Why do geostationary satellites all have the same orbital radius?

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Geostationary satellites maintain a fixed position relative to the Earth by orbiting at the same rotational speed as the planet. This requires them to be placed at a specific orbital radius above the equator, ensuring they match the Earth's rotation period of approximately 24 hours. The slight difference in time for the satellite's orbit compared to the Earth's rotation is negligible, allowing for a stable position. All geostationary satellites thus share the same orbital radius to achieve this synchronization. This unique positioning is crucial for communication and weather monitoring purposes.
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Homework Statement



Geostationary satellites appear to remain stationary to an observer on Earth. Such satellites are placed in orbit far above the equator.

Using principles of physics, explain why such satellites all have the same orbital radius.


Homework Equations





The Attempt at a Solution



Is it because the sattilites stay on the same longitutal degree. they stay at the same spot and rotate with the earth.Thats why they seem sationary?

thanks in advance for any help
 
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bobby22 said:

Homework Statement



Geostationary satellites appear to remain stationary to an observer on Earth. Such satellites are placed in orbit far above the equator.

Using principles of physics, explain why such satellites all have the same orbital radius.


Homework Equations





The Attempt at a Solution



Is it because the sattilites stay on the same longitutal degree. they stay at the same spot and rotate with the earth.Thats why they seem sationary?

thanks in advance for any help


How long does it take a point on the equator to make one complete revolution?

How long would it take a satellite in orbit above this point to make one complete revolution?
 
they are about the same. they are only about a minute off, not a huge difference
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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