Dropping and launching space shuttles

[WarnK]

Take two identical of those nice NASA space shuttles and at the same time as you launch one you drop the other from its orbit around earth. What happens first? Do the one going up reach orbit before the one falling hits the ground?

There's a nice little thread about the shuttles acceleration here:
https://www.physicsforums.com/showthread.php?t=224305

But I have no idea. Any ideas are welcome, thanks!

 

[cjameshuff]

Take two identical of those nice NASA space shuttles and at the same time as you launch one you drop the other from its orbit around earth. What happens first? Do the one going up reach orbit before the one falling hits the ground?

There's a nice little thread about the shuttles acceleration here:
https://www.physicsforums.com/showthread.php?t=224305

But I have no idea. Any ideas are welcome, thanks!

The two situations are not particularly comparable. As it starts its way into orbit, the Shuttle is accelerating at several gravities and gaining velocity more than altitude. On the way back from orbit, the Shuttle is using atmospheric braking to shed most of that velocity, after using a smaller maneuvering thruster burn to change its orbit to dip into the atmosphere, and then gliding to a runway. A Shuttle dropped from a relative halt at orbital altitude would hit ground sooner, but this doesn't resemble anything the Shuttle ever actually does. The specifics of how long it'd take would be non-trivial to calculate and would also depend on how the Shuttle was oriented during reentry and flown once in the atmosphere, and would also not hold much meaning.

 

[NatSusan]

It's a very interesting question! According to the thread you linked, the acceleration of the space shuttle is around 3g (3 times the acceleration due to gravity). So, if we assume that the shuttle is dropped from a low orbit around Earth, it would experience an acceleration of approximately 3g towards the ground.

On the other hand, the shuttle that is launched would experience an acceleration of around 1g (due to Earth's gravity) and also an additional acceleration due to the thrust of its engines. However, this acceleration would be much smaller compared to the 3g acceleration of the falling shuttle.

Therefore, it is likely that the falling shuttle would reach the ground first, since it is experiencing a greater acceleration towards the ground. However, this also depends on the initial altitude and speed of the shuttle before it is dropped. If the shuttle is dropped from a higher orbit, it may take longer to reach the ground compared to the shuttle that is launched.

In any case, both shuttles would eventually reach their respective destinations (ground and orbit) at different times. It's a fascinating thought experiment and would be interesting to see in action (although I hope it never actually happens!).