Slingshot Effect / Space Elevator

[The Geoff]

I'm hoping this isn't speculation as it's part of a SF plotline I'm playing with and I want it to be as good as Clarke's stuff

 

We know the slingshot effect works from various spaceprobes that have used it.

 

We know (theoretically) that the space elevator works.

 

So....if you had a ship in geosynchronous orbit, on the end of a space elevator, and then rapidly shortened the tether from the ground before releasing it, it should impart a slingshot effect on the ship? Basically the energy put in by the power station on the ground would accelerate the ship without having to carry all of the fuel into orbit?

 

 

I'm pretty sure it works in theory (and the practicalities are what makes it SF rather than a proposal for a paper!)

[D H]

Welcome to Science Forums, Geoff!

 

You are misunderstanding how the gravity slingshot technique (gravity assist) works and how the space elevator might work. Gravity assist works because the planet is moving with respect to the Sun and the vehicle is moving with respect to the planet (and Sun). Gravity assist does not work in a simple two-body problem world. It is a consequence of interactions between three bodies: the Sun, the planet, and the vehicle.

 

The other problem here is a misunderstanding of how the space elevator would work. You are assuming several things here. First, you are assuming that it would even be possible to "rapidly shorten the tether". It wouldn't. A tether to geocentric orbit (and beyond) is very long and very massive, a lot more massive than the vehicle itself.

 

A space elevator would not end at geosynchronous orbit. It needs to go out a lot longer than that. A counterbalance is needed at the end of the elevator to keep the elevator more-or-less stable. There would be no way to reel it in. There is no need to do so. A vehicle could get a significant boost just be climbing the elevator past the geosynchronous point.

[The Geoff]

Welcome to Science Forums, Geoff!

 

Why thank you

 

You are misunderstanding how the gravity slingshot technique (gravity assist) works and how the space elevator might work. Gravity assist works because the planet is moving with respect to the Sun and the vehicle is moving with respect to the planet (and Sun). Gravity assist does not work in a simple two-body problem world. It is a consequence of interactions between three bodies: the Sun, the planet, and the vehicle.

 

Really? I was under the impression it was a simple result of the relative motion of two massive bodies?

 

Simplified version: Picture a spaceship approaching the earth with velocity v (for clarity, the ship is moving left to right in our external field of view). The ship skims past the earth at the correct speed to be caught in half an "orbit" and exits moving right to left, new velocity is -v. Total change 2v, no sun required?

 

To phrase the idea differently, a ship comes in with such a velocity that a "normal" gravity assist would only divert its course by a few degrees, but instead it catches the end of a tether and holds on until it completes a 180 degree change of course, in effect amplifying the delta-v many times. The earth would of course be diverted from its normal course, sun-orbiting or not, to balance the books.

 

The other problem here is a misunderstanding of how the space elevator would work. You are assuming several things here. First, you are assuming that it would even be possible to "rapidly shorten the tether". It wouldn't. A tether to geocentric orbit (and beyond) is very long and very massive, a lot more massive than the vehicle itself.

 

Yup, I'm perfectly aware that the practicalities are firmly in the SF realm

[D H]

I was under the impression it was a simple result of the relative motion of two massive bodies?

A quibble over terminology. You appear to be talking about the interaction between (for example) a spacecraft and a planet. Spacecraft are typically not considered to be "massive bodies". The restricted three body problem for instance involves the interaction between two massive bodies and one other body of inconsequential mass.

 

That said, I should have been more specific. The goal of a gravity assist is to get both a change in speed [math]v_{\infty}[/math] and direction. In the two body problem, a flyby will achieve a change in direction but not in [math]v_{\infty}[/math]. A change in speed and direction requires the interaction of multiple (more than two) bodies.

 

Simplified version: Picture a spaceship approaching the earth with velocity v (for clarity, the ship is moving left to right in our external field of view). The ship skims past the earth at the correct speed to be caught in half an "orbit" and exits moving right to left, new velocity is -v. Total change 2v, no sun required?

First off, note that there is no change in speed here. Secondly, that isn't how things work. The spaceship is not "caught in half an orbit". It is always in orbit, in this case a hyperbolic orbit. Note well: With only two bodies (e.g., a planet and a spacecraft), the magnitude of the spacecraft's velocity far from the planet ("[math]v_{\infty}[/math]") can not be changed by the encounter.

 

A couple of articles on gravity assists:

http://www.ams.org/featurecolumn/archive/slingshot.html

http://www.dur.ac.uk/bob.johnson/SL/AJP00448.pdf

[The Geoff]

Right......so in effect you can change the direction of the vector all you want with two bodies, but it takes a third to provide an actual transfer of kinetic energy?