Does Earth's Gravity Do Work on Satellites?

In summary, The gravity of Earth does not do any work on satellites in perfect circular orbit as the force vector and displacement vector are always perpendicular, leading to a 0 value for work done. This is due to the fact that in a perfect circular orbit, the potential and kinetic energy do not change, resulting in no work being required.
  • #1
putongren
125
1
Does the gravity of Earth do any work on satellites orbiting the planet, assuming perfect circular orbit?

General Definition of work: W=(line integral) F * ds , F=force vector, ds=infinitesimal displacement vector, *=dot product.

We know that in circular motion, the velocity vector is always perpendicular to the centripetal acceleration (I think we assume that centripetal acceleration is equated to gravitational acceleration), so 0 = F * v for all positions. so that means that 0 = F * ds/dt. If F * ds =0 for all positions, then W = 0. Does 0 = F * ds/dt imply F * ds = 0?

Thank you.
 
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  • #3
putongren said:
Does the gravity of Earth do any work on satellites orbiting the planet, assuming perfect circular orbit?
Perfect circular orbit means: potential energy doesn't change and kinetic energy doesn't change so there is no work to do.
 

Related to Does Earth's Gravity Do Work on Satellites?

1. How does Earth's gravity affect satellites?

Earth's gravity affects satellites by keeping them in orbit around the planet. The force of gravity between the Earth and the satellite is what allows the satellite to maintain its orbit and prevents it from drifting off into space.

2. Does Earth's gravity do work on satellites?

Yes, Earth's gravity does do work on satellites. The force of gravity is a type of work, known as potential work, which is the energy required to move an object from one position to another. In the case of satellites, Earth's gravity is constantly doing work on them by maintaining their orbital motion.

3. What is the relationship between Earth's gravity and the orbital speed of satellites?

The relationship between Earth's gravity and the orbital speed of satellites is known as the orbital velocity. This velocity is determined by the mass of the Earth and the distance of the satellite from the Earth's surface. The stronger the Earth's gravity, the faster the orbital speed of the satellite will be.

4. Can Earth's gravity affect the trajectory of satellites?

Yes, Earth's gravity can affect the trajectory of satellites. This is because the gravitational force of the Earth is constantly pulling on the satellite and changing its direction. This is why satellites need to be constantly monitored and adjusted to maintain their desired orbit.

5. Does Earth's gravity affect all satellites equally?

No, Earth's gravity does not affect all satellites equally. The strength of the gravitational force depends on the mass and distance of the satellite from the Earth. Therefore, larger and closer satellites will experience a stronger gravitational force compared to smaller and farther ones.

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