Urakkalan and Vland

[Kakistocrat]

In the Wiki pages for Urakkalan (star) and Vland (system), in the “Vland Monostellar System” table, Urakkalan’s mass is given as 1.144 times that of Sol, its (effective) temperature is given as a range, 5700–6400 K, its luminosity is given as 2.126 times that of Sol, and its diameter is given as 0.01096 au [1639593 km]. However, on page 7 of Vilani & Vargr, its mass is given (in item 7) as 1.14 rather than 1.144, and its luminosity is given (in item 20) as 1.21 rather than 2.126. Note that in the upper-right corner of the Urakkalan (star) Wiki page, though, a luminosity of 1.21, a temperature of 6000 K, and a radius of 1.19 times that of Sol [827883 km, thus a diameter of 1655766 km] is given.

Urakkalan is a F8 V star. I looked in the MegaTraveller Consolidated Errata document, but no errata for either the World Builder’s Handbook or Vilani & Vargr was given for any data that are associated with F8 V stars in general or Urakkalan in particular. A typical F8 V star has a mass of 1.18 Solar masses, a radius of 1.221 Solar radii [849450 km, thus a diameter of 1698900 km], a luminosity of 1.95 Solar luminosities, and an effective temperature of 6180 K. (If any two of a star’s radius, luminosity, and effective temperature are known, the third can be calculated.)

In the Wiki page for Vland (world), its orbital period is given as 478.72 standard days, which is the number given in Vilani & Vargr. However, Kepler’s third law puts that orbital period around Urakkalan (presuming that 1.14 Solar masses is its correct mass) at a distance of 1.08623 au from Urakkalan, which is starward of the inner limit of its habitable zone. To put it in the habitable zone, roughly analogously to where Terra is in Sol’s habitable zone, its orbital period would need to be increased by about one-third.

 

[Kakistocrat]

A typical F8 V star has a mass of 1.18 Solar masses, a radius of 1.221 Solar radii [849450 km, thus a diameter of 1698900 km], a luminosity of 1.95 Solar luminosities, and an effective temperature of 6180 K.

Taking 1.14 Solar masses as Urakkalan’s correct mass, I’d estimate Urakkalan as having a radius of 1.207 Solar radii [840485 km, thus a diameter of 1680970 km = 0.01123659 au], a luminosity of 1.817 Solar luminosities, and an effective temperature of 6110 K. However, if Urakkalan is an F8 V star that is currently known to Terran astronomy, I’d be glad to learn what its current Terran identifiers are.

To put [Vland] in [Urakkalan’s] habitable zone, roughly analogously to where Terra is in Sol’s habitable zone, its orbital period would need to be increased by about one-third [over 478.72 standard days].

Changing Vland’s orbital period to 637.292246 standard days would not only put Vland in Urakkalan’s habitable zone, but it would also justify the existing intercalation rule of the Vilani calendar in VIlani & Vargr, which made no sense with the 478.72 standard day orbital period. To accommodate the increased length of the Vilani year (gurkula), I’d suggest changing the definition of a Vilani month (kidash) from six Vilani weeks (uumash) to eight uumash. 637.292246 standard days equates to 480.899666845 Vilani days (drandir), so after a Vilani decade (kargurkula) comprising ten gurkula of 480 drandir each, there would be an intercalated short kidash of nine drandir. As an additional intercalation detail, after every 300th kargurkula, the intercalated short kidash would only have eight drandir.

 

[Kakistocrat]

With the changes above to Urakkalan’s radius and Vland’s orbital period, the mean angular diameter of Urakkalan from Vland becomes approximately 0° 29′ 23.1″, which is a bit smaller than the mean angular diameter of Sol from Terra (which is about 0° 32′ 0.2″). I then started to wonder about the orbital periods of Vland’s three moons, to see how common eclipses of Urakkalan might be. I started looking into Kalaguur first, since it’s the largest of its moons.

If Kalaguur has the same density as Vland, then its mass would be nearly half that of Vland, which would mean that Vland and Kalaguur orbit a common barycenter — they would orbit each other, and would be tidally locked to each other (something like Pluto and Charon, only moreso, given the respective mass ratios). However, since the Hill sphere for Vland has a smaller radius than the distance from Vland to Kalaguur (if their densities are similar), either Kalaguur has an orbit that is unstable in the long term (e.g. perhaps it was captured into an orbit around Vland, and will someday escape), or — if its orbit is stable — the density of Kalaguur is significantly less than that of Vland.

