NASA wants to do an near Earth asteroid retrieval. The ideal candidates have low delta-v requirements to move to cislunar space, such as to L2 or lunar capture. For one known asteroid it's particularly low, 2008Hu4, at only 170 m/s. It's orbital parameters are given here:
2008 HU4
http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=2008%20HU4;orb=1 The closest approach is in April, 2016. How would a chemical propulsion transfer look that provided the needed 170 m/s? For the chemical propulsion transfer you may assume the delta-v is provided in a single short impulse. How long would it take for the transfer at the closest approach?
Note that when you click on the "Close-Approach Data" link on that page for 2008HU4 it gives the V-infinity with respect to the Earth as 1.28 km/s. This means their relative speed before it is effected by Earth's gravity and speeded up. This is relevant because remember we don't want to put it in Earth orbit but put it in lunar orbit or at L2:
Asteroid Redirect Mission.
https://en.wikipedia.org/wiki/Asteroid_Redirect_Mission Then since the Moon's orbital speed around Earth is 1.1 km/s, it could be a small relative speed between the asteroid and the Moon. But this would depend on the position of the Moon when the asteroid makes its closest approach.
Most discussions of ARM just look at solar electric propulsion(SEP) because it would give a smaller mission size. But the thing is when the delta-v is so small as 170 m/s you could move a 500 metric ton (mT) asteroid with just a single Centaur upper stage, at ca. 20 mT gross mass.
That's the case I want to look at because of the 5 to 10 year transfer time for the SEP case. It should be a shorter transfer time when using chemical propulsion. If you want, you can just calculate what would be the transfer time for the asteroid to get within the Moon's distance of the Earth. We can assume we use ballistic capture or small delta-v burn when it comes close to the Moon to put it in lunar orbit or at L2.
Bob Clark
