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As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates due to gravity. It can reach a point where its velocity is high enough to keep falling but also keep missing the object it is falling towards. What keeps it from accelerating (because of gravity) and eventually reaching escape velocity? I feel like I'm either looking at things the wrong way or I have the entire thing wrong.

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Acceleceration and currect velocity do not point in the same direction for orbiting bodies. – ACuriousMind Jun 28 '14 at 23:40
In really simple terms, an object in orbit, as it moves away from the object it orbits, it slows down (like a ball thrown in the air, as it gains height, it loses velocity). This is kinetic energy becoming potential energy. As it moves into a lower orbit, it re-gains velocity - which conveniently the velocity moves it back into a higher orbit. - that's kind of a clumsy way of explaining it. – userLTK Jun 4 '15 at 3:18
up vote 4 down vote accepted

It does keep accelerating. It's velocity in the direction of the object being orbited keeps increasing.

But this direction keeps changing. The reason the satellite's total speed doesn't increase, at least in the case of a circular orbit, is that while it's velocity towards the object increases, it's tangential motion moves it forward so that that direction is always perpendicular to the direction of motion. Thus while the satellite is undergoing constant acceleration, that acceleration is always perpendicular to the direction of motion and the speed of the object never changes.

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Thanks! I'll go read up on how velocity vectors work when adding in different directions. – chriskievit Jun 29 '14 at 9:25

You're right - the objects are always accelerating while orbiting, and this acceleration is due to gravitational influence.

However, force/acceleration don't always cause an increase in speed. For example, a force acting opposite to the velocity will slow an object, and a force acting perpendicular to the velocity will merely change its direction. In an object moving in a low-eccentricity orbit, the gravitational force is always nearly perpendicular to the velocity, so there isn't a large speed change.

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If we draw in the acceleration and velocity vectors of an orbiting body, you'll see why it acceleration due to gravity does not cause an orbiting body to fall towards an object.

First, assume the orbit is circular. In any motion of an object, the velocity vector is tangent to the object's path. Because acceleration due to gravity is straight towards the center of the body, the acceleration vector connects the object to the center of the body being orbited. This vector is perpendicular to the tangent vector because the radius of a circle is perpendicular to any tangent to that circle. Thus acceleration is perpendicular to velocity and cannot change the velocity's magnitude.

But, the object is still technically falling towards the center of the attracting body. The reason the object doesn't hit terminal velocity is because perpendicular accelerations don't change magnitude of a moving object.

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The reason it does not reach terminal velocity is because terminal velocity is a feature of falling through a viscous fluid. – dmckee Jun 29 '14 at 2:17

Even simpler than what's been posted: the curvature of the earth keeps slowing the orbiting body. While grabity is pulling it down the tendency to travel forward resists that pull thus keeps the "fall at a balance"

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The curvature of the earth has nothing to do with the object slowing down. The object slows when its velocity has a component opposite the acceleration vector ($\vec{v}\cdot\vec{a} < 0$). – Bill N Apr 2 at 4:01

protected by Qmechanic Apr 2 at 7:25

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