Why Doesn't a Satellite's Radial Velocity Increase as It Revolves?

[john fairbanks]

Why doesn't a satellite's radial velocity (falling toward the Earth's center of gravity) increase as it it revolving --- I understand why its tangential speed stays the same but what is stopping the satellite from accelerating in its fall -- there is no air resistance up there. In other words, why does it fall at a constant speed and not accelerate by the force of gravity. thanks

 

[OlderDan]

Why doesn't a satellite's radial velocity (falling toward the Earth's center of gravity) increase as it it revolving --- I understand why its tangential speed stays the same but what is stopping the satellite from accelerating in its fall -- there is no air resistance up there. In other words, why does it fall at a constant speed and not accelerate by the force of gravity. thanks

It is accelerating toward the center of its motion all the time. It is called centripetal acceleration. It is the acceleration toward the center of its orbit that casues the direction of its veloctiy to constantly be changing. Some would say it is actually falling all the time, but the path of its fall never intersects the Earth and in fact keeps it at a constant distance from the Earth as it falls past the edge of the earth.

 

[andrevdh]

The attractive force is perpendicular to its motion. This means that only the direction of its motion is changed (to change its speed there need to be a force component in the direction of its motion, which is not the case if the sattelite is in a circular orbit). For objects in other orbits we do find that the radial velocity component changes.

 

[john fairbanks]

but isn't it wrong to say the object (satellite) is falling at a constant rate, because the rate would increase the longer it falls... the speed increases in a free fall -- especially with no air resistance -- so all this language about an object free falling around the Earth is wrong I think.

 

[OlderDan]

but isn't it wrong to say the object (satellite) is falling at a constant rate, because the rate would increase the longer it falls... the speed increases in a free fall -- especially with no air resistance -- so all this language about an object free falling around the Earth is wrong I think.

I don't particularly like the notion of saying a satellite in orbit is "falling", but suppose you could fire a cannon ball over a parabolic shaped mountain on a path that keeps the ball a few cm off the ground the whole time. Is the ball "falling" when it comes down the other side of the mountain? It's just a matter of how you want to describe the motion. The impoortant thing is to recognize that the ball and the satellite are both accelerating the whole time.