Tex doesn't seem to work in preview mode anymore. So sorry for the hard-to-read formulas. In a paper recently published astronauts Edward T. Lu and Stanley G. Love propose using a spaceship as a "gravitational tractor for towing asteroids". http://arxiv.org/ftp/astro-ph/papers/0509/0509595.pdf There's some math I don't understand in this paper: Since the formula is in the form x=y=z, I imagine that if I computed them seperately, that I'd get 3 identical answers. I'll try the 2nd and 3rd approaches: Since it gives the asteroid diameter as 200m, and its density as 2g/cc, this means the asteroid's mass (M) is 8377580410 kg. It states the spacecraft is 20 tons. Tons has a few different meanings. I'm assuming they mean metric tons or 20,000 kg. Distance from center of mass is 150m. GMm/d^2 (6.67e-11 * 8377580409.57278 * 20000) / 150^2 = 0.496696224 N 1.12(p/2g/cm^3)(r/d)^3(m/2x10^4Kg)(d/100m) 1.12((2g)/2g/cm^3)(1.5)^3(20000Kg/2x10^4Kg)(150m/100m) 1.12(1)(1.5)^3(1)(1.5) 1.12*1.5^3*1.5 = 5.67 (no units. They all cancel, so how can this equal thrust? Also, there's no M (asteroid mass) in this formula. How can I compute the amount of thrust needed to hover over an asteroid without the asteroid's mass?) 0.4967 N does not equal 5.67 does not equal 1 N. What am I failing to understand?