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 Post subject: Aurore
PostPosted: Thu Jan 24, 2019 6:36 am 
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Good evening. Forums for discussing 2300, and people to discuss it with, are becoming scarce. This is going to be something of a test post, making sure that I can post images and links, as well as opening the discussion.

2300 is an interesting setting, one of the few that makes an attempt to ground itself in real world astronomy. As we all know, and as EDG has dealt with in detail, there are still some issues with it and those issues relating 2300 to the real world have become noticeable given the dramatic increase in exoplanet and exosystem knowledge developed in the past 10 years. I am not sure of the utility in trying to reconcile the real world with 2300 - some of which would require throwing away much of the 2300 setting - but I don't want to get into that in my first topic.

Another problem that can be more immediately dealt with is specific to the η Boötis system. There are several versions of Aurore out there: in one version Aurore is a more distant moon of a brown dwarf orbiting Tithonus, and in another (influenced, I believe, by EDG) Aurore is very close to Tithonus, orbiting every 8.9 hours (canonically) or 9.14 hours (32904.1 seconds) by math. At least, by my math. I make lots of mistakes -

System of moons around Tithonus
The Tithonus system of moons is not well defined other than Aurore. We know there are three other major moons, but we know little more about them than their names, Memnon, Selene and Antilochus, the first two being closer orbiting than even Aurore and airless balls of rock. Antilochus is only described as being ice covered and appears as a small, brilliant disc in Aurore's sky.

This is one proposed configuration. The four major moons are in 1:2:4:8 Laplacian MMR.
Image

and an edge view:
Image

As that is drawn, at that moment both Antilochus and Memnon are visible from Tanstaafl (if its position of 12ºS 88ºW is accurate - which it may not be, another topic). Antilochus with an apparent magnitude of -10.6 (and a 20 arc minute disc) and Memnon at -7.6 just shy of 13 arc minutes).

Though I tried to set the system up as a stable resonant system, it does not remain stable, which will start to introduce slight (but important) eccentricities in the orbits which in turn have implications for Aurore's suitability for colonization.

Satellites of Aurore, Communications

I believe that the only stable locations to place satellites for communication use around Aurore are at the Tithonus-Aurore L4 and L5 points. L1 and L2 are not stable in this system:
Image

with this test satellite placed at L1 entering independent orbit around Tithonus after only 1/2 an orbital period. Even very slight eccentricities in Aurore's orbit seem to exacerbate the problem. Very low orbiting satellites are also, somewhat surprisingly, not stable in even the short term. Mid-altitude retrograde satellites will remain in orbit for a fair amount of time but have unusual and unpredictable shaped orbits and would probably not be useful as communications satellite orbits. L4 and L5 are long term stable, however, surviving a test run of 100 years of simulation without departing more than about 20 km (in a psuedo-orbit) from the nominal L4 and L5 points. The takeaway from that is that the canonical solar power satellites would likely have to have been placed at L4 and L5 - 1.9 light-seconds away from Aurore.

It is mentioned that radio communications is difficult on Aurore, with only line of sight microwave in use. optical and near optical laser communications with spacecraft are already becoming a thing in the real world in 2019 (622 mbps downlink, 20 mbps uplink from cislunar space having been done in reality) and communications between ground station hubs and L4 and L5 could be done the same way. Communications between Nova Kiev and Tanstaafl have to take the more difficult route of going from one of the cities, to one of the Lagrange points, to the other one, and then back down. That is, Nova Kiev->L5->L4->Tanstaafl, about 8 light seconds light speed delay.

