ASTRO 106-Some civilizations in the Galaxy might develop the level of

Subject: Physics    / General Physics
Question
Some civilizations in the Galaxy might develop the level of technology and have the will to colonize other planetary systems. Given what we know about the laws of physics and our current state of medicine (i.e., no hypersleep or warp travel allowed), a possible practical path to colonization is hollowing out an asteroid and making a self-sustaining colony ship that will travel at substantially sub-light speeds to nearby planetary systems.

[20pt] For the following calculation, assume travel atv = 0.01c (c is the speed of light). Look up the mass of an asteroid with diameter >10 miles. The energyE required to accelerate an object of mass m to a velocityv isE=0.5mv2. How much energy is needed to accelerate your asteroid? Assume the colony is about the mass of the asteroid, so it doubles the total mass. To arrive to a destination, you will need to double the energy again – once to speed up, once to slow down (there is little friction in space). Keep velocity in units ofc and expressE in units of “kg c2“.

[20pt] How much fossil fuel, uranium for a fission reactor, or hydrogen for a fusion reactor would one need at 100 percent efficiency to power this craft (Hydrogen nuclear fusion gives0.007mc2 energy for a given mass m, fission gives0.001mc2, and fossil fuels are 1 million times less energy per kg than fission). This is obviously a lower limit and does not account for any energy required to keep the crew alive for centuries. Give some analogies or comparisons that give a sense of scale as to how large the energetic requirements are (e.g., how large would the mass of hydrogen to fuse need to be – given that only 2/18 of water ice is hydrogen, how large would the comet need to be that you drag along with you as fuel?; how manyyears supply of uranium would be needed for fusion? How does the amount of fossil fuel required compare with theworld supply of coal?)