# Flight paths in orbit around Ceres?

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.

• Do you need the cargo shuttles for your story? If not just land the freighters on Ceres. The gravity well is shallow and fuel is cheap. Should you not want to use ship engines near the surface, just capture and launch the freighters with an electromagnetic railroad. On a railroad spanning Ceres equator, the trains can accelerate at a leisurely pace of $0,18 m/s^2$ to get up to the $514 m/s$ escape velocity in about $1,6 hours$. Generally this concept is called a mass driver, yet I´m hesitant to consider this one as it operates so slowly. Should this fit your needs I´ll post a detailed answer. – TheDyingOfLight Apr 12 at 15:10
• Yep, the near-surface flying is critical. I can have some freighters land, some hang around in orbit, this is fine. Mass drivers are also ok, and I can easily incorporate any data you provide, but the shuttles, tugs and loading/unloading craft I have to have buzzing around, as the main protagonist is a pilot of these small craft. Do you think the mass driver is much more complicated than constructing train tracks? – Innovine Apr 12 at 15:43
• I fail to see the difference between train tracks and a mass-driver, to be honest. A train track is used to drive mass in one direction. A mass-driver... you get the point. The propulsion technology is what matters. The options are maglev [1], Gauss Cannon [2], railgun [3] or friction [4]. My money would be on maglev though, as it seems to create the smallest magnetical, acceleration and electrical hazards. [1] en.wikipedia.org/wiki/Maglev [2] en.wikipedia.org/wiki/Coilgun [3] en.wikipedia.org/wiki/Railgun [4] en.wikipedia.org/wiki/Vehicle – TheDyingOfLight Apr 12 at 23:01

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 as long as you have an orbital GPS system, and good topographical data to coordinate everything.

• A train that you have to hold down. – MongoTheGeek Apr 11 at 20:15
• Regarding traffic, if point-to-point transport was popular I guess we'd see something like todays commercial airline airways and corridors. This would be cool in my world actually. I was already considering using beacons on the surface for navigation. – Innovine Apr 11 at 21:09
• @MongoTheGeek: trains would probably be fine, but moving more than half the speed of a commercial airliner would mean having to spend fuel to not fly away. I suspect this speed limit would probably become the standard flight velocity since it would be so much cheaper than going faster or slower, and the planetoid is small enough that you could still go anywhere in under 4hr at that speed. – Nosajimiki Apr 11 at 21:32
• @Innovine, Orbital GPS and communications satellites may still be ideal. A smaller planetary radius means that ground based beacons and radio towers will disappear over the horizon more quickly. – Nosajimiki Apr 11 at 21:39
• That is a benefit in my case, for other reasons. – Innovine Apr 11 at 21:41

## Space Elevators

Ceres's has a "Day" of 9 hours and low mass puts its Cere-stationary orbit about 1800km above its surface. With its 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.

• Well, that just ruins my entire world. :( – Innovine Apr 11 at 19:31
• with such low gravity, I suspect the friction and electrical dissipation loss of a space elevator would expend more energy than simply launching supplies into orbit. – Nosajimiki Apr 11 at 19:36
• @Nosajimiki you'd still want the elevator for bringing stuff back down without having to give every return trip a big retro-rocket. It might even be a net power generator in that mode, depending on losses in the system. – Starfish Prime Apr 11 at 19:38
• (also, it might well be possible to make a solar-powered cable-climber, though I'm not going to work out the plausibility of that at Ceres' orbit) – Starfish Prime Apr 11 at 19:39
• On a Cererian scale, a space elevator, even one made from nylon rope or whatever, is a megastructure. If you want to get into orbit, a simple catapult and an apogee kick motor is smaller, cheaper, and takes less time. Launch velocity from the equator into an eastward orbit is only 157 m/s (565 km/h). – Mark Apr 11 at 20:50

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.

• Thanks. I see my next question is going to be about the role a human pilot would fill in this scenario :/ What do you think of popping up the cargo into cererian stationary orbit, catching and managing it with little tugs, and attaching it to the interplanetary engine? – Innovine Apr 11 at 19:48
• @Innovine the easiest way to justify the presence of humans is to make your setting a Heinlein-esque alt-history where computer technology simply hasn't developed enough yet. This won't help alt-present and near-future scenarios, which are much harder to justify, but I don't doubt there's plenty of material about that sort of thing out there already. – Starfish Prime Apr 11 at 20:05
• Even if no one else ever notices, its always an irritation to me if something isn't quite right. This is a thorn in my side. Having some plausible handwaving from this group is often a real help for getting me to relax into my own fiction. – Innovine Apr 11 at 20:09
• @Innovine I think that's a common feeling on this site ;-) – Starfish Prime Apr 11 at 20:10
• @Nosajimiki so the handwave is perhaps more "you need people to fix, jury-rig, kitbash, bodge and hack the things that inevitably go wrong, because the spare part will either get here in 5 years on the slowboat or in 3 months if you pay a million bucks". Everything can still come to those who wait, up to and including entire fusion reactor assemblies. – Starfish Prime Apr 11 at 21:59

Your freighters don´t sit in a parking swarm, they land on trains on Ceres. As Ceres is an airless world we needn´t concern ourselves with aerodynamic drag or entry stresses. Yet this is an incidental detail, as the point of using mass-driver trains to launch vessels it to free them to the Tyranny of the Rocket Equation [1]. The Rocket Equation basically says one of three things. The vessel needs to be mostly fuel (current rockets), be efficient and horribly boring (ion drives) or be a torchship [2](which may fall under your restriction of "no super tech" and might be a bit on the dangerous side (Kzinti Lesson) [3]). The mass drivers are still a case for the Kzinti Lesson, but looking at Johns Law [4] that is unavoidable.

