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.