Relative angular velocity of a satellite

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The discussion centers on the concept of relative angular velocity of a satellite in relation to Earth's rotation. The expression "Vs - Ve" is questioned regarding the inertial frame of reference used for defining these velocities, with the Earth being a non-inertial frame due to its rotation. It is suggested that an imaginary non-rotating Earth serves as the inertial frame for this calculation. The phrase "1 year = 1 day" is explained as a hypothetical scenario where, without Earth's rotation, one complete revolution around the sun would equate to a single day in terms of solar motion. This highlights the complexities of defining relative velocity in a rotating frame versus an inertial frame.
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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 Vs - Ve."

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

VP,S1 = VP,S - VS1,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 Vs - Ve, what is the inertial frame w.r.t to which we define these velocities? Is it Earth again or some other imaginary inertial frame ?
 
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Abdul Quadeer said:
My question is, in the expression Vs - Ve, 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).
 
1 year = 1 day? What does that mean?
 
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.
 
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