Physics Question for Science Fiction Story

[CaptKronos]

I hope this is an appropriate forum for this question.

I'm writing a science fiction story set on the moon. In the story, my heroes, inside a rover type vehicle are blasted into a ballistic arc by a comet impact. The rover has limited "jump" rockets but they and the fuel supply are inadequate to land the vehicle back down on the lunar surface, or kick it into lunar orbit. The rover does carry a smaller two-person rocket powered "flyer" but it also lacks sufficent power/fuel to safely land given their altitude and speed.

Question: is it possible for my heroes to grapple onto a large rotating hunk of lunar rock, also blasted into the ballistic arc, and close to them, and with a line and winch, using the the rock's angular momentum "slingshot" the flyer with enough transferred vectored momentum to slow the flyer enough to land safely?

I would appreciate any help with this problem.

 

[NoTime]

Well, the amount of energy to kick the rover up is the same amount that they have to get rid of to stop going down.
Since they survived the "Takeoff" they should survive the landing.
If they have any delta v capability at all, then the landing should be less stressful.

 

[CaptKronos]

Thanks for the response.

I didn't make the back story clear.

I have a "snowball" type comet strike the lunar surface close to the rover. The kinetic energy of impact flashes the volatiles (mostly water ice) into vapor. It is this expanding gas that launches the rover into its suborbital track with a relatively gentle (read: survivable) gradual acceleration. The plot requires a ballistic arc from the lunar north pole to short of the south pole, max. altitude 60-100 miles. Neither the rover or the flyer have enough delta vee capability to land safely, hence the need to somehow acquire some from other ejecta.

 

[Nabeshin]

Let me see if I understand your question correctly.

Another large rock was blasted off the moon as well, presumably spinning. You want your heroes to latch onto the rock so they acquire the angular momentum, and then, presumably, let go while facing downwards in order to [hopefully] acquire the necessary velocity to land?

 

[CaptKronos]

The rover, like the rock, is following a ballistic arc, so both will fall back to the lunar surface unaided.

I'm wondering if it is possible for my heroes to approach the spinning chuck of ejecta, "land" near the center of rotation, then, using a piton and cable, winch back along the major axis of rotation to the edge of the rock (assume the rock is a flattened ellipsoid). At some point in the rock's descent, near impact, when the angular momentum is vectoring roughly opposite the angle of descent, the cable is released.

If I remember my high school physics correctly, like a slingshot, this would transfer part of the rock's angular momentum to the flyer. flinging it in a path trangential to the rock's radius of rotation and giving it an opposing delta vee. If the rock is sufficiently massive and the length from its center of gravity suitably long, could the impetus be enough to allow the flyer to land safely with its limited power and fuel?

Thanks for your help!

 

[Nabeshin]

I don't see why not. All you need is to have the rock be rotating fast enough to give the delta v that will allow the rover to land safely. Consider the angle they'd have to release at too, assuming you want to minimize fuel use on the decent.

 

[CaptKronos]

It would be a difficult trick to time the release properly on a plummeting, spinning chunk of rock, but my heroes have no alternative but to try and hope for the best.

I don't have the math ability to calculate the ratios of rock mass, flyer mass, rotational velocity at the CG radius, to determine the flyer's acquired delta-vee. If we assume the flyer masses at 1/4 US ton (earth gravity, including two crew) and the rock at, say, a thousand tons, with a long axis of two hundred feet, spinning at one revolution per minute, can anyone tell me what delta-vee the flyer would have once the cable is released? If it was enough to cancel the descent velocity at one mile above the lunar surface, it would be reasonable that the flyer would have enough power/fuel to land safely from that altitude.

Of course, once my heroes are back on the surface their greatest challenges have just begun...now, just why is there no water ice in those permanently shadowed craters?

 

[NoTime]

I'm no expert, but orbital mechanics being what they are, I'm sure there is an exact minimum energy solution to your scenario.
Just a thought.
By specifying the trajectory as being from the north to south pole then it just barely fails to be an orbit.
This says to me that the delta v required to make it an orbit is very much less than the amount required to land safely.
By saying that the rover has insufficient delta v capability to make it an orbit you have put a maximum limit on what the rover can do.
I'm inclined to think that the tether idea would turn the intrepid heroes into jelly long before it made much of a difference in the impact.
Incidentally, since they need to have some appreciable fraction of the moons 5,324 mph escape velocity, I'm having some issue with them avoiding that fate in the first place.

 

[CaptKronos]

NoTime,

I think you're right on all issues. A north-to-south ballistic arc would make the burn into orbit (for later rescue) far more practiable than trying to lasso a spinning hunk of basalt. And if I shorten the arc my heroes wouldn't have enough time to even attempt it.

Bottom line: my scenario doesn't work; so, unlike way too many of my writing brethren (have you read what passes for "science" fiction these days?), I am forced to abandon this really nifty and dramatic device.

Actually, the theme of the story would allow something of a deus ex machina, to nudge around the physics, but I can't bring myself to do it.

Back to the word processor.

Thanks to all for your help.

 

[LURCH]

I think you're right on all issues. A north-to-south ballistic arc would make the burn into orbit (for later rescue) far more practiable than trying to lasso a spinning hunk of basalt. And if I shorten the arc my heroes wouldn't have enough time to even attempt it.

If a more "rapid response" solution would help:

Your intrepid heroes could achieve the same results much more rapidly by simply firing their harpoon or grapple or whatever at a point near the equator of the spinning debris. They could then achieve acceleration similar to the firing of their thrusters by gradually applying the break to the winch.

 

[CaptKronos]

Hmmm...that might just work.

Another physics question that might work itself into the story:

If you have two equal masses separated and connected by a thousand feet truss, orbiting perpendicular to its orbital path at the CG, would not the masses, orbiting on different paths apply a torque to the lever arm created by the truss at the CG?