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In my sci-fi world, mankind has begun colonization of the large asteroid Ceres. It's a mining hub, with a lot of cargo vessels transporting things in and out.

Hydrogen peroxide fuel is cheap and plentiful around Ceres, and the gravity well very shallow, so the kind of fuel efficient rendezvous moves we see in low earth orbit may not apply here. What kind of flight paths would be used by the small vessels loading and unloading the cargo from the big freighters (who sit in a parking orbit)? Would they just fly mostly in straightish lines?

A good answer will sketch out the kind of flight profile and rendezvous process likely to be employed, both in surface-orbit and orbit-orbit scenarios. Delta-v is naturally a concern but answers don't have to contain (much) math. I would love to know if complex flight planning would be required to calculate intercept trajectories, or if the pilots would just home in on a beacon, with little concern for orbital mechanics. Please try keep the technology to todays standard, or even a bit more retro, ie no warp drives or antimatter engines.

Space Elevators

Ceres's has a "Day" of 9 hours and low mass puts its Cere-stationary orbit about 1800km above its surface. With it's weaker gravity of 0.03g's, any number of modern polymers have sufficient strength to simply lower from a stationary orbit to any point on the surface.

Escape velocity for a vertical take-off on Ceres is about 510 m/s with a gravitational resistance of 0.27 m/s and no atmosphere to cause drag, meaning you'd be spending a LOT more fuel just getting up to speeds appropriate for interplanetary travel than you would just getting stuff into deep space. This means that landing a heavy freighter to make loading easier might be more worthwhile than orbiting it and loading it one little shuttle at a time.

You could also maintain an orbit of about ~112 m/s flying at near surface altitudes making point to point transportation around the asteroid practically free; so, you could have a central loading airbase for your freighters that smaller shuttles bring stuff to from around the "globe". My guess is that people would focus more on time efficiency than fuel efficiency meaning flying in straight lines wherever possible would be the ideal way to go.

Complex flight planning may still be needed to the point of making sure people don't crash into each other, but by the time we're advanced enough to colonize Ceres, I'm sure AI will be far enough along to automate flight paths and navigation making local flight traffic a bit of a non-issue in the colonists daily lives.

Delta-v is naturally a concern but

$Delta_v$ isn't a concern. Escape velocity is ~514m/s, and using a peroxide rocket, a teeny-tiny mass ratio of 1.5 is enough to get you into solar orbit from Ceres' surface (for reference, the spaceshuttle had a mass ratio of 15, and it used engines with more than triple the specific impulse of peroxide). Not that you'd be doing such a thing, because you'd just use an electromagnetic or steam catapult to boost you up instead and use a tiny rocket motor to circularise your orbit. Orbital speed at cererean synchronous altitude is a miniscule ~186m/s so you don't need a whole lot of fuel to boost up and down or out as you wish.

In fact, $Delta_v$ is such a non-issue that it could easily make sense to not bother with your freighters at all, and simply boost stuff into space on an Earth (or wherever) intercept trajectory with a little engine to do mid-course correction and the final destination orbit injection burn. You'd either have to wait for a transfer window to open (which is infrequent, though I don't recall of the top of my head how infrequent) or you just put up with the fact that your cargo will take a few extra years to get home. If it is just dumb matter, that's not exactly a big deal. It is rather boring from a space-traffic-control-story point of view, however.

Besides a static space elevator, we might also use a crane, or temporary space elevator. Basically a rope from a ship in stationary orbit unloading supplies and loading resources.

Catapulting things into orbit, as mentioned above, would also work. A ship could choose an elliptic orbit to catch the rocks at about the same speed and their highest elevation or or a suitable tangential movement. I'll leave the mathematics to you. It may collect the rocks or mount engines on them which put them onto desired paths and then return for refuelling - maybe after pushing something from another asteroid or moon towards ceres.

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 s s o o=Resources

A gravity assist maneuver could put a ship at very slow speeds and synced to the rotation of Ceres very close to the surface - enough to push a large container with very little energy into the holding bay, and to push loads towards Ceres with just some balloons on the outside to cushion the impact. Once the ship is behind Ceres (as seen relativ to it's movement around the sun), gravity would accelerate the ship again, so no significant energy is lost.

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 s <CCCCCCCC< s C=Ceres
 s *CCCC* s s=Ship
 s s #=Resources