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There are spaceships. They have powerful and efficient engines, but not powerful and efficient enough to ignore gravity or delta V issues.

Sometimes they battle each other in complex systems (like a lot of moons orbiting a gas giant) where there are many crucial maintenance stations, and other civilian infrastructure, that neither site wants to destroy. So orbital tricks matter a lot: Can we set a course to reach Neutral Station 3 while not giving too fast encounter to those missiles and avoiding line of sight with the enemy cruiser while burning?

I am looking for some useful and creative solution to visualize (or otherwise communicate to the crew) orbital information and possible courses (based on remaining delta V) of many objects, which is not simply projecting all orbits in a hologramm.

My first idea was to use seven dimensions, three for position, three for velocity, and one for time. Every point in this 7D space corresponds one state, (being in r at t time with v velocity) which a spaceship is may able or not able to reach. So the possible rendezvouses with the enemy will take the form of some higher dimensional plane or solid.

But then I realized, that although this approach may work for a tactical analysis computer, you can't communicate 7D to humans. But I don't want to stick to boring, old 3D conics.

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    $\begingroup$ It might be boring, but sometimes the simplest solution is the best one... $\endgroup$ – Mithrandir24601 Mar 19 '17 at 19:25
  • $\begingroup$ Statistical mechanics routinely uses 6*N dimensional phase spaces with N approaching infinity. Within mathematical framework it's possible to work on them, with practice it's possible to have some form of idea what's going on, but there's no way you can get any readers or viewers to comprehend that. I'm afraid conics is your only option, at least it's the only thing I can imagine being easy to show to someone unfamiliar. $\endgroup$ – M i ech Mar 19 '17 at 20:00
  • $\begingroup$ @M i ech I don't want unfamiliars to understand it. Well trained Captains and astrogators are working with this display. $\endgroup$ – b.Lorenz Mar 19 '17 at 20:29
  • $\begingroup$ Just as an observation, you can still have the three separate dimensions for velocity if you'd like, but in reality velocity is simply the change in position, so it seems kind of redundant to create three new dimensions to only be the derivate of three other dimensions. $\endgroup$ – Jaich Mar 20 '17 at 0:15
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    $\begingroup$ @Jaich Yes, of course, you can reformulate 'being in r with velocity v at time t' as 'being in r at time t and being in r+dr at time t+dt', but it does not change the fact, that one needs 7 independent numbers to describe the state of the ship. (Ignoring orientation, damage, fuel reserves..) $\endgroup$ – b.Lorenz Mar 20 '17 at 11:41
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Show a projected path of the orbit as a line. Have the line be color coded for time, e.g. starting out as red, shifting to blue, then green, then fading out.

Lines that appear to cross in space will be seen to miss each other in time, if the color doesn’t match. Red crossing green is a large time separation; two different blues mean they will be close together. Where this happens, further annotation is added, showing a dot on each track at the positions of closest approach.

If you need velocity in general, you can add marks to the tracks at various sample positions. Arrows would add to the tangle and is hard to see the length accuratly, so how about something like the wind speed marks on a weather map?

wind barbs

The velocity is given at a few points along the track, and these can be well chosen to show maximums and minimums and where ships approach closely.

That gives 7D of data in a readable form: 3D plot of all positions, color to show time dimension, sample vectors showing velocity at various points.

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    $\begingroup$ Nice answer! It captures what I was going to put into an answer: don't provide them with all the information. Provide them with the information that is useful! $\endgroup$ – Cort Ammon - Reinstate Monica Mar 20 '17 at 1:02
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My approach:

Your planner is a hologram displaying the objects normally in 3D. Each friendly ship is smooth, each hostile ship is spiky (I am using color for another thing).

If a ship is inside an interesting gravitational potential, the equipotential area is displayed. A ship following this area (which will be sphere for a plane and much more complicated for several celestial bodies) will neither win nor lose speed with gravity. On this area three component speed vectors are projected: upside/downside for the current gravitational influence and two more perpendicular vectors: one for the movement towards/away the target, two for the movement sideways of the target.

The size of the vectors show the current speed, their color the accleration: Green means no acceleration, Red is positive acceleration (gaining speed), Blue is braking.

Example: You fire a missile up the north pole. The vector shows only upwards, glows red and gets longer and longer. You switch the engine off. The vector is now weak blue, the same length as before but slowly shortening as the missile slows down. Once the missile stops, no vector is present and the ship glows green. Then the vector points again downward, but gets longer and longer and more and more red.

The computer now tracks the optimal course for a constraint: a specific delta-v, time, fuel consumption. You can then see at once how the orbit changes.

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  • $\begingroup$ The vector would not point downwards after turning the engine off, it still has a positive velocity but now a negative (net) acceleration. The sentence should read: The vector is now weak blue, the same length as before but slowly shortening as the missile slows down. Everything after it is fine $\endgroup$ – Jaich Mar 20 '17 at 0:55
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    $\begingroup$ @Jaich Please note that you can propose edits yourself. While we discourage edits that change the intent of a post, I think an edit like the one you proposed would be perfectly acceptable. If the edit is accepted, it also earns you a little bit of reputation (2 points). It is however generally a good idea to leave a comment to the point of "I have proposed an edit to fix Issue X in your post", if nothing else as a signpost to others on the site. That comment can be deleted once the edit is approved. $\endgroup$ – a CVn Mar 20 '17 at 12:57
  • $\begingroup$ @MichaelKjörling thanks for the heads up $\endgroup$ – Jaich Mar 20 '17 at 15:12
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There are some board games which offer decent approximations of space combat. GMT's Talon comes to mind (downloadable rules are at: http://www.gmtgames.com/p-581-talon-reprint-edition.aspx) A much more detailed (and thereby arguably too complex for the board game market) is the old SPI "Battlefleet Mars" (info at https://boardgamegeek.com/boardgame/3662/battlefleet-mars)

A bit from the rules:

Relative positions of planets are tracked from turn to turn, affecting the travel times between planets during play [...] Combat can be resolved using a simplified chart system or played out ship to ship in 3D space.

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  • $\begingroup$ Can you summarize how those charts work? This is a link-only answer, and we always want the summary of the content as well. $\endgroup$ – JDługosz Jun 29 '17 at 23:06

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