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 low Earth orbit?(1 point)
Responses
v=1(7,000 km)Gmp−−−−√
v=1(200 km)Gmp−−−−√
v=Gmp(7,000 km)−−−−−−−√
v=Gmp(200 km)−−−−−−√
The correct equation to find the velocity of the satellite in a low Earth orbit is:
v = (G * mp)^(1/2) / (7,000 km)^(1/2)
The correct equation that could be used to find the velocity of the satellite if it is placed in a low Earth orbit is:
v = (G * mp * (7,000 km))^0.5
To find the velocity of a satellite in a low Earth orbit, we need to use the formula that relates orbital velocity with the mass of the planet and the distance from the center of the planet to the satellite.
The correct equation to find the velocity of the satellite is:
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
- r is the distance between the center of the planet and the satellite
Now, looking at the options given:
- v = 1(7,000 km)Gmp√ is not the correct equation as it is missing the division sign (/) between G and mp.
- v = 1(200 km)Gmp√ is also not the correct equation as it is missing the division sign (/) between G and mp.
- v = Gmp(7,000 km)√ is not the correct equation as it is missing the division sign (/) between G and mp.
- v = Gmp(200 km)√ is the correct equation as it has the proper division sign (/) and the square root (√) is correctly applied to the whole term (G * mp * 200 km).
Therefore, the correct equation to find the velocity of the satellite in a low Earth orbit is:
v = Gmp(200 km)√