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I know that centripetal force for planetary motion is the same as the force of gravity between that satellite and planet. For example (I know these numbers may be completely unrealistic but just for the sake of easy calculation...) if the mass of the Earth is 1x10^30 kg and the mass of a satellite is 1000kg and the mean distance between their centers is 3000m, then the force of gravity between the two will be about 7.41x10^15 N according to Newton's law of universal gravitation.

This is also the centripetal force for the satellite in relative circular motion. So 7.41x10^15 N = m(of satellite)v^2/r. Now, if the radius of the orbit of the satellite increases, the force of gravity decreases, the radius in mv^2/r increases and so therefore the velocity decreases.

But I am wondering how you can explain why my reasoning is wrong if I look at it from this viewpoint. I said that if the radius of orbit increases in mv^2/r, then could we not keep the gravitational force the same by also increasing the velocity? Just like all points on the hand of a clock experience different velocities(higher as you go farther out from the center) but the same centripetal force. But my problem is that I know that the force of gravity MUST decrease with an increasing distance, so is the force of gravity something of a constant? You must solve for it first and then solve for the centripetal acceleration (velocity and radius)?

Thank you!

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# Is the Force of Gravity act as a constant when solving for centripetal acceleration?

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