Re: Moving rocks around
- From: James Burns <burns.87@xxxxxxx>
- Date: Mon, 02 Feb 2009 09:56:02 -0500
Dr J R Stockton wrote:
In rec.arts.sf.science message <497F91AB.1080504@xxxxxxx>, Tue, 27 Jan
2009 17:58:51, James Burns <burns.87@xxxxxxx> posted:
The plan as I envision it would be to (1) wrap a cable
around 2009 BD (or one of its cousins), which will
trail one end out into space like a single-spoked
bicycle wheel, (2) "lower" a chunk of the asteroid
down the cable (assisted by centrifugal force),
and then (3) let go of the chunk when it's moving
in a direction that carries away the correct momentum
to push the rock toward an orbit around Earth.
(4) Repeat with new chunks until the rock is in the desired
orbit.
I haven't worked out any numbers, but I imagine that
this is a way to move these rocks without having to
launch a big motor and lot of propellant.
One does not need numbers; one only needs to think.
Your source of propulsive momentum is the rotational momentum of the
body, which is conserved except when a piece is released (that redefines
the body). That momentum must be less, by a factor of the order of 0.5,
than what the rotational momentum would be if all the mass were
concentrated at the equator of the body.
No natural body can rotate in significantly less time than the Roche
Period of a particle of the same density, unless it is relatively
strong. That period is a few hours, weakly dependent on the body's
density. Therefore the surface speed is about (two pi R) / (a few
hours). That speed is much smaller than the change in speed needed for
almost any useful orbital manoeuvre.
Therefore, to do almost any useful manoeuvre, most of the mass of the
body will have to be thrown away - to a much greater extent than with a
chemical rocket, where exhaust speeds are IIRC several kps.
You are in fact launching very many chunks into the inner Solar System,
in order to deliver a pebble. Better, of course, to launch dust, so
that it can spread.
The exception to the above would be where the propulsive effort needed
in very small; in that case, it's easier to use a very small rocket.
Especially as you can use whatever "engine" would be used to deliver
your flinging-machine, if you arrange for it to arrive not fuel-
depleted.
OTOH, if you can get to the Belt, and install the flinger on one of the
larger spinning asteroids, you may well be able to send boulders into an
Earth-intercept orbit.
But if the rotational axis of the asteroid is not nearly perpendicular
to the ecliptic, you may not be able to do even that very often, long-
term.
ICBW.
Thank you for trying to explain this to me (and thanks to
Eivind and IsaacKuo, as well). I needed to try to work it
out for myself before I understood what you all were
getting at. I see now that my idea is a non-starter,
and why.
I tried several different ways of deciding on an optimum
delta vee. The most optimistic (and the easiest to
calculate) assumed that 100% of the rotational kinetic
energy could be transformed into linear kinetic energy
with no loss of mass:
If we assume a mass M, radius R, angular velocity W,
delta vee V for our target asteroid and that its shape
is a sphere, then
(rot KE)
= 1/2*I*W^2 = 1/2*(2/3*M*R^2)*W^2
= (lin KE) = 1/2*M*V^2
thus
V ~ R*W
At best, I might get a delta vee approximately equal
to the rock's original surface speed. If I only wanted
to move 10% of the original mass, I could increase
this limit by a factor of 10, and so on, but the
surface velocity is so low, that, in order to make
it to Earth orbit, I could only toss a pebble.
What confused me was that everyone kept referring to
the surface velocity of the asteroid. Surface velocity
certainly was not relevant in the illustrative example
I gave, where spaceships could be launched throughout
the inner solar system, at the very least, from the
end of an Earthly beanstalk.
However, that example corresponds to tossing a pebble
from the asteroid, where the launched mass is much
smaller than the stay-at-home mass. There is no
such simple limit to the launched mass's velocity,
although there are limits (strength of the tether
material, inteference from the Moon, for example).
Jim Burns
.
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