Re: Just Like 2 - Relative Velocity

On Oct 15, 6:42 pm, Brian Davis <brda...@xxxxxxxx> wrote:
On Oct 15, 12:13 pm, Frank <fpfrankpal...@xxxxxxxxx> wrote:

I even understood that he was assuming the optimum
relationship between the asteroid and Earth, a relationship
which would only occur periodically with a period significantly
greater than a year.

I'm not sure why you popped that into the conversation. I'm not sure
that's really a problem - you just plan ahead. In this case, decades
ahead, but still an option.

I've seen serious suggestions that we should plan to visit
one or another comet "when it gets closest to Earth."

That's a valid constraint. If you want to match orbits with Halley's
comet, it's easiest (in terms of delta-v) to do it near apocentron.
That doesn't mean it's easiest from the standpoint of a survivable
mission, or the supplies needed. It's a trade-off, one that needs to
be carefully considered in each case.

You would always need a rocket on the freight to change the
relative velocity to match the target. (Yes, even if the target is a
Lagrange point.)  One problem with the launch tube is that it would
have to be both very long and anchored to something solid along its
entire length. The "something solid" would experience an equal-and-
opposite force to what the freight did, That's fine, if the mass ratio
is astronomical; it's not so fine if you are planning to mine most of
the mass of an asteroid eventually and use the asteroid as your launch
platform. By the time that you had sent off any significant fraction
of the mass, the orbit would be significantly different.

Use that. You use a mass driver to sling away asteroidal mass at high
speed, to change the orbit of the entire asteroid. When (after a
possibly complicated trajectory) it arrives near the Earth, you use
the mass driver again to modify the orbit into a capture orbit. That's
really unlikely to be a one-step process: probably a capture into a
highly-elliptic Earth orbit, which is then modified until you can
start doing close lunar passes to take advantage of that to modify the
orbit still more.

End result is an asteroid in Earth-Moon space, having thrown away some
of it's own mass as reaction mass. That seems to work well everywhere
else (Galileo at Jupiter, Cassini at Saturn, etc.)

Um, the Hohmann trajectory from Mars requires 0.086 of the Earth's
speed about the Sun in delta-V at mars and 0.104 of that speed in
delta-v iin Earth orbit. (Not counting planetary influences at either
point.)
That works out to 25.5 m/sec at Mars orbit and 30.7 m/sec at Earth
orbit.
If your mass driver gets 100 m/sec/sec (10 g and a bit), then a 450
meter mass driver would get you 300 m/sec "exhaust veklocity."
1) That requires 10% of the mass that approaches Earth orbit must be
thrown away to match Earth velocity -- remember this is from about as
close as an asteroid usually gets and it's a Hohmann trajectory which
is not available more than once every two years from there -- not
available as much as once a year from anywhere outside Earth's orbit.
2) 450 meters is a long mass driver -- how bigg is your asteroid?
3) Where would you put it?
If you tunnel into the asteroid to get a central thrust, your talking
building a fairly long tunnel with equipment you have to take there.
If you put the mass driver on the "side" of the asteroid, you generate
spin -- which interferes with yuor ability to steer.
4) How long do you have to fire to get 30.7 m/sec delta v.

.. Or if you're
*really* gutsy, try aerobraking that sucker.

No thanks. Not on the planet I livve on, you don't.


what do we use for the braking rockets, and where do we get
that?

Another option, for small packages, is rotovators. Catch near the
midpoint, toss away smaller masses from near the end, spin up at
leisure. Yes, you can do it conserving both linear and angular
momentum.

You could also fire pellets towards the incoming packages: put your
accelerator where it's easy to supply with energy and mass, and have
it toss objects ("pellets") at high speed into the object to
decelerate them. If you can afford to put an electromagnetic catapult
on the package, it could catch, decelerate, & reverse the pellet
stream, doubling the momentum transfer.

1) What is the accuracy that your design requires?
Every real-world mechaism has a certain amount of error. This seems
like "hitting as bullet with a bullet" at megameter ranges.
2) 300 m/sec is as erious collision velocity. 1000 kph 600 mph.



Or use solar sails. Plenty of cheap, low-impulse methods... you just
have a trade-off to figure out.

Geting inside with solar sails is something which sounds good when
you're speaking metaphorically. I'd love to see womebody try to figure
out a design.

A third is how long a period of the lunar day would be
appropriate for the launch.  Hey! I do BOTE calculations.
I don't program mainframes.

I don't either, but since you seem to be talking about orbits that
link the Moon to L4 or L5... I'd respectfully suggest the answer to
this is "all lunar day long", at least to first order (if solar
perturbations aren't important). Think about it.

I've thought about it.
Obviously, you are a deeper thinker than I am.
From the moon centered system, Earth is at 0 degrees, your target at
-60 degreees, the accelerator is pointing 90 degrees. What's the
velocity which takes the package to the target?

Tell me your simplifications, if it works for an approximation of the
mass, distance, etc. of teh Earth-Moon system, it would work for the
real thing.


--
Brian Davis

.

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