 

[Kakistocrat]

The approximate mean angular diameters of Vland’s moons from Vland are as follows:

moon of Vland	distance from Vland	approximate diameter of moon	approximate mean angular diameter from Vland
Irukka	170,000 km	6,400 km	2° 9′ 24.3″
Gashema	505,000 km	6,400 km	0° 43′ 34.0″
Kalaguur	720,000 km	11,200 km	0° 53′ 28.5″

Thus, if the moons’ orbits are close enough to the ecliptic of Urakkalan, all three moons could eclipse Urakkalan, since their mean angular diameters from Vland are all larger than that for Urakkalan — and if the moons’ orbits are in a similar plane to each other, Irukka could eclipse either of the other moons, and Gashema could partially (but not totally) eclipse Kalaguur.

If the densities of Irukka and Gashema are similar to that of Vland, then their masses would also be large enough for mutual tidal locking with Vland, though not as strongly as with Kalaguur. The orbits of both Irukka and Gashema are within their respective Hill spheres, but not by enough to ensure stable orbits. Thus, the Vland system is best described as a “four-body system”; the system’s barycenter is not within Vland, and the interactions of the four bodies (if they all have similar densities) could be quite complex to determine — e.g. what orbital eccentricity should each of the moons have to maximize the system’s stability? which hemisphere of Vland would each moon be tidally locked to?

As an aside, given that Irukka is described as “a barren ball of rock”, why does it have a hydrographics digit of 4? (Was it mistakenly copied from Gashema’s UWP?)

 

[Kakistocrat]

Since Irukka and Gashema are both similarly sized to Mars, some numeric tweaking on the moons’ densities and diameters revealed combinations that give both of these moons stable orbits around Vland:

moon of Vland	mean density of moon	mean diameter of moon	mean angular diameter from Vland
Irukka	3653.5 kg⁄m³ = 3.6535 g⁄cm³	5719 km	1° 55′ 38.3″
Gashema	3694.5 kg⁄m³ = 3.6945 g⁄cm³	5706 km	0° 38′ 50.6″

(The diameters given above are on the low end of the 4 size digit in their UWPs.)

Interestingly, although all of Vland’s moons are tidally locked to Vland (and thus unable to eclipse each other), Vland may no longer be tidally locked to Irukka, although it is still tidally locked to Gashema (and Kalaguur). I’ll need to do some research to see if a stable orbit can be devised for Kalaguur.

 

[G. Kashkanun Anderson]

All right. Let's break down some of the wiki numbers first. None of this, of course, should be taken as anything critical about your post! This is all about the numbers as presented by other sources:

Urakkalan’s mass is given as 1.144 times that of Sol

So far, so good. Whether Urakkalan is 1.144 or 1.14 Solar masses doesn't make any real difference at all, in the grand scheme of things, and that's still a viable size for a life supporting star system.

its (effective) temperature is given as a range, 5700–6400 K

Well, that's pretty worthless for determining anything, as it's effectively saying Urakkalan is somewhere between a G3 to an F6 star -- a rather huge range, as far as Teff and luminosity (and habitable zone readings) go.

its luminosity is given as 2.126 times that of Sol, and its diameter is given as 0.01096 au [1639593 km].

Which, taken at face value, would mean that Urakkalan's Teff is 6427K -- the equivalent of an F6 star. Much too hot!

However, on page 7 of Vilani & Vargr ... its luminosity is given (in item 20) as 1.21

Very unlikely. According to my notes, a 1.14 Solar mass star at Solar metallicity (0.0 Fe/H) starts out at a luminosity of 1.314 Sol. So even at Zero Age Main Sequence (ZAMS), it is brighter than that. Of course, one could lower the luminosity by increasing the metallicity (bumping it up to about 175% the metallicity of Sol, or Fe/H 0.2, should do the trick), but that achieves this by lowering the star's effective temperature (Teff). In this case, it would reduce it to about 5752K, which would make it cooler than Sol, and result in it being classified as a G2 star.

Note that in the upper-right corner of the Urakkalan (star) Wiki page, though, a luminosity of 1.21, a temperature of 6000 K, and a radius of 1.19 times that of Sol [827883 km, thus a diameter of 1655766 km] is given.

A 6000K star with a radius of 1.19 Sol has a luminosity of 1.647 Sol.

It is not possible for an F8 star to have a radius of 1.19 Sol and a luminosity of 1.21 Sol; it is simply too hot.

