Solving time for a satellite to circle the earth using velocity equation

• garcia1
In summary, the velocity equation, v = 2πr/T, is used to calculate the time for a satellite to circle the earth by solving for T. The radius, or distance from the center of the earth, is a crucial factor in this equation as it determines the satellite's orbital path and speed. The mass of the earth does not directly affect the time for a satellite to circle the earth, but it does affect the force of gravity and therefore the satellite's velocity. The velocity equation is not the only method for calculating orbital time, as other equations like Kepler's third law can also be used. Factors like atmospheric drag and orbital decay can significantly impact the time it takes for a satellite to circle the earth and must be accounted for
garcia1

Homework Statement

The average speed of an orbiting space shuttle
is 19800 mi/h. The shuttle is orbiting about
233 mi above the Earth’s surface. Assume the
How long does it take to circle the earth?

Homework Equations

I think it may use V= x/t.

The Attempt at a Solution

t = 4199 mi / 19800 mi/h = .2120 h.

Orbiting the Earth means it's traveling in a circle with radius 3963+233 mi. So the x in your equation is the circumference of that circle. What would that be?

1. How is the velocity equation used to calculate the time for a satellite to circle the earth?

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).

2. What is the significance of the radius in the velocity equation for calculating the time for a satellite to circle the earth?

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.

3. How does the mass of the earth affect the time it takes for a satellite to circle the earth?

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.

4. Is the velocity equation the only way to calculate the time for a satellite to circle the earth?

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.

5. How do factors like atmospheric drag and orbital decay affect the time for a satellite to circle the earth?

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.

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