Colonization of the Sun.

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Can you estimate the velocity? I'm not arsed to do it.
It could be some obscenely large speed.

So here's your formula for free orbit:

http://en.wikipedia.org/wiki/Orbital_pe ... ntral_body

Orbiting very close to the sun's surface, you have these inputs:

a=695500 kilometers (solar radius)
G=6.67300 × 10-11 m3 kg-1 s-2 (constant)
M=1.98892 × 1030 kilograms (mass of the sun)

Plugging those in gives an orbital period of 2.7787221 hours.

Using 2*pi*a to get the circumference of the sun I calculate the speed of *free orbit* (0G) at the surface of the sun to be 436847.029 meters per second, or 977198.973 mph. The speed of light is 299792458 m / s, so we're talking about .14% of the speed of light, so we might be able to ignore relativistic effects.

To achieve Earth gravity (1G) gets a little trickier. The acceleration due to gravity at the Sun's surface is 27.94G. To simulate Earth gravity we need to achieve 26.94G or 28.94G, which translates to 264.012 or 283.612 meters per second per second respectively. Centripetal acceleration is given as v^2/r. We have acceleration and radius so we need to solve for v. Doing a little algebra and substitution I come up with these formulas:

sqrt( 264.012 m/s^2 * 6.955*10^8 m ) / sqrt( 264.012 m/s^2 * 6.955*10^8 m )

These evaluate to:

428509.447 / 444130.776 meters per second, or:

958,548.333 miles per hour if you want to feel 1G *toward* the sun, and
993,492.251 miles per hour if you want to feel 1G *away from* the sun.

My hunch is there's more than enough solar radiation at surface level to power the additional acceleration required to produce these gravitational forces. That will be a trick in itself because at that distance the colony would be one giant solar sail and be continually pushed out.

With the repellent forces addressed, and adequate shielding, the one remaining trick is figuring out how to harness the solar radiation to provide the air conditioning needed to sustain the bio-enclosure inside at a comfortable temperature. Now, you could insulate the interior with a large vacuum separating the shielding from the enclosure. This will go a long way to temperature regulation, but with the extreme conditions on the solar surface you will need climate control, bad. How air conditioning works is you're essentially creating additional entropy to move heat out of the enclosure, but the problem is, outside the enclosure is... space. So conduction is out, and unless you want to continually eject mass from the enclosure, convection is out too. That leaves radiation. So you'd have to figure out an engine that could radiate the excess heat to cool the enclosure to ~80F somehow, perhaps somehow incorporating this into the thrust necessary to achieve the requisite artificial gravity.

If anyone did figure it out it would be a technical marvel.