a geostationary orbit is:
v = Gmp(42,164 km)^(-0.5)
The equation that could be used to find the velocity of a satellite in a geostationary orbit is:
v = √(Gmp / 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 radius of the orbit from the center of the planet.
In this case, the correct equation would be:
v = Gmp / √(42,164 km)
To find the velocity of a satellite in a geostationary orbit, you can use the equation:
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 distance between the center of the planet and the satellite.
To determine the correct equation from the options given, you need to choose the equation that uses the correct value for the distance from the satellite to the planet's center in a geostationary orbit.
A geostationary orbit is an orbit in which the satellite appears to be stationary relative to a point on the surface of the planet. This occurs when the satellite's orbital period matches the rotation period of the planet. It is achieved when the satellite is placed at a distance from the planet's center that allows it to complete one orbit in the same time it takes for the planet to complete one rotation.
The distance from the satellite to the planet's center in a geostationary orbit is approximately 42,164 kilometers. Therefore, the correct equation to find the velocity of the satellite in a geostationary orbit is:
v = √(G * mp / 42,164 km)
Therefore, the correct option is:
v = Gmp(42,164 km)−−−−−−−−√