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How did the spaceships travel from the Milky Way to the Andromeda galaxy for 6 centuries? How did they not run out of fuel? Or do those spaceship have nigh infinite fuel?

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    The engines run on unobtainium, I mean Eezo, which might be a super effective form of propulsion, I dunno. But remember that you only spend fuel when you accelerate. After you've reached your desired speed, you don't need any fuel to remain travelling at that speed. – tobiasvl Apr 7 '17 at 8:41
  • Yeah, the only fuel they'd really need for most of the journey would be for basic life support (and maybe scanners to look for obstacles), so perhaps they calculated how much would be required and took that much with them, or perhaps they substituted it with solar or collected fuel. In previous games the Normandy could scan for fuel - I don't think the mechanics behind this were ever detailed, but I would guess it's some kind of fuel scoop deal to collect and burn gasses. – delinear Apr 7 '17 at 11:21
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    In space, constant thrust equals constant acceleration (an issue which is addressed in the original ME trilogy at least once, IIRC - and it's why they occasionally talk about turning the ship around to decelerate for the latter half of any given interstellar journey.) So, on top of the whole unobtanium fuel thing, they only need enough propulsion to get up to speed for the journey. Then they can shut the engines off and coast for 600 years until they need to start slowing down at the end. – Steve-O Apr 7 '17 at 13:44
  • It's not made clear exactly what the command class ships like the Nexus and the Arks use - smaller ships use Helium-3. It they run on something similar to a Bussard Ramjet, they could collect the elements needed as they go. – VBartilucci Apr 25 '17 at 19:57
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For a start, there is very little friction in space. As a result, constant thrust is not required to maintain velocity, leading to this joke:

Key line:

Shepard: You wouldn't believe how often I hear [from clueless people] "Why's the ship turning around? We're only halfway there!"

The joke is that, if the ship is constantly firing its thrusters, it will need to begin decelerating at the halfway point in order to be roughly at rest when it arrives. This could be done with reverse-mounted thrusters, but that requires an unreasonable amount of extra weight and engineering compared to using reaction wheels to turn the ship around. Of course, you could instead accelerate up to some cruising velocity and then turn the thrusters off entirely, if you wanted to save on fuel.

Nevertheless, thrusters are required for course corrections, and a constant acceleration profile can shave a substantial amount of time off of the overall trip (which is more important than the use of cryo might suggest, given that the whole ark already has to function reliably and without non-automated maintenance for six centuries). So to properly explain this, we need to go to the codex (Ships and Vehicles > Tempest: ODSY drive):

Standard ship drive cores build up static electricity, and require periodic discharge on a planet or at specialized facilities to prevent static from building to dangerous levels. With few such suitable discharge points in dark space, the ODSY drive core was developed for the arks' long-haul journey to Andromeda. [...]

The ODSY (out-galaxy distributed static synch) drive core is designed to minimize static build-up, and transfers the remaining charge to specially designed capacitors attached to the core. The recycled electricity is used to run ship systems, reducing power requirements and lowering heat generation.

Cross-galaxy, the arks gathered hydrogen using an electromagnetic ramscoop, converting it into protons with an ionizing laser. Proton collision in the arks' fusion reactors provided power for their thrusters. [...]

(The elided portions relate to the Tempest, which is a different ship altogether.)

TL;DR: They found a way to convert the excess static charge which we previously discussed into electrical energy, and then used it to power electromagnetic ramscoops and ultimately fuse hydrogen.

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