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Geostationary Satellite

Physics Asked by user118752 on January 3, 2021

I am unable to understand one particular thing about geostationary satellite. Let us assume that I am on earth at a particular place and remain there (moving with the place during rotation) such that the satellite is just above me all the time.

Now my orbital velocity will be

$$ v_o = sqrt{GM_e/R_e} $$

Talking about the geostationary satellite at a height $h$ we can say that the orbital velocity is

$$ v_{geo} = sqrt{GM_e/(R_e+h) } $$

This showa that the velocity of the satellite has decreased and simultaneously its radius has increased.

But it must have my angular velocity to have the same time period.

$omega =v/r$

For the satellite $v$ has decreased and $r $ has increased. How can the angular velocity of satellite be equal to that of mine.

One Answer

You wrote $v_o = sqrt{G M_e / R_e}$ for your orbital velocity. But you're not in orbit! Rather, you're going in a circle with the angular frequency of the Earth, $Omega approx frac{2 pi}{1;text{day}}$. This makes it possible to set your angular frequency equal to that of the satellite.

Correct answer by Scott Lawrence on January 3, 2021

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