Binary orbits and orbital periods: inquiry

[Qohen Leth]

I'm not sure I even grasp the basics in mathematics, so I'm not sure my doubts are legitimate here. But anyway, here's the situation.

CASE 1

On the 29th of December 3302, I came across the Tosia KF-A d11 system, where I found a very close pair of HMCs. The Orbital Period entry for *both* these planets shows 49.5 days. On the day of discovery, I took a screenie, originally posted in the photo thread (here; relinked below). Today I came back and had a second look.

3302, 29th Dec.

Spoiler

No trick here, they were that close when I found them.

3303, 24 Feb.

In 57 days, little more than one full orbital period, the configuration changed from closest to quasi-farthest apart. Seems to me that either the entry in the system map is wrong, or something snapped in the game. Or I'm missing something


CASE 2

There is a second close pair of HMCs in that system, that I did not check the first time, but looked closely today. This is what it looks like now:

From what we observed in Case 1, can we infere a similar behaviour for this pair? Their common Orbital Period is 33.9 days; thus, following observations, in 33.9 days, the two planets should be close to each other, on the same side of the barycenter, right? And a few days before or after, would there be a chance to see them pass right by each other near one of the intersect points? I'm currently parked at the exact location of one of those intersections; let's see what happens

So, legitimate question? Lack of maths during highschool?

 

[Edelgard von Rhein]

No complicated maths needed (and I would not try to do that on a Friday night...)
.
case 1: you have come back about one and a quarter orbital periods later: the planets are not going around their orbits in the same direction. One goes clockwise; the other anticlockwise. Thus they go from being opposite to passing by each other at closest approach. Another quarter of an orbital period later and they will be opposite each other again.
.
case 2: one orbital period later they will both be in the same location in their orbit.

 

[Qohen Leth]

So I was indeed missing something, make a lot more sense now Gee, I step away for a month and it's like I'm a virgin again!

(bit disappointed that I won't get to see two of those collide!)

 

[CMDR Smior]

It's not possible. Binary planets orbiting in "opposite directions" does not obey the laws of gravity. These orbits would only be possible if they were both orbiting a more massive planet. Looks like lazy coding. SHAME! SHAME!

 

[CMDR EfilOne]

It's not possible. Binary planets orbiting in "opposite directions" does not obey the laws of gravity. These orbits would only be possible if they were both orbiting a more massive planet. Looks like lazy coding. SHAME! SHAME!

Excuse me ...
https://arxiv.org/abs/1204.4718

Also, those planet don't really need to have prograde and retrograde orbits respectively for them to meet, an identical orbital period on a smaller semi-major axis from one of them effectively breaks orbital symmetry, so one planet would as a result orbit slightly faster than the other one, resulting in a "close" meeting every so often.

What's mindbreaking is that it's hard to tell what the sysmap details are telling in such cases : Orbital period of said planet relative to the main star, or to its local center of rotation ? Same question for the Semi-Major Axis ?

If indeed those details are "local", then the close meeting is entirely explained by a difference in SMA between the two, even 0.01AU would make a difference.

 

[Qohen Leth]

What's mindbreaking is that it's hard to tell what the sysmap details are telling in such cases : Orbital period of said planet relative to the main star, or to its local center of rotation ? Same question for the Semi-Major Axis ?

If indeed those details are "local", then the close meeting is entirely explained by a difference in SMA between the two, even 0.01AU would make a difference.

Hence why I brought maths into the equation (hahaha), if they have the same direction, I don't see how there could be such a difference in a little more than *one* orbital period. After dozens or hundreds of periods, sure, but only one, no; they would have to have 1 and 1,5 periods or something, or orbits much more different from each other. Plus, I'm not sure the orbits themselves make an actual difference, *if* the two planets have the exact same orbital period. They should then find themselves in the exact same configuration at the 'start' of every new period, whatever their respective orbit, right?

So yeah, the info in the sysmap seems vague.

 

[MattG]

Have you got screenshots of both sysmaps?

 

[Qohen Leth]

Have you got screenshots of both sysmaps?

Here you go. Case 1: planet 3 and 4; case 2: planets 1 and 2.

 

[marx]

I think that for binary pairs of planets, the sysmap displays orbital period relative to the local center, and not to the parent star. Same probably goes for the SMA. I mean, there are class A stars in all four cases, but the axes* are small enough that they get rounded down from 0.01 AU even. Thankfully, the journal stores more precise info, in kilometers. Qohen Leth could help us decide on the SMA at least: would you mind looking up the semi-major axes and the distances to arrival point for these four planets?


*: fun fact: "axes" is the plural of "ax", "axe" and "axis".

 

[ASC]

I don't see how the first screenshot of the planets close together is possible.

Planets that orbit one another are orbiting in the same direction around their barycenter, which is directly between them. If the orbits are circular or nearly so, as seems to be the case here, then they can't come close to each other.

There are some simple animations on wikipedia demonstrating this - https://en.wikipedia.org/wiki/Barycenter#Gallery

If the planets had highly eccentric orbits, as in the last animation linked above, then they could come close together, but not where the orbit lines intersect, as the planets are at opposite ones.

