Will a satellite stay in orbit forever without thrust?

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jsbhk
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Forgive my rusty English. But I really need urgent and Professional help, teachers and professors, please:

A satellite has been put on Earth's orbit at a high speed, (forget atmosphere friction, forget moon attraction, forget sun gravity), theoretically, without any further thrust, will it stay on Earth's orbit forever?

Many people in my country told me it will, but I doubt it, because Earth's gravity pull is continuous (in acceleration = a), and the satellite needs force to balance out the gravitational pull (F=m a) as centripedal/centrifugal force, then the gravity's <a> has been canceled in the equation F=m<a>, since mass is constant, then that means WE NEED <CONSTANT> FORCE to balance out the gravity pull, that means the satellite needs CONSTANT Force to stay on orbit. Am I correct? Thanks.
 

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Moon is under the Sun's gravitational pull, some scientists consider it not the satellite of Earth because its barycenter is not in the center of Earth. Some even called Earth-Moon a twin star. We don't want to go into it. Just wanted to know will artificial satellite centrifugal force need constant force to stay on orbit?
 
in other words, if an artificial satellite is circling the Earth, without any air friction, will it revolve forever without any thrust? Thanks!
 
jsbhk said:
Moon is under the Sun's gravitational pull, some scientists consider it not the satellite of Earth because its barycenter is not in the center of Earth. Some even called Earth-Moon a twin star. We don't want to go into it. Just wanted to know will artificial satellite centrifugal force need constant force to stay on orbit?
None of that is correct, but even if it were, how would that change the scenario? The Earth and moon are orbiting the sun and have been for billions of years...

What does that tell you about the stability of an orbit?

Anyway, your logic in the OP is odd. The Earth's gravity provides a constant F and the result is a constant acceleration of a mass. f=ma. Where's the inequality?
 
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