What would be the most fuel-efficient propulsion solution to accelerate a 100-ton piece of NEO asteroid towards Earth?

We need acceleration to about 300-500 m/s relative to an NEO asteroid - to get to an LEO.

What is needed is the lightest package possible, that includes engine, fuel tanks, control module and thrusters for maneuvering.

• We can assume that we already have mining operations going on asteroid and we have portable nuclear reactor to produce propellent (oxygen/hydrogen). But we don't want to use a 120-ton SpaceX Starship to accelerate a 100-ton rock, and then again burn fuel to return the Starship back to the asteroid. Jan 26 at 21:01
• And we need to send a 100-ton rock towards LEO every month or so. Jan 26 at 21:18
• The most fuel-efficient way to move a chunk of asteroid is the most fuel-efficient way to move anything, but photon rockets/sails may not be the most practical, particularly if the application is time sensitive. And an asteroid that is 500 m/s from LEO is an asteroid that is already in a somewhat higher Earth orbit...what can you do in LEO that you can't do in that higher orbit? Jan 26 at 23:31
• OSIRIS-REx's return capsule isn't entering low Earth orbit, it's slamming into the atmosphere at 12.2 km/s. Jan 27 at 1:26
• Taking the ISS orbit as a reference, it means a burn of somewhere between 4.5 km/s and 14.4 km/s, depending on how bad the plane change ends up being. You can get closer to the first number if things are lined up poorly by burning for a km/s or two to get into an elliptical orbit, then doing further maneuvers back at apogee to modify that orbit before the final brake for entry into your final orbit, but that could add months. Jan 27 at 2:48

Question has been edited since this answer was posted, making it no longer valid.

With 2020 era tech 'most fuel efficient' with a nuclear reactor available is probably some form of ion engine.

Taking the X3 engine and most generous numbers from here we get a thrust of 5.4 Newtons and a fuel consumption of .2 grams a second. 5.4 newtons on 100 tonnes gets a per second acceleration of 0.054 mm/s, so our 300ms burn is 5.5 million seconds or 64 days and around a tonne of Xenon, so we do not need to venture deep into the rocket equation.

Note that is several million dollars in Xenon for 100 tonnes of payload, so less efficient gases may be better if this is intended to be sensible cost wise.

The X3 needs 100 kw of power, so using 10 of these masses 15 tonnes so the amount of Xenon needed to do a minimum escape burn from earth (3200ms) for our 20 tonne (15 for engines, 1.1 for fuel coming back, 4 tonnes structure) of craft involves several months of departure burn and several more tonnes of xenon, realistic intercept and capture probably involves another month of burn and tonne or so of Xenon.

The 2040 most fuel efficient solution probably involves harvesting mass from the asteroid to power the flight home, but in 2022 there are a lot of unknowns in how to process a rubble pile into usable fuel (and ideally structure, power plant and engines).

• Several points: Jan 27 at 3:25
• Several points: 1. 100-ton chunk from M-Type asteroid will cost around \$100 million when landed on Earth, so it can pay for the fuel. \n------------- 2. What you cannot afford, is to schlep all the fuel you need for return trips from Earth, so I was thinking about propellant produced from water, on asteroid or on the Moon. \n------------- 3. For the light space tug and 100-ton piece of asteroid I calculated about 20-ton (hydrogen/oxygen) burn – to get on a trajectory towards Earth (please let me know if this does not make sense). Jan 27 at 3:33
• @TheMatrixEquation-balance The edited question is asking for a book worth of design and engineering work, recommend breaking it down into smaller chunks, or paying someone to write that book for you. As a starting point if your interest is in situ fuel generation start a new question with less photo and more chemical breakdown of your target asteroid and ask what chemical processes might get usable rocket fuel from it. Then your follow up question becomes likely masses for such a processing system, then the third would be for the masses of the total system. Jan 27 at 4:25
• @TheMatrixEquation-balance re-reading your question and comment, are you interested in the mass of system that harvests water, electrolysis it into H and O then burns it? Your maths for 20 tonnes of fuel to nudge 100 tonnes seems about right but extracting 20 tonnes of water to start with is where the interesting engineering would be. Jan 27 at 4:36
• Depending on what the asteroid is made of, you can probably derive oxygen from the rock itself. And on the plus side, that's refinement you don't need to do to your target metal later. Jan 27 at 4:55