# Relative angular velocity of a satellite

• zorro
In summary, the statement in the book states that the relative velocity of a satellite moving in the direction of Earth's rotation, as observed from Earth, is represented by Vs - Ve. However, since Earth is not an inertial frame of reference due to its rotation, it is unclear which inertial frame is being used to define these velocities. One possibility mentioned is an imaginary non-rotating Earth where one year is equivalent to one day.
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 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 ?

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.

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.

## 1) What is relative angular velocity of a satellite?

The relative angular velocity of a satellite is the rate at which the satellite rotates around a central axis in relation to an observer on the ground. It is measured in degrees per unit of time, such as degrees per second.

## 2) How is relative angular velocity of a satellite calculated?

The relative angular velocity of a satellite can be calculated using the formula: ω = 2π/T, where ω is the angular velocity, and T is the time it takes for one full revolution of the satellite.

## 3) Why is relative angular velocity important in satellite orbiting?

Relative angular velocity is important in satellite orbiting because it determines the speed and direction at which the satellite moves around the Earth. It also affects the stability and accuracy of the satellite's orbit, which is crucial for communication and navigation purposes.

## 4) What factors can affect the relative angular velocity of a satellite?

The relative angular velocity of a satellite can be affected by the satellite's distance from the Earth, its mass, and the gravitational pull of other celestial bodies. Changes in these factors can alter the satellite's orbit and therefore its angular velocity.

## 5) How does the relative angular velocity of a satellite differ from its orbital velocity?

The relative angular velocity of a satellite is the speed at which it rotates around a central axis, while the orbital velocity is the speed at which it moves along its orbit around the Earth. These two velocities are related, but they are not the same. The relative angular velocity is dependent on the orbital velocity, but it also takes into account the distance between the satellite and the observer on the ground.

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