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Can it be shown that angular velocity of a planet = (orbital velocity/h+Radius): $$\frac{v_{c,1}}{h + R_{⊕}} = \omega_e $$

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    $\begingroup$ I think you might want to elaborate your problem slightly more and also tell us a bit more about your own attempts on how to solve the problem. Even when I might guess, h and R_Earth are not introduced... and h is... the observer height above the reference geoid? $\endgroup$ Jul 9 at 10:34
  • $\begingroup$ Also, if the text you're working from defines $v_{c,1}$, define that as well. From what's included in the question, it looks like the specific version of the equation provided only works for circular orbits over Earth. $\endgroup$
    – notovny
    Jul 9 at 11:00
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For a very restricted set of conditions, yes.

If $v_{c,1}$ is the First Cosmic Velocity, also known as the Circular Orbit Velocity, then what you have written is the definition of the angular velocity of an object in a circular orbit of altitude $h$ over Earth.

In general, no.

For objects in elliptical orbits, there will only be two points on their orbits where they will be moving at exactly the circular orbit speed for their distances from the whatever it is they are orbiting, and at both such points, the angular velocity will be lower than the value obtained by dividing the circular orbit speed by the radial distance.

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