Kalpana One design (was Rotating space colonies)

Chris,
I'll grant you the math and the physics...it sounds about right to me. You are using an 'average' velocity for the NEA. we can target slower rocks to begin with until our ion tech can produce larger specific impulses. As to the time line, even if the 'average' NEA takes a couple decades to bring it into orbit, there's nothing to stop us from beginning a continuous pipeline of rocks being deccelerated to orbit. As the slower rocks begin to show up for processing the faster and later captures will be slowly alligning themselves to be processed as they arrive. We're not going to maintain and expand a spacefaring society by targeting asteroids as we need them, but by ensuring a steady supply. Meanwhile, we can be developing lunaside operations, building infrastructure, etc.
Victor

From: csmyth3025
Sent: Saturday, October 02, 2010 10:18 AM
To: spacesettlers@yahoogroups.com
Subject: [spacesettlers] Kalpana One design (was Re: Rotating space colonies)

--- In spacesettlers@yahoogroups.com, "csmyth3025"
>
> Let's do a "back-of -the-envelope" reality check on the Brooks'
> proposals listed below (edited for brevity). Wikipedia is the source
of
> all the basic information used in the forthcoming calculations except
> for the density of meteorites ( (www.meteorites.com.au
> ).
>
> 1) The orbital velocity of the ISS is about 7.7 km/s at an average
> altitude of about 350 km.
>
> 2) Meteoroids (small NEA's that enter the Earth's atmosphere) travel
at
> various orbital speeds in the vicinity of the Earth ranging up to 42
> km/s. They also approach Earth in its orbit around the Sun at various
> angles along the plane of the elliptic - from "overtaking" Earth from
> behind to coming "head-on". The orbital speed of the Earth around the
> Sun is about 29 km/s. Thus, any given small NEA could have a velocity
> relative to the Earth ranging from 13 km/s ("overtaking" - 42 km/s
minus
> 29 km/s)) to 71 km/s ("head-on - 42 km/s plus 29 km/s). The average of
> these velocities is 42 km/s. For the sake of argument (and to simplify
> our calculation), lets say that we only want to try to capture the
> slower NEA's with a velocity relative to the Earth of about 20 km/s.
>
> 3) The density of stony/iron NEA's averages about 4.5 gm/cm^3. The
> density of nickel/iron NEA's ranges from 7gm/cm^3 to 8 gm/cm^3. We'll
> call them about 7.5 gm/cm^3. If we want to use asteroids for
> construction material (initially) we would prefer the nickel/iron
NEA's.
> We may not have the luxury of being that picky, though, so lets say we
> capture a mixture of both - with an average density of about 6 gm/cm^3
> (6000 kg/m^3).
>
> 4) We'll assume that we're only going to pick the NEA's that are about
> 4m. Again, for the sake of simplifying the calculations, lets assume
our
> NEA's are cubes. A 4 meter NEA would then be 64 m^3. This is about the
> volume occupied by my (rather small) living room.
>
> ....to be continued - I have to go to work.

Continuing on.....If we assume our NEA is a perfect 4 m sphere, its
volume will be about 33.5 m^3. We'll be conservative and say that the
NEA's we're going to capture are about 30 m^3. At an average density of
6,000 kg/m^3 our NEA will have a mass of 180,000 kg (180 metric tons).

5) In order to put our NEA in an orbit around the Earth close to the
orbit of the ISS, we'll need to slow it down from about 20 km/s to about
7.7 km/s (the orbital velocity of the ISS). This is a change of 12.3
km/s, or 12,300 m/s. If we multiply the mass of our NEA (180,000 kg)
times the change in velocity we need to make (12,300 m/s) we get
2,214,000,000 kg*m/s (for the scientifically minded, this is called a
NEWTON*s and is a measure of momentum - in this case it's a measure of
the change in the momentum of our NEA that we need to make in order to
slow it down enough to orbit the Earth somewhere in the general vicinity
of the ISS).

6) In rocketry they use the term "specific impulse" (Isp). This is a
measure of the change in momentum that a particular rocket engine (using
a given fuel) can produce per unit of propellant used. In this case
we're using kg for units of propellant. The Isp of a rocket engine/fuel
type is usually given in "seconds". Because this term is normally
applied to lifting things from the ground to orbit, the units "seconds"
works or mathematically for the formulas that the "rocket scientists"
use. In our case we need to convert this term to one we can use to
figure out how much fuel we'll need to move our NEA. As it turns out,
one Isp (second)=9.8 N*s/kg (fuel used).

7) The Space Shuttle's main engines (burning LOX and LH2) produce a
specific impulse of about 455 seconds. This is about as good as it gets
for a chemical rocket engine. Ion engines have higher Isp's, but the
only ones we have today produce very low overall thrust. If we plug our
numbers for the Shuttle's main engines into the above formula we have
455*Isp (seconds)=455*9.8 N*s/kg (fuel used). In the case of the Shuttle
main engines, one kg of fuel will give us 4459 N*s change in momentum of
our NEA.

