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=Gmp(7,000 km)−−−−−−−√
v=1(7,000 km)Gmp−−−−√
v=1(7,000 km)Gmp−−−−√
v=1(200 km)Gmp−−−−√
v=1(200 km)Gmp−−−−√
v=Gmp(200 km)−−−−−−√
v=Gmp(200 km)−−−−−−√
The equation that could be used to find the velocity of the satellite if it is placed in a low Earth orbit is:
v = √(Gmp/200 km)
The equation that could be used to find the velocity of the satellite is:
v = √(G * mp / 7,000 km)
The equation that could be used to find the velocity of the satellite if it is placed in a low Earth orbit is:
v = √(Gmp / (7,000 km))
Explanation:
In this equation, v represents the velocity of the satellite, G is the universal gravitational constant, mp is the mass of the planet, and (7,000 km) is the radius of the low Earth orbit.
To understand why this equation is used, we need to consider the law of gravity. According to Newton's law of universal gravitation, the gravitational force between two objects is given by:
F = (G * m1 * m2) / r^2
Where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
In the case of a satellite in orbit around a planet, the gravitational force provides the centripetal force required to keep the satellite in its orbit. The centripetal force is given by:
F = (m * v^2) / r
Where m is the mass of the satellite, v is its velocity, and r is the radius of the orbit.
Since the gravitational force and the centripetal force are the same in this case, we can equate the equations:
(G * m1 * m2) / r^2 = (m * v^2) / r
Simplifying the equation, we get:
v = √(G * m2 / r)
In the context of a low Earth orbit, the mass of the satellite (m) can be assumed to be negligible compared to the mass of the planet (mp). Therefore, we can replace m with mp in the equation.
Also, in a low Earth orbit, the distance from the center of the planet to the satellite (r) is approximately equal to the radius of the orbit (7,000 km).
Substituting these values into the equation, we get:
v = √(G * mp / (7,000 km))
So, the correct equation to find the velocity of the satellite in a low Earth orbit is:
v = √(Gmp / (7,000 km))