 

[MattG]

Exactly this. Really interested to see original Journal entries, and Arg of Periapsis...

 

[Qohen Leth]

I don't see how the first screenshot of the planets close together is possible.

Ant yet that's how they were... Hence my inquiry

Qohen Leth could help us decide on the SMA at least: would you mind looking up the semi-major axes and the distances to arrival point for these four planets?

Exactly this. Really interested to see original Journal entries, and Arg of Periapsis...

Here you go: the answer to everything.

 

[CMDR EfilOne]

Yeah, given the SMA is specified using the local center of gravitation, Just by looking at A1 and A2 there's a difference of 9'554'368km between the two. Without any further math involved (All I did was SMA(planetA2)-SMA(planetA1) by the way), this means :

The Orbital radius of A1 is smaller than A2, effectively, that means that in the same exact period of time, (33.9 days), A1 will have to travel on a shorter circumference than A2, effectively rotating "faster" around the local center of mass.

In the same manner between A3 and A4, planet A3 has less distance to cover on the same period of time than A4 (49.5 days), because of a difference of 62'787'056km between each one's SMA.

(PS: Read this in complement : https://en.wikipedia.org/wiki/Retrograde_and_prograde_motion )

 

[Qohen Leth]

That's what I was thinking at first.

Then again, ~10Mkm of difference is merely ~20% of their SMA. To me, that still doesn't account for the fact that over the course of a little more than one orbital period, they switch from one configuration (closest) to the opposite (farthest). That's not 20% difference between the two orbits, even with a margin of error to account for the longer SMA, that's a difference of about 100%: one planet is back at the original spot, the other is at the opposite.

To address the opposite directions idea: at t=0 the two planets are at their closest; at t=0.25, they'd be at their farthest; at t=0.5, at their closest again, etc... But I came back 57 days later, so 7-8 days after the end of one period. Or, for them to be at their farthest, they should be at 0.25 or 0.75 of their orbital period. A quarter of ~50 days being 12.5 days, the 1/6 of period that is 7-8 days doesn't quite fit the observation. According to this theory, they should be at their farthest at Day 12.5, Day 37.5, Day 50 and Day 67.5... Not Day 57.

A1 will have to travel on a shorter circumference than A2, effectively rotating "faster" around the local center of mass.

I don't follow you. If they have the exact same orbital period, it seems to me that their speed makes up for the distance difference. So, the shortest path would be travelled more slowly than the longest, and would complete an orbit in, obviously, the exact same amount of time.

 

[Qohen Leth]

Actually, it just occured to me that the chance of having two binary pairs of planets in the same system both sharing a common *exact* orbital period is probably pretty, pretty, pretty, pretty thin. So what if in the case of binary (and ternary, etc.) planets/stars, the given orbital period is a sort of average?

Guess I'll have to stick around and take daily screenshots of their ballet

 

[CMDR EfilOne]

Yeah, it this case that wouldn't be enough in such a short period of time for them to differ in position that much, indeed. It this very case, each planet have a prograde and retrograde orbits relative to their common center of mass due to their axial tilt :

- A1 has a prograde orbit, axial tilt is 9.38°
- A2 has a retrograde orbit, axial tilt is -20.16°

In the same way :

- A3 has a prograde orbit, axial tilt is 12.69°
- A4 has a retrograde orbit, axial tilt is -19.42°

AND THIS DOES NOT BREAK THE LAWS OF GRAVITY, like said in the horrifying comment above. As to the why, the wikipedia link says a bit more, but isn't entirely detailed --> Angles are flipped, and so is the mechanic

 

[Qohen Leth]

Read my antepenultimate post above, I edited it. I'm still not convinced

 

[CMDR EfilOne]

Then this is probably heading off of my celestial mechanics knowledge ... [where is it]

But the Argument of Periapsis must take a huge part in that if it is also provided relative to the local center of mass, as given the HUGE difference there is between each binary pairs, their orbits are highly elliptical as well .. problem here is that we'd have to find the common center of mass for each to settle the case as well, and be 100% certain as to which celestial mechanic parameters are given in "local" means in a binary pair situation, and which are not.

PMing Howard Chalkley, I strongly feel the need to know now

 

[CMDR Smior]

AND THIS DOES NOT BREAK THE LAWS OF GRAVITY, like said in the horrifying comment above.

I'll give you 1 chance to reply nicely. No one was talking about prograde and retrograde orbits. Someone implied that the planets were moving in opposite directions around the barycenter. I assume you would agree that this is impossible. Planets staring at east and west would move south and have a close approach. Then they would inexplicably move north, as if they were on rails...

 

[Qohen Leth]

Guys, don't forget that this is Elite physics, not real life physics.

I've taken another screenie tonight, 28 hours after the first one. I've superimposed both pics and tweaked one to match orbits. In pink are the locations of the planets 28 hours ago, in blue the current one. Of course, this is very sloppy, but it clearly appears that both planets 1 and 2 follow their orbit in the same direction.

And with some more sloppy work on Ps, the movement arc seems consistent with about 1/33th of an orbit. So that's one case closed. I'll need a bit more time for the other one (longer orbital period).