A typical F8 V star has a mass of 1.18 Solar masses, a radius of 1.221 Solar radii [849450 km, thus a diameter of 1698900 km], a luminosity of 1.95 Solar luminosities, and an effective temperature of 6180 K. (If any two of a star’s radius, luminosity, and effective temperature are known, the third can be calculated.)

Kinda sorta. An F8V star of Solar metallicity will be around that size. But most stars are distinctively more metal weak than Sol. The average star, if I recall correctly, is about -0.2 Fe/H, or about 60-65% as metal rich as our star. The lower the metallicity of a star, the higher the effective temperature for its mass. At -0.2 Fe/H, an F8V star could be as low as 1.11 Sol in mass, so it would not be at all odd to find an F8V star around Urakkalan's given mass of 1.14 Sol.

As for stellar radii -- well, they are highly variable, and based largely on the age of the star. Urakkalan's main sequence radius could range anywhere from 1.06 Sol (at ZAMS) to 1.55+ Sol (at EMS), depending on its age.

For Teff, my most loose definition for an F8 star would be a range of about 6100-6200K, although I would prefer a more limited one of 6120-6170K myself, with 6150K being most typical temperature to me.

In the Wiki page for Vland (world), its orbital period is given as 478.72 standard days, which is the number given in Vilani & Vargr. However, Kepler’s third law puts that orbital period around Urakkalan (presuming that 1.14 Solar masses is its correct mass) at a distance of 1.08623 au from Urakkalan, which is starward of the inner limit of its habitable zone. To put it in the habitable zone, roughly analogously to where Terra is in Sol’s habitable zone, its orbital period would need to be increased by about one-third.

The calendar page on the wiki gives the standard Vilani year as being 1.312 Solar years, or about 479.21 standard days. That's a minor discrepancy, to be sure, but still worth noting.

Applying Keppler's Third Law to Urakkalan's mass, coupled with using some of the numbers given for Vland to reverse engineer the world temperature formula in Book 6, is a good way to figure out a workable luminosity for the star, and from there (assuming a Teff of 6120-6170K), its radius. I'll get on that later, though; right now I need to get some rest.

 

[kilemall]

To what extent does star metallicity affect probability of rock planet formation?

At first blush I would think more metallicity more rocks, but maybe it’s the opposite- more of the metals ended up in the planets.

Or maybe it divides along mass/temperature/gravity thresholds, or ‘it depends’.

 

[Kakistocrat]

All right. Let’s break down some of the wiki numbers first. None of this, of course, should be taken as anything critical about your post! This is all about the numbers as presented by other sources:

By all means, please let me know where my presumptions and/or calculations are off — more eyes looking at this can only help improve the data in the wiki. The temperature and luminosity ranges for Urakkalan that are in the Wiki were what first grabbed my attention. I haven’t looked at other wiki pages on stars, so I don’t know how well the quality of the Urakkalan data compares to that of other star wiki pages, or if the Urakkalan data were drawn from multiple Traveller-based sources (e.g. if some of the numbers were modified from one version of Traveller to another).

A typical F8 V star has a mass of 1.18 Solar masses, a radius of 1.221 Solar radii [849450 km, thus a diameter of 1698900 km], a luminosity of 1.95 Solar luminosities, and an effective temperature of 6180 K.

Kinda sorta. […]

By “typical”, I was going by the data in Eric Mamajek’s document A Modern Mean Dwarf Stellar Color and Effective Temperature Sequence, which (like Book 6) doesn’t explicitly address variations in either metallicity or age.

[…] I’ll get on that later, though; right now I need to get some rest.

Thanks for your input — I look forward to your future findings.

 

[G. Kashkanun Anderson]

To what extent does star metallicity affect probability of rock planet formation?

At first blush I would think more metallicity more rocks, but maybe it’s the opposite- more of the metals ended up in the planets.

Or maybe it divides along mass/temperature/gravity thresholds, or ‘it depends’.

It appears to be very important, although 'in what way' is still mostly confined to different degrees of 'theoretically', since we still do not have enough empirical examples to go on yet.

Empirically, it is known that increased metallicity in a star does increase its odds of having one or more Jovian companions. Sol is, of course, a good example of this in action. At even higher metallicities, it becomes increasingly common for such worlds to occupy closer orbits to a star than Jupiter is to Sol. In the science-fictioney sense, this could mean a plethora of Hoths or Reginas, but I believe most astrophysicist, being the killjoys that they are, think even a Mars sized world orbiting a gas giant is a bit of a stretch.

For the record, it is theorized that Jupiter may, at one point in the early Solar System's history, have taken a wander into the region currently occupied by Earth and Venus, disrupting any prior planets that might have been there. In other words, we may live here on Earth, and not some supersized version of it, because Jupiter ate our orbit's previous inhabitant.

The size of a star likely also matters with Jovians too, in that few, if any, are expected to be orbiting type M or early type K stars, regardless of their metallicities. This would lead to more room for good sized ice giants, however, particularly with metal rich versions of these stars. And it's also expected (and observed to be so, so far) that there will be many more super-Earths around these smaller stars, regardless of their metallicities, as there won't be any Jovians careening around the system in the early years hoovering up the materials that would otherwise go to larger terrestrial worlds.

On the other side of the scale, less metallic stars can have terrestrial worlds around them, down to the point where, of course, they are simply too metal poor for their accompanying protoplanetary disc to keep up with the disruptive stellar winds of the system's prestellar years. In this case, the useful part of the disc is believed to shrink in accordance with the metallicity of the star, to the point where it becomes so close to the star that the heat and accompanying stellar winds disrupt the accretion process before it begins.

 

[G. Kashkanun Anderson]

I haven’t looked at other wiki pages on stars, so I don’t know how well the quality of the Urakkalan data compares to that of other star wiki pages, or if the Urakkalan data were drawn from multiple Traveller-based sources (e.g. if some of the numbers were modified from one version of Traveller to another).

I don't think so. I do not believe anything about the Vland system itself was detailed until Vilani & Vargr came out, other than Vland itself being given a UPP and described as basically habitable, but made up of marginally edible foodstuffs. And for all that, V&V is only semi-canon, last I heard.

By “typical”, I was going by the data in Eric Mamajek’s document A Modern Mean Dwarf Stellar Color and Effective Temperature Sequence, which (like Book 6) doesn’t explicitly address variations in either metallicity or age.

That's a good document. I believe I did use that exact source in determining the ranges for stellar types by Teff in my own tables and formulae. But as for luminosites and radii (and to a lesser extent, mass), those numbers are really only the broadest of guidelines. Think median, rather than mean. Metallicity and age are definitely very, very important -- even indispensable -- in considering stellar characteristics at the individual level.

Our nearest neighboring system, Alpha Centauri, is a terrific example of this. It's main star is a G2V (5790K), just like, or at least very nearly like, our own Sol (5770-80K) in that category. Yet, it is about 8% more massive than our sun (1.0788 Sol), has a significantly wider radius (about 847,000km, or 1.21 Sol) and is over 50% brighter (1.51 Solar luminosity). Its higher mass also means that it is aging much, much faster than Sol; Alpha Centauri A is going to become a subgiant almost 2.2 billion years before our sun does, despite the fact that it's only 250 million years older.

The fact that it is a 'sunlike' G2V star despite being otherwise so very different from Sol is largely because, at Fe/H 0.2, it is one of those rare stars that is significantly more metallic than Sol (about 65%). And as I mentioned above, one of the effects of higher metallicities in a star is lower stellar effective temperatures for a given mass.

If Alpha Centauri A were a star of Solar metallicity at its age and mass, it would currently be a hotter G0-F9.5V star (5965K), with a radius of about 861,000km (1.22 Sol) and a resulting luminosity of 1.68 Sol. And, at only 1.9 billion years from its subgiant phase, it would be aging even faster.

Thanks for your input — I look forward to your future findings.

Still working on it!

 

[whartung]

Still working on it!

Where are you getting your formulas and such for this analysis?

 

[kilemall]

It appears to be very important, although 'in what way' is still mostly confined to different degrees of 'theoretically', since we still do not have enough empirical examples to go on yet.

Empirically, it is known that increased metallicity in a star does increase its odds of having one or more Jovian companions. Sol is, of course, a good example of this in action. At even higher metallicities, it becomes increasingly common for such worlds to occupy closer orbits to a star than Jupiter is to Sol. In the science-fictioney sense, this could mean a plethora of Hoths or Reginas, but I believe most astrophysicist, being the killjoys that they are, think even a Mars sized world orbiting a gas giant is a bit of a stretch.

For the record, it is theorized that Jupiter may, at one point in the early Solar System's history, have taken a wander into the region currently occupied by Earth and Venus, disrupting any prior planets that might have been there. In other words, we may live here on Earth, and not some supersized version of it, because Jupiter ate our orbit's previous inhabitant.

The size of a star likely also matters with Jovians too, in that few, if any, are expected to be orbiting type M or early type K stars, regardless of their metallicities. This would lead to more room for good sized ice giants, however, particularly with metal rich versions of these stars. And it's also expected (and observed to be so, so far) that there will be many more super-Earths around these smaller stars, regardless of their metallicities, as there won't be any Jovians careening around the system in the early years hoovering up the materials that would otherwise go to larger terrestrial worlds.

On the other side of the scale, less metallic stars can have terrestrial worlds around them, down to the point where, of course, they are simply too metal poor for their accompanying protoplanetary disc to keep up with the disruptive stellar winds of the system's prestellar years. In this case, the useful part of the disc is believed to shrink in accordance with the metallicity of the star, to the point where it becomes so close to the star that the heat and accompanying stellar winds disrupt the accretion process before it begins.

Looking more like the it depends answer.

That’s ok, we are no strangers to the principles of weird result baked in.

 

[tjoneslo]

The data presented in the Monostellar date table derives from a list within the wiki: https://wiki.travellerrpg.com/Star/data - This was compiled from know, current existing data on star types, sizes and luminosity. It doesn't match any of the existing Traveller books (Book 6 in particular, but any of the Traveller books) as the project was to present, to the extent possible, real world data about the existing stars.

If you know of a source of data for this information which you think is more accurate or more up-to-date please let me know. The original person who worked on the project did most of their work with data from 2019 or earlier.

The error in positioning of Vland in the system is a consequence of the use of the Titus-Bode law applied to other stars and a number of errors introduced by rounding errors. This would not be the first time someone has pointed out that the random system generation presented in Traveller creates unstable or wildly incorrect systems.

 

[Kakistocrat]

The data presented in the Monostellar [System] table derives from a list within the wiki: https://wiki.travellerrpg.com/Star/data - This was compiled from known, current existing data on star types, sizes and luminosity. It doesn’t match any of the existing Traveller books (Book 6 in particular, but any of the Traveller books) as the project was to present, to the extent possible, real world data about the existing stars.

I found it surprising that in the Vland Monostellar System table, a particular mass, diameter, and luminosity was given, but a range of effective temperatures were given — but the link that you’d provided shows why that happens to be the case. (My first thought was that Urakkalan’s mass in the table was a typo for its mass as given in Vilani & Vargr, but that was before I was aware of the data in the tables at your link.) For a particular star system, identified by name, my initial expectation would have been that the details would apply only to the star(s) in that system, so that details such as planetary semi-major axes could be used to determine planetary orbital periods around its star(s).

If you know of a source of data for this information which you think is more accurate or more up-to-date please let me know. The original person who worked on the project did most of their work with data from 2019 or earlier.

As G. Kashkanun Anderson noted above, the temperature range that was given for Urakkalan could apply not just to F8 V stars, but to stars ranging from G3 V (at the low end) to F6 V (at the high end), so such wide temperature ranges in particular are probably of limited value. Is the intention for the data in the tables at your link to provide information on a typical star of each of the various types, or to provide information on the full range of stars of each of the various types?

For dwarf (main sequence) stars, the link to Eric Mamajek’s document (from 2022) in a previous comment above provides data for a typical star of each of the various types (with star color being one of the primary factors that he’d used in determining the type), but that document, like Book 6, doesn’t account for varying metallicity or ages of stars. I don’t know if there are analogous documents for stars that aren’t on the main sequence.

The error in positioning of Vland in the system is a consequence of the use of the Titius-Bode law applied to other stars and a number of errors introduced by rounding errors. This would not be the first time someone has pointed out that the random system generation presented in Traveller creates unstable or wildly incorrect systems.

Yes, the radius information in the Planetary Orbit table of Book 6, page 28 only applies to a Sol-like G2 V star; orbits around other types of stars will alter the radius information for each orbit. I don’t know how the authors of Vilani & Vargr came up with the 478.72 standard day orbital period of Vland, since its semi-major axis wasn’t among the data on page 7, but it was correctly identified as being in orbit 4 (which is in the habitable zone of a F8 V star), despite Kepler’s third law placing a 478.72 standard day year around Urakkalan in orbit 3-and-a-bit (which is starward of its habitable zone).

The possibility of a size 9 world such as Vland having three satellites of sizes 4, 4, and 7 seems something of a stretch — for which I suppose the Ancients could be held responsible, veteres ex machina — but satellites of those sizes are within the realm of the possible with the Book 6 rules.

 

[tjoneslo]

I added a