### Re: What is the best way to move one billion pounds into space?

Date: Fri Dec 10 10:06:38 2004
Posted By: Andy Goddard, Staff, Teaching and Learning Resources, Strathclyde University
Area of science: Physics
ID: 1102664937.Ph
Message:
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Hi Tony,

You want to move a billion pounds into orbit in a month. That's about
454000 metric tonnes, which is more payload than all our rockets
have achieved during the last fifty years by a factor of around ten or so,
so it would be a huge undertaking.

To get a body into orbit requires energy. To achieve a low-Earth orbit
(LEO) from a good equatorial site, every kilogram of payload requires about
33 megajoules of energy - slightly more if we factor in air resistance.
Let's say to orbit a kilogramme of mass after passing through the
atmosphere requires us to spend 40MJ. Therefore the mass you wish to orbit
will require 18.16*10^15 joules of energy. This is a huge amount - more or
less the output of a five megaton nuclear weapon.

Your spring idea will sadly not work, though I suspect NASA would love to
be able to use such a technique. Orbital velocities are just short of 8
kilometres per second. Even at the top of Everest where the air is thinner,
an object travelling at these speeds will, without protection, simply burn
up through friction. But let's assume the payload has some form of advanced
heat-shielding, and can withstand 100 gravities of acceleration induced by
the spring. (A human cargo would be best kept down to 5 gravities or so.)
Physics has some handy formulae for dealing with times, speeds,
accelerations and distances. One appropriate one gives us the length
of the spring during the period that its force is applied to the payload.
This would be equal to:

velocity * velocity / (2 * acceleration)

Using SI units, the spring would have to be 32 kilometres long, and it
would be difficult to imagine it recovered for use once a minute.

However, two methods of launching lots of material into orbit do "spring"
to mind. ;-) One would be to use an orbital tower. (You said there were no
current construction limitations, and the materials required to build such
a tower are close to being realised.)

The orbital tower would be a thin band of material connecting a satellite
in geostationary orbit to the ground at the equator. Geostationary orbit is
an altitude at which satellites orbit the Earth once a day. Therefore, as
the Earth rotates under them at the same rate, they appear to remain fixed
over a particular spot. Web searches on "orbital tower" and "beanstalk"
will give you many pointers to the challenges that such a construction
would face. To reach geostationary orbit in an elevator running up the
tower, the energy costs work out to about 58MJ per kilogramme - only
slightly more energy than that to reach LEO, but with a final altitude of
around 36000km compared to a couple of hundred kilometres. You want to lift
the mass in a month, so we can work out the power required:

Power = 58MJ * 4.54*10^8kg / (30days*86400seconds) = 10.2 gigawatts

While this is a lot of power, it could be provided by a solar array,
operating at 10% efficiency, if the array was about 9km in diameter. A
large structure by any means, but not outside the scope for the makers of a
tower.

The second technique is less environmentally friendly. ;-) Do a web search
on "Project Orion". This was a serious investigation into using atomic
bombs to propel a very large spacecraft into orbit, and off to the planets.
We've seen that 5MT is enough to orbit 454000 metric tonnes...but the
world's nuclear arsenal is approximately 4000MT. Even given low
efficiencies, there's enough fissile material in the military's hands to
launch substantial masses to orbit, well above the mass you suggest, though
the fallout and resultant mess would make this an extremely bad choice.

Andy Goddard

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