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Changing velocity rapidly in space is a bit of a problem requiring either the expense of propellant, or aiming past a planet for a gravitational slingshot.

If you could fire out a strong tether and anchor to a large mass such as an asteroid temporarily, would it be an effective and efficient way to change course rapidly?

My analogy is with the Batmobile grappling hook as illustrated by this screenshot hosted on chickslovethecar.com:

enter image description here

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If you can make and break this connection safely and reliably, you would be able to exchange momentum very efficiently.

This is effectively what a skyhook does with the addition of making the tethered connection in reverse.

Challenges:

  • You probably won't be able to make and break this connection safely and reliably, so you will need a back-up plan!
  • These are probably large distances, so the mass of the tethering system will probably be large.
  • Because the mass will be large, you will probably be exchanging momentum in the wrong direction to make the connection. So you might make your situation worse if you try and fail to make the connection.
  • Tether dynamics are crazy complicated. They will probably bite you.
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  • $\begingroup$ And then there is this article... motherboard.vice.com/read/… $\endgroup$ – Erik Jan 27 '15 at 15:46
  • $\begingroup$ Id make an analogy of trying this with the batmobile and a brick wall. If you dont cut it off before you hit the brick wall you explode. $\endgroup$ – Magic Octopus Urn Aug 18 '18 at 5:15
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Not only can it be done, it has been done. But how, might you ask. Well, it hasn't been done using a rope, but it has been done using gravity, and it's done all the time. That's the basic premise of a Gravity Slingshot, come close enough to a big object to have it help you change your course.

In the end, this will only change your velocity with respect to the outside world. Your speed relative to the Asteroid will be more or less the same after. But you will change speed with respect to the outside world.

As for the use of the tether itself, it would have to be very strong, and have a very strong grip. You'd have to get it placed very close to the target, and let go at the precise moment, or else it would spell disaster. But it could be done, in theory, and would save some fuel, if you can make everything line up perfectly. But any object small enough to allow for this to happen would be difficult to get with the required precision to intercept it, most likely losing most of the gain you would get.

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Momentum exchange tethers are similar/related mechanisms that have been studied in the past. It has not been flown/tested however, due to the various complexities involved, some of which have been mentioned by @Erik.

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