The velocity equation, v = 2πr/T, is used to calculate the time for a satellite to circle the earth by solving for T, which represents the period or time it takes for the satellite to complete one full orbit around the earth. This equation relates the satellite's velocity (v) to its distance from the center of the earth (r) and the time it takes to complete one orbit (T).
The radius, or distance from the center of the earth, is a crucial factor in the velocity equation because it determines the satellite's orbital path and therefore its speed. The closer the satellite is to the center of the earth, the faster it will need to travel to maintain its orbit. This is why the radius is included in the equation as a key variable.
The mass of the earth does not have a direct impact on the time it takes for a satellite to circle the earth. As long as the satellite's distance from the center of the earth remains constant, the time it takes to complete one orbit will also remain constant. However, the mass of the earth does affect the force of gravity acting on the satellite, which in turn affects its velocity and therefore its time to complete one orbit.
No, the velocity equation is not the only way to calculate the time for a satellite to circle the earth. There are other equations and methods that can be used, such as Kepler's third law, which relates the period of an orbit to the semi-major axis of the orbit and the mass of the central body.
Atmospheric drag and orbital decay can cause a satellite to slow down and eventually fall out of orbit, which would significantly affect the time it takes for the satellite to circle the earth. These factors must be taken into account when calculating orbital time and may require adjustments to be made over time to maintain the satellite's orbit.