Final answer:
The velocity of a satellite in low Earth orbit can be calculated using the formula v = sqrt(GMp/r), where G is the gravitational constant, Mp is the mass of the planet, and r is the orbital radius of the satellite.
Step-by-step explanation:
To find the velocity of a satellite in low Earth orbit, we can apply the principles of centripetal force and Newton's law of gravitation. The gravitational force acting on the satellite provides the necessary centripetal force to keep it in a circular orbit. For a satellite of mass m orbiting at radius r from the center of a planet with mass Mp, the gravitational force (F) is given by Newton's equation:
F = GmMp/r2
For a satellite in a stable orbit, the gravitational force is equal to the centripetal force required to maintain its circular motion:
F = mv2/r
Equating these two forces gives us the equation to solve for the orbital velocity (v) of the satellite:
v = sqrt(GMp/r)
In the equation for orbital velocity, the mass of the satellite cancels out, which implies that the velocity depends only on the mass of the planet and the radius of the orbit.