Feasibility of a L1 Gravity Swing Cold Launch?

[hmmm27]

At an L1 LaGrangian point between two bodies, one could - materials science notwithstanding - pit two of Newton's Laws (LM3,UG) against each other to provide thruster-free stationkeeping.

Would it be feasible to use that to launch free from the system ? either spit out like a watermelon seed from between the two, or at least get into position to use one or the other for a slingshot manoeuver. [edit: a "cold" launch, without using rockets at all]Apologia for brevity:

In case it isn't a "thing", we're talking about a space station trying to stay parked at the Earth<>Moon "null gravity" point, where there's a natural tendency to slide towards one or the other gravitational source, along the line connecting their centers of mass.

In the case of drifting towards (say)the Moon, one could toss out a smaller mass on a tether out the side towards the Earth, letting the exponential increase in gravity increase its weight, then reeling it back in for a net position change, Earthwards.

The same principle could be used to move a craft forwards or backwards, tossing the weight out angled more towards front or back, "poling"(one weight) creatively, or "sculling"(two weights, easier to visualize).

L1 is of course a "trough" in the longitudinal direction, so assumed for convenience is a build-up of a back and forth reciprocation, like on a playground swing.

Question is : could such gymnastics eventually lead to a direct or indirect escape of the system ? without jettisoning mass in any way. (Or, for that matter, use a station, to launch a spacecraft literally like a slingshot, retaining the two working masses)

 

[Dale]

It is conceivable. The Lagrange orbits are known to have trajectories that are very easy to escape on and it takes very little thrust to dramatically change escape trajectories. That is the basis of the so called interplanetary transport network.

https://en.m.wikipedia.org/wiki/Interplanetary_Transport_Network

It could be that the orbits are so sensitive that dramatic changes in tidal forces would be enough to shift from one to another.

 

[hmmm27]

Thanks for the quick reply, Dale.

(I'll assume your answer covers using a bi/tri-partite station/ spacecraft , for station-keeping and "cold" launching as well)

 

[Dale]

Well, I wouldn’t call it an answer, I don’t know for sure, but it doesn’t seem obviously impossible. So it’s a definite maybe.

 

[Dale]

So it’s a definite maybe.

After thinking about it I am going to upgrade this from “definite maybe” to “maybe probably”. It is well known that tidal effects can be used to transfer both energy and angular momentum between gravitationally interacting objects and shift the orbit. The amounts are very small, but very small is all you need.

 

[hmmm27]

Thanks for applying : I thought up the paradigms while ruminating with friends concerning the mechanics of cold-starting a regular swingset, and found it odd that somethings reasonably obvious, in the same toolbox as "orbital tether" and "slingshot", didn't appear in SF anywhere.

cheers.

 

[Bandersnatch]

In the case of drifting towards (say)the Moon, one could toss out a smaller mass on a tether out the side towards the Earth, letting the exponential increase in gravity increase its weight, then reeling it back in for a net position change, Earthwards.

This sounds like a reactionless drive. How is this not a violation of conservation of momentum?

 

[hmmm27]

Propellant-less, not reactionless.

From a station at an L1 point, tossing a tethered small mass towards one or the other g-sources will - thanks to Newton's Third Law of Motion - result in displacements from the assemblage's center of mass (which is the zero-g point) proportional to the masses. At which time - thanks to Newton's Law of Universal Gravitation - the smaller mass will be exerting a larger force on the tether than the larger mass.

(to be clear, I worked it out with equal gravitational sources, not the Earth<>Moon disparity)

 

[Drakkith]

In the case of drifting towards (say)the Moon, one could toss out a smaller mass on a tether out the side towards the Earth, letting the exponential increase in gravity increase its weight, then reeling it back in for a net position change, Earthwards.

I expect that the change in the position of the station (moonwards) would cancel out whatever you'd get from the tether. The Moon pulls too, and I'm betting that the increase in the gravitational pull on the station by the Moon cancels out the increase in the gravitational pull on the tether by the Earth.

 

[hmmm27]

If I may... this example uses two identical gravitational sources.

Say I want to move a station at an L1 LaGrange point closer to one or the other gravitational sources.

Specs:
- Station masses twice as much as the cannonball.
- Station is situated halfway between two identical point sources of gravity, 4 distance units away from each.
- Tether is conveniently 3 units long.

So we start by tossing the cannonball at one of the grav sources. It runs away really fast then stops short. At this time, thanks to Newton's meddling, the station will be 3 units away from one source; the cannonball is 2 units away from the other.

Before we separated them, at 4u away from each grav source, net gravity (influence of each grav source) on the station was 1/16g - 1/16g = 0g, ie: balanced: the station's not going anywhere. But now, in their new positions...

Station: 1/9g - 1/25g
Cannonball: 1/4g - 1/36g

The pull of the cannonball on the tether - even though it's half the mass of the station - is still more than that of the station.

So the system will move towards the cannonball side.

 

[Drakkith]

I haven't gone through all the math yet, but that just doesn't look right to me. The center of mass of your station-cannonball system remains the same both before and after firing, and we can model the two as if all of their mass is concentrated at the CoM. Since the CoM hasn't moved, there should be no net force on the system.

 

[hmmm27]

The center of mass of your station-cannonball system remains the same both before and after firing,

True.

and we can model the two as if all of their mass is concentrated at the CoM.

False. Well, not false : you can model it like that, but the result would be incorrect.

Since the CoM hasn't moved, there should be no net force on the system.

The CoM is still the same after firing, the station still masses twice as much but, in their new positions, the cannonball weighs more than 1.5x as much as the station. The cannonball will drag the station over (changing the CoM).

I think I've accounted for everything except orbits.

 

[Drakkith]

True.

False. Well, not false : you can model it like that, but the result would be incorrect.

The CoM is still the same after firing, the station still masses more than the cannonball, but the cannonball weighs more than 1.5x the station. The cannonball will drag the station over (changing the CoM).

I think I've accounted for everything except orbits.

Hmmm. I can't find fault with your math, but I haven't done these kinds of calculations in a while, so I'm not that confident in my own results.

 

[hmmm27]

Admittedly the example's arithmetic is definitely premise-dependant ; however, for illustrative purposes imagine an ocean liner, weightless or nearso, between two widespread black holes : toss the anchor close enough to one and you could then yank the liner around like a toy, regardless of the inches it might have moved towards the other in the meantime.

(proper math forthcoming, in principle)

 

[A.T.]

The pull of the cannonball on the tether - even though it's half the mass of the station - is still more than that of the station.

The force of the cannonball on the tether is more than the force of the station on the tether?

 

[LURCH]

The force of the cannonball on the tether is more than the force of the station on the tether?

I noticed that too, but I’m pretty sure it means the ball is heavier than the station.

 

[LURCH]

Consider the fact that each gravity source is pulling on both objects (the station AND the cannon ball). What do you calculate the total effect to be on the over all system?

 

[Drakkith]

Consider the fact that each gravity source is pulling on both objects (the station AND the cannon ball). What do you calculate the total effect to be on the over all system?

That's in post #10.

 

[hmmm27]

~ 22.2 and 14.2 units of force : the cannonball masses less, but weighs more, than the station.

Sorry, the cut'n'paste example in #10 was for a different audience and no LaTex : At the time I just eyeballed the gross acceleration figures to see if they matched general expectations. Should have mentioned that 'g' was at 1 distance unit from a grav source (which could have been inferred, but shouldn't have had to be).

Retroactive math - which will boil down to "whichever side window you stick your arm out of, the station will go in that direction" - forthcoming.