8) Since the change in our NEA's momentum has to be 2.214*10^9 N*s and
our best chemical rocket engine will give us 4.459*10^3 N*s per kg of
fuel we have: kg (fuel)=(2.214*10^9 N*s)/(4.459*10^3 N*s)=about 496,500
kg of fuel. For comparison, the Shuttle external (fuel) tank holds about
735,600 kg of fuel (LOX and LH2) - the specifications for this tank,
according to Wikipedia, are as follows:

SLWT Specifications [3]
07-2> (Super Light Weight Tank)

* Length: 153.8 ft (46.9 m) * Diameter: 27.6 ft (8.4 m) *
Empty Weight: 58,500 lb (26,500 kg) * Gross Liftoff Weight:
1,680,000 lb (760,000 kg)

9) If we use current technology, we'll have to find some way to loft
nearly 500,000 kg of fuel (plus a rocket engine complete with plumbing
and pumps) into LEO (7.7 km/s) and then accelerate it another 12.3 km/s
to catch up to our 30 m^3 NEA. Then we'll have to use our fuel to
remotely slow down our NEA so that it settles into an orbit somewhere in
the vicinity of the ISS. This is a pretty tall order.

10) A problem that hasn't yet been mentioned - but is critical - is that
we can't see 4 m NEA's until they're on top of us or are past us. We'll
have to vastly improve our tracking and observation capabilities if we
hope to capture one of these things.

11) We could greatly reduce our fuel requirements by using ion drives.
The trade-off is that - with the ion engines we have (or are on the
drawing boards today) - it will literally take many decades to produce
the change in orbital velocity needed for a 180 metric ton NEA. Also,
ion drives need a power source - solar panels or a nuclear reactor - to
produce the electricity needed to accelerate the ions to high
velocities.
>
> Chris
>
> --- In spacesettlers@yahoogroups.com, "brooksn" bhn1700@ wrote:
> >
> > --- In spacesettlers@yahoogroups.com, Matt Gallimore happygallimore@
> wrote:
> > >
> > > From: brooksn bhn1700@
> > >
> > > "But we aren't taking large asteroids from the asteroid belt, we
are
> taking 5 to
> > > 10 meter asteroids that are passing by Earth, in fact they pass
> within the
> > > moon's orbit all the time. The amount of fuel needed to divert
that
> small an
> > > asteroid just enough to enter the upper atmosphere for
aerobraking,
> strap on a
> > > heat shield and you preserve more of the asteroid, is not very
> costly
> > > energetically. And then adjust the new elliptical orbit until you
> meet up with
> > > the ISS. "
> > >
> > > Agree that this can be done, but I have liability concerns
bringing
> objects
> > > larger than 1 to 2 meters into the LEO.
> >
> > http://en.wikipedia.org/wiki/Meteoroid
> > "Beech & Steel writing in Quarterly Journal of the Royal
Astronomical
> Society proposed a new definition where a meteoroid is between 100
m
> and 10 m across."
> >
> > "The biggest asteroid to hit Earth on any given day is likely to be
> about 40 centimeters, in a given year about 4 meters, and in a given
> century about 20 meters."...
> >
> > >... "You have to travel to the location, mine it, then strap it to
a
> rocket (or
> > > expensive mass driver) and then launch it. An asteroid can weight
> 100's of tons
> > > and can be captured easily by adjusting an already Earth crossing
> orbit. I doubt
> > > 100's of tons can be sent up from the moon for the same cost."
> > > .....
> > > "But the purpose of your base was to launch material into orbit,
you
> need fuel
> > > for that and volatiles in particular. Regolith or asteroid scrap,
> radiation
> > > shielding will be the easy part. What should be the number one
> concern is cost,
> > > energetically and monetarily and I don't see how a new lunar base
> beats an ISS
> > > small NEA capture. "...
> > >
> > > 1. Production scheduling
> > > If we are doing orbital processing, then asteroid capture is done
on
> a schedule
> > > of years to minimized fuel use adjusting dv....
> >
> >... Why? We can agree that start up costs favor ISS, but if 4 m
bodies
> are raining down on Earth once a year, how many are coming between
Earth
> and the moon? The Earth is ~6,300 km in radius, from Earth to the moon
> is ~375,000 km, if we get one 4 m a year hitting Earth I can only
> imagine we are getting over a dozen a year (being very conservative)
> between us and the moon. 12 a year to pick from sounds like a pretty
> generous production schedule. Sure you'll have to plan ahead for these
> encounters and the first one will be a couple of years out (depending
on