The mass drivers will be maglev trains [5] where vessels land on wagons and are pushed up to speed or slowed down. While this takes energy the energy isn´t fully lost if regenerative brakes [6] are used. To power the thing fusion would be nice but messing around with solar panels or fission plants would work, too. It matters that a lot of energy is needed. I´ll come back to that later. If you want to calculate the dimensions of the mass drivers this formula is relevant.

$$v = d/\sqrt[2](d/(0,5*a))$$

$$v$$ = velocity

$$d$$ = distance (track length)

$$a$$ = acceleration

$$v$$ should at least be at 510 $$m/s$$, as that is Ceres escape velocity. At the still human tolerable acceleration of 5 $$g$$ this gives you a track length of ca. 120 km. Play and plug as you like. It should be noted that the logical conclusion of this technology is a track around the equator, setting $$d$$ to infinite and allowing all kinds of funny high-velocity launching. Furthermore, this will allow Brachistochrone Orbitals [7] which are the opposite of our current Hohmann Transfers [8]. A note on $$a$$, 5 $$g$$ seems to be the save human maximum but I would go for 3 $$g$$ as that is more comfortable. Unmanned vessels could be shot off at hundreds of $$g$$´s.

With the infrastructure of the spaceports cleared up let´s look at trajectories. Freighters will need to time their flight plans to the rotation of Ceres and need to maneuver to correct their courses in a manner allowing for save capture and beneficial departure. If both target and launch point have mass drivers only ion drives are needed for corrections. If not the mass drivers will still lower fuel demands and be economically viable, especially as using the power directly to launch vessels will be more efficient than producing Hydrogen Peroxide. (tell me in a comment should you want me to run the numbers). Hohman transfers will be dominant during the early phase of colonization, with Brachistochrone Orbitals only possible at certain times and only in the Belt. As mass-driver infrastructure improves the windows for Brachistochrone Orbitals will grow bigger until Hohman Trajectories will be a thing of the past like travel by horse is today. This obviously assumes that you don't have torchships.

As for your shuttle flight paths, there are two things I mentioned earlier that are relevant to this discussion. That running mass-driver takes a lot of energy and that according to you the colonisation of Ceres is in an early state. This leads to the conclusions that there will be few and short mass-drivers on Ceres. Around those the major settlements will grow but what about those far from these spaceports? Here your shuttle pilot comes in. He will pilot one of the many shuttles and thugs carrying people and materials to and from the mass-drivers. Now, why does this shuttle hopping happen? Ceres has a surface area of ca. 2.7 mil $$m²$$, roughly comparable to Kazakhstan. But the land is mountainous and the ice keeps melting and moving, so installing hyperloop trains [9] will take another century. Even roads are impractical.

As Ceres orbital speed at surface level is only 336 $$m/s$$ and the fuel is cheap the small vessels will fly extremely low trajectories, those who are risk-conscious a few kilometers high, those who want to cut cost only meters above the highest peaks. This is great story material as figuring out that there isn´t enough fuel to get you over the next mountain and pirates harpooning transport vessels down can create a lot of conflicts. The orbits would spread out like the canopy of a tree from the spaceports. it might be more accurate to call them "Jumps" because this isn't really different from jumping on Earth.

Finally, I would recommend the game "Kerbal Space Programm" [10] to you as it will allow you to get an intuitive understanding of orbital mechanics and delivers you the feel of being a spacefarer.

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.

        s    os
s xCCCCx    o s
s CCCCCCCCCC   o  s                            .
s CCCCCCCCCCCC  o   s                     .
s CCCCCCCCCCCC o    s               o
s CCCCCCCCCCo     s         o                     C=Ceres
s *CCCC*      s    o                            s=Ship/Station
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.

                       <s
s
s
s xCCCCx
s  <CCCCCCCC<
s  <CCCCCCCCCC<                            s>
s #<CCCCCCCCCC<                     s              >=Direction
s  <CCCCCCCC<               s                     C=Ceres
s *CCCC*          s                            s=Ship
s    s                                    #=Resources

• Comments are not for extended discussion; this conversation has been moved to chat. – L.Dutch Apr 13 at 9:15

As Nosajimiki said on his answer:

You could also maintain an orbit of about ~112 m/s flying at near surface altitudes.

That is very slow for our aerospatial standards. Jets within Earth's atmosphere usually fly at around double that speed.

As you increase altitude, orbital speeds decrease. So your smaller vesses could do it like this:

1. Wait for a launch window (with 9h 4m days, wait times should be relatively short).

2. Launch. Match orbital plane during ascent.

3. You should achieve orbit within a handful kilometers of the target ship.

4. At such small distances and with such low orbital speeds, just accelerate towards target and, when getting close, match speed. The path towards the target will be a very open curve.

5. Use RCS thrusters to maneuver and dock.

To land: undock and land as always.

• Would you even need to wait for a launch window? The craft will have high delta-v and cheap fuel. Maybe its possible to just launch into space and chase down an orbiting vessel regardless of where it is..? I'm starting to think phase angles and out of plane angles of 45° are not going to be an obstacle, just point at the target and accelerate, slow again when you get tkere :/ – Innovine Apr 12 at 18:42
• @Innovine yes, wait for a lunch window. Ceres may be a small planet but it is still a planet, and spending 5 hours burning fuel to chase a target is not economically in your interest. – Renan Apr 12 at 18:48
• @Innovine, between the 9-hour day and the low velocities involved, a launch window from anywhere to anywhere is never more than four and a half hours away. Spending four hours in the spaceport lounge waiting for a good launch time is preferable to spending that time in cramped quarters trying to catch up with something on the far side of Ceres. – Mark Apr 12 at 19:55