Relative angular velocity of a satellite

[zorro]

This is a statement in my book - "The relative velocity of a satellite moving in the direction of Earth's rotation (for an observer on earth) is given as V_s - V_e."

We always define relative velocity of a particle say P in a frame of reference S₁ accelerating w.r.t to an inertial frame of reference say S as

V_P,S1 = V_P,S - V_S1,S

But in this case the Earth itself has some angular velocity and it is not an inertial frame of reference. My question is, in the expression V_s - V_e, what is the inertial frame w.r.t to which we define these velocities? Is it Earth again or some other imaginary inertial frame ?

 

[rcgldr]

My question is, in the expression V_s - V_e, what is the inertial frame w.r.t to which we define these velocities? Is it Earth again or some other imaginary inertial frame?

Inertial frame would be an imaginary non-rotating Earth (1 year = 1 day).

 

[zorro]

1 year = 1 day? What does that mean?

 

[Xishem]

If Earth did not rotate, one day would be the same as one year. One day is generally accepted as the time it takes for the Earth to perform a full rotation. If the Earth did not rotate, one full revolution around the sun would simulate a normal 24-hour day as far as the sun's motion relative to Earth, but would occur over the period of a year. Thus, 1 year = 1 day. I believe that's what he was referring to.

 

[PJC01]

I would first clarify that the expression given in your book is not entirely accurate. The relative velocity of a satellite moving in the direction of Earth's rotation (for an observer on Earth) is not simply given as Vs - Ve. This expression only holds true if the satellite is in a circular orbit directly above the Earth's equator.

In reality, the relative angular velocity of a satellite is a more complex concept that takes into account the Earth's rotation and the satellite's orbital motion around the Earth. It is defined as the angular velocity of the satellite relative to an inertial frame of reference, which is typically taken to be the center of the Earth.

In the expression Vs - Ve, Vs represents the angular velocity of the satellite around the Earth, while Ve represents the angular velocity of the Earth's rotation. The inertial frame of reference in this case is the center of the Earth.

It is important to note that this expression only applies to a specific scenario where the satellite's orbit is directly above the equator. In other cases, the relative angular velocity would be different and would require a more complex calculation.

In conclusion, the relative angular velocity of a satellite is a concept that takes into account the Earth's rotation and the satellite's orbital motion. It is defined relative to an inertial frame of reference, which is typically the center of the Earth. The expression Vs - Ve only applies to a specific scenario and should not be generalized.