Of note, both L5 and L4 are visible from the hot pole and neither are visible from the cold pole, nor within 30º of the pole.

that's probably enough for a test post, but in general the questions that I think should be resolved for the setting are:
1) Is Aurore plausible at all?
2) Where exactly, in latitude and longitude, are the cities of Aurore? Two of them have specific coordinates stated, but the published maps do not line up with those coordinates. In the case of Nova Kiev, it isn't even close.
3) Given the relocation of Aurore inward to its ~9 hour orbit, does it make sense to declare Aurore the only major satellite of Tithonus? If not, perhaps making the other satellites distant orbiting satellites, in order to minimize their influence in numerical simulation and thus make in-game stability more plausible.
4) How are communications conducted at distance on Aurore, particularly between the two hemisphere?

and with every single system in Traveller 2300, with the exception of the solar system itself, what is the orbit normal and axis of rotation of Aurore? I gave it an arbitrary 8º inclination vs the system inclination (that is, the orbit normal of Tithonus and Aurore have 8º difference between them) but it isn't stated anywhere.


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 Post subject: Re: Aurore
PostPosted: Thu Jan 24, 2019 7:43 am 
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Thanks for joining us! :)

For everyone else - Caleuche and I have gone over a lot of this elsewhere already to get to this point.

There's a few more notes I have on Aurore:
- Tithonius is a 55 MJ (1.09401E+29 kg) Brown Dwarf orbiting Muphrid at a distance of 5.85 AU. At 2.7 billion years old it'd have luminosity 0.0000141, and a radius of 61,095 km (slightly larger than Saturn, but 192 times more massive).
- Aurore would have been too hot for life early in its history. At an age of 1 billion years, its BB temp was 380K. So it only dropped below the boiling point of water about 1.6 billion years ago (at least on the dayside)! As Tithonius cools, its habitable zone moves inwards. Aurore only entered the habitable zone 500 million years ago (at age 2.2 billion years). Up until then, any life probably would have been concentrated in the twilight zone/coldside oceans. Maybe Aurore had a "cambrian explosion" about 500 million years ago when life moved further onto the dayside as it became more habitable? Though it could have used the light from Muphrid for some weak photosynthesis before then. I think that might work...
- the orbit of Muphrid and Rubis around eachother varies the temperature of Aurore by about 5K over their orbit - so it could be warmer on Aurore when the two stars are at quadrature (widest separation in Aurore's sky, which would happen roughly every 8 months), and cooler when they're in line (which occurs halfway between quadrature) - so that could pass for seasons that occur multiple times over an Auroran year (orbit of Tithonius around the binary)? Rubis is a 0.1 solar mass M7 V star with an orbital distance of 1.493 AU (from Muphrid), eccentricity of 0.19 and orbital period of 495 days.
- Muphrid would be very bright in Aurore's sky - certainly bright enough to turn "night" into day when it's in Aurore's sky (apparent magnitude of -25.28, pretty much as bright as the Sun from earth!).
- Rubis would be much dimmer - only apparent magnitude of 0.87, which is a bit dimmer than Betelgeuse in Earth's sky (so it'd basically look like a reasonably bright star).
- if any other satellites do exist around Tithonius, they're most likely small asteroidal objects and can't be closer than than about 300,000 km from Tithonius - they'd be torn apart by tides within about 290,000 km. Not sure if Tithonius has a ring system, I don't think it's been described.
- I calculate Aurore's orbital period to be 8.929 hours (0.37 days) given Tithonius' mass (its orbital distance is 576000 km).

Is Aurore plausible? I think it is - it's probably pretty unlikely but the goal here was to make a habitable world around a brown dwarf work somehow :). I think I've made it as plausible as it can be (and at least it actually works as a system now - the GDW version just didn't work at all because Tithonius there wasn't anywhere near massive enough to be considered even a small brown dwarf). Whether it works in all the tiny details though, I don't know.

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 Post subject: Re: Aurore
PostPosted: Thu Jan 24, 2019 7:41 pm 
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Part of talking about all of this is checking my work so far. One difference I noticed already:

I ended up with an apparent magnitude of about -12.1 for Rubis. By way of comparison, Proxima Centauri, a M5 V star and probably less luminous and less luminous in the V (Visual) passband at apparent visual magnitude 11.13, giving an absolute visual magnitude of about 15.5 given 4.2 ly distance.

