Space Elevator Vehicle: Acceleration After Cable Release

[nuclear tan]

Say you have a space elevator 47000 km* long (well past the point where centripetal acceleration cancels out gravity)

There is a vehicle traveling up the cable with a pretty high velocity, and instead of braking it just shoots off the top. (assume the counter weight allows this)

At the instant the vehicle leaves the cable, itwould be traveling at the magnitude of the normal and tangential velocity... I think.

Would it slow as it escapes Earth's gravity, or has that already been taking care of?


Now I apologize if this is the wrong forum.

This isn't homework, it's just something I have been thinking about.


*fyi I read about this enormous length in a NASA pdf...

 

[CFDFEAGURU]

Space elevators are very interesting. Could you post a link to the NASA pdf?

Thanks
Matt

 

[mgb_phys]

Would it slow as it escapes Earth's gravity, or has that already been taking care of?

Yes it will continue to slow down.
Every metre higher it gets it gains potential energy - it must pay for this with kinetic energy by reducing it's speed.
As it gets further away the extra energy in going each metre is less (because Earth's gravity is progressively weaker) so the amount of slowing down is less with each metre.

It never leaves Earth's gravity - there is no limit to gravity (it goes on forever) but eventually it reaches a distance where the gravity is so weak that there is very little difference in potential energy at each extra metre and so the rate of deceleration goes to almost zero.

Escape velocity is the speed you would need to start at so that when you got an infinite distance from Earth you would still have some kinetic energy (and hence speed) left.

 

[nuclear tan]

Yes it will continue to slow down.
Every metre higher it gets it gains potential energy - it must pay for this with kinetic energy by reducing it's speed.
As it gets further away the extra energy in going each metre is less (because Earth's gravity is progressively weaker) so the amount of slowing down is less with each metre.

It never leaves Earth's gravity - there is no limit to gravity (it goes on forever) but eventually it reaches a distance where the gravity is so weak that there is very little difference in potential energy at each extra metre and so the rate of deceleration goes to almost zero.

Escape velocity is the speed you would need to start at so that when you got an infinite distance from Earth you would still have some kinetic energy (and hence speed) left.

Ha! Thank you.