Centripetal force equal to gravitational force

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I'm struggling conceptually on why gravitational force must equal centripetal force for an orbiting body. I was wondering if someone could provide an explanation?

Thanks!


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Assuming an object has a constant speed orbiting earth, which is to say that it has a uniform circular motion, the object must have a force that is just large enough to change the angle of the orbiting object. Any force larger than that would provide an acceleration toward the center of the earth. At each instantaneous moment the velocity of the object has to be perpendicular to the gravity. This is centripetal force applied to a uniform circular motion. Of course an orbiting object is not quite uniform circular motion, its pathway is oval in shape. However, you can think of the gravitational force which is variable depending on how far away from the earth at each instantaneous moment. That is why you see speed changes during the motion, and it rather takes an oval shape than perfect circle. I no it is little bit confusing to you. The orbiting object is more complex than the usual circular motion we observe like a swinging a mass in a perfect circle horizontally.
 
I'm struggling conceptually on why gravitational force must equal centripetal force for an orbiting body. I was wondering if someone could provide an explanation?

Thanks!


Posted using SDN Mobile
For an object in circular motion (in this case an orbit), the sum of all the forces equals the centripetal force (net force). The orbiting body experiences only one force and that is the gravitational force. In this case, you have to be careful which equation you use. You cannot use the simplified equation 'mg' because the pre-calculated 'g' term applies only when you're at the surface of the earth. The more appropriate relationship to use is: GMm/r^2 which equals mv^2/r (centripetal acceleration). The 'r' is the total distance between the two objects (the radius of the earth + amplitude).
 
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