Planetary distances

[PeterDebney]

Easy interplanetary distances​

When not jumping between star systems, travellers sometimes need to fly between planets, but what is the distance between them? The referee can keep careful track of exactly where all the planets are or take the easy approach (as long as their ship has an M Drive), such as the suggested options here.

Using the following variables:

Orbital radius of the inner planet = Ri​

Orbital radius of the outer planet = Ro​

Option 1: the minimum distance​

Distance = Ro - Ri

This is wrong most of the time, as planets don’t actually line up like they do in the classic pictures of the solar system. This is wonderfully explained by QI in

I would not use this option.

Option 2: the average distance​

If we just take the average of the minimum and maximum distance we get:

Distance = ((Ro – Ri) + (Ro + Ri)) / 2
Distance = Ro

Surprisingly, this is just the orbital radius of the outer planet. The inner planet has no impact on the value. But, as planets are in orbits, surely the average distance including the points when the inner and outer planets are at 90 degrees to each other with regard to their sun will be significantly higher.

Note that the orbits are elliptical, but for simplicity we can assume circular:

Distance = ((Ro – Ri) + (Ro + Ri) + 2√(Ro^2 + Ri^2)) / 4 = (2Ro + 2√(Ro^2 + Ri^2)) / 4
Distance = (Ro + √(Ro^2 + Ri^2)) / 2

But if you run the numbers, even with adjacent orbits, the influence of the inner orbit distance is minimal, and it quickly resolves down to Distance = Ro

Even if you include all the points round the orbits, the average distance between adjacent orbits is only about 5% more than Ro, and for two orbit distances the difference is down to about 1%. For simplicity:

Distance = Ro

Option 3: random distance​

Knowing that the straight-line assumption is near enough, we can take the minimum distance between the orbits and randomise the relative location of the inner planet:

Distance = Ro – Ri + 2Ri(2D-2) / 10
Distance = Ro + Ri((2D-2) / 5 – 1)

Option 4: full detail​

I can imagine that this might be an option if your campaign is set entirely in just one system or if you are using reaction drives with minimum fuel (such as contemporary spacecraft).

Start with randomised orbital angles then keep a detailed track of the planetary locations as the campaign progresses. Use trigonometry or orbital mechanics to calculate the distances at the time of flight as appropriate. I gather that the Pioneer kick-starter will have rules for taking the slow road to the planets.



What option would you normally choose for your game?

 

[MonsterX]

When it doesn't matter, I happily ignore this issue. When it does, I role a dice for each planet, 1 is in the 0-60 degree arch from an arbitrary "North" on the ecliptic. 2 is 61-120, 3 121-180 etc. This puts in them in a kind-of-about location in their orbits. If the players want to go from one to the other, I pretty much gestimate and approximate the distance, and come up with a plausible but obviously very inexact number. This is good enough for me; the players need enough understanding of where things are to make their decisions, but I don't think their game experience is enhanced by do the exact calculations. If M drive fuel were a constraint, it would be different, but it almost never is in Traveller.

 

[Arkathan]

We did a Star Fleet Battles campaign way back when, just after Federation Space. Expanded that map to make several minor planets in each zone. Used the LBB Scout world building to create systems, and each system had a different radius for the orbitals. Each system started at "noon" and then I rolled several dice for each system as a seed. The planets moved that many hexes on a system scale map around their orbit. That put them at varied positions, and then they moved a set number of hexes each game turn, further varying their positions.

Much easier to pull off with a spreadsheet today verses the index cards I was stuck with.

 

[Terry Mixon]

Having seen this, I’ll be going with option two. Thanks.

 

[PeterDebney]

Having seen this, I’ll be going with option two. Thanks.

Option 2 is my favourite as well.

 

[PeterDebney]

… If M drive fuel were a constraint, it would be different, but it almost never is in Traveller.

Rather than fuel, I would use one of these options (usually #2) if time was important.

 

[MasterGwydion]

Option 2 is my favourite as well.

Option 2 for me as well unless more exacting detail was required.

 

[NotASnark]

I go with option 4.

I wrote some software which generated full system data (either based on imported UWPs, or through random generation), and which tracks the current position of each planet in the system. It doesn't tell me the exact distance between the planets, but I can figure out a rough estimate by looking at the system map. It also works out jump masks and jump shadows for the system, and shows them on the map. It wouldn't be that hard to display exact distance, but given that the planets move during the journey, it would still be an estimate.

It currently has data for 30,948 star systems (I've been using it for sector generation for my Deepnight campaign).

It's probably more detail than is needed, but once you've got useful data in the database, such as planetary distance and year length, then working out where each planet is at any given time is a trivial extra bonus.

 

[Condottiere]

If you're not coming back to that system, you can randomize it.

Otherwise, I'd look at it as seasonal, like Monsoon Winds.

 

[CordwainerFish]

I go with option 4.

Ook.

I already have code that takes a master random number seed and further alters it for an individual system, based on name and hex [1]; if I'm not working in TTU I generate the UWP using the altered seed. I haven't yet, but could easily, generate the entire system with that seed (most likely using Book 6, because it's more adventurey than contemporary astronomy permits), along with each body's orbit plus position on that orbit at 1105-001 [2] 00h00m00s. The rest is detail.

[1] That way every system is, in a sense, 'created' as soon as I pick the seed for MTU. I can defer actually generating it until the moment when I want it.

[2] IMTU dates are YYYY-DDD, for reasons that anyone who has ever put dates in filenames already knows.

 

[Starglim]

I noted:

• Nearest approach: distance = Ro - Ri
• Furthest apart: distance = Ro + Ri
• 90 degrees apart is a bit of trigonometry that works out to at minimum over 70% of Ro + Ri, or to put it another way at minimum root 2 x Ro, more? as the difference in radii increases?

I think the third case is close enough to the second, so I roll a d4, 1 = minimum distance, 2-4 = close enough to maximum distance. I suppose, though it hasn't come up, if the crew remain in the system or return at an interval long enough for the inner planet to have moved 25% of its orbit, I should go to the next quadrant.

Not too different from option 2, but I think the conjunction / minimum distance result adds interest.

 

[CordwainerFish]

• Nearest approach: distance = Ro - Ri
• Furthest apart: distance = Ro + Ri
• 90 degrees apart is

sqrt(Ro^2 + Ri^2). Did Pythagoras live and die for nothing?