Then placing that star at the distance that Aurore is from Rubis at one point in its orbit (9.0365*10^11 meters) and solving for apparent magnitude I get -12.1. Still a very bight star and Rubis should be even a bit brighter than that. The relationship equation I have for absolute magnitude, apparent magnitude and distance is: apparentmag == -1.08574 Ln[(1051.74 e^(-0.921034 absmag))/dist^2] - constants set to presume distance is in light years. I checked that against the sun and got the appropriate -26.0 or so apparent magnitude.

Appropriate visual magnitude for a M0 V star is probably around that of HD147379, which is Mv = +8.47, which would make Rubis an even more bight -15 or so.

And now I realize my mistake, Rubis is M7, not M0.

(another edit): though I do still get a fairly bright apparent visual magnitude of -9.81.

and in fact, it looks like Rubis would be as bright as -6 or so even if it were totally dark and lit only by Muprid, when at maximum elongation, I think.


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 Post subject: Re: Aurore
PostPosted: Fri Jan 25, 2019 6:02 am 
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EDG wrote:
- Tithonius is a 55 MJ (1.09401E+29 kg) Brown Dwarf


I think that's why I have a slightly longer orbital period. I have a Jupiter mass as 1.89813*10^27 kg, and 55x that would be 1.04397*10^29 kg. To check against solar system data for Jupiter's mass, I have Io's orbital period as 152900 seconds and semimajor axis as 4.218*10^8 meters, which checks out within about 46.5 seconds known orbital period for Io (wikipedia says 152853.5 seconds). Using your mass for Jupiter (that is, Tithonus / 55) I get an orbital period for Io about 1 hour shorter than its wikipedia orbital period.


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 Post subject: Re: Aurore
PostPosted: Fri Jan 25, 2019 7:00 am 
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EDG wrote:
- the orbit of Muphrid and Rubis around eachother varies the temperature of Aurore by about 5K over their orbit - so it could be warmer on Aurore when the two stars are at quadrature (widest separation in Aurore's sky, which would happen roughly every 8 months), and cooler when they're in line (which occurs halfway between quadrature) - so that could pass for seasons that occur multiple times over an Auroran year (orbit of Tithonius around the binary)? Rubis is a 0.1 solar mass M7 V star with an orbital distance of 1.493 AU (from Muphrid), eccentricity of 0.19 and orbital period of 495 days.


I hadn't realized that Rubis would induce quite as much wobble, or how far Muphrid would be from the barycenter. It becomes more obvious in a plot - notice the counter-intuitive non-circular orbit Tithonus has when the system is plotted against a muphrid-centric frame rather than a barycentric one.

Image

And plotting the position of Muphrid over time (40 years, units on the axis are in AU - clearly the system starts out with an over all +X momentum that should be balanced) you can see the effects of the two large masses in the system, the short period Rubis as the rapid loops and the longer period Tithonus causing that slow loop with a period of about 10 years:

Image

(it's uneven because of the initial eccentricity that Rubis has)
I'll have to make sure to do some work to properly balance the momentum of the system, but it's going to be difficult to state a singular eccentricity for Rubis (or Tithonus!) in a system like this, it isn't a typical two-body system. Jupiter is only 0.1% of the Sun's mass, in the Traveller 2300 eta Bootis system, Muphrid is 91.76% of the mass, Rubis 5.37%, and Tithonus 2.82%. Tithonus's distance from Muphrid is going to vary enough to produce significant climate effects on Aurore, I think. Computing instantaneous eccentricity for Tithonus over the course of a single orbit it varies between 0 and 0.4 or so.


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 Post subject: Re: Aurore
PostPosted: Mon Jan 28, 2019 2:39 pm 
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Interesting stuff.

I have been thinking about the TRAPPIST-1 system, with 4-6 planets in the "habitable zone" of a brown dwarf, so this kind of detailed analysis has implications in a lot of other places.

I am curious why the 2:1 resonance orbit between the larger moons doesn't work in your calculations since it works for Jupiter and the four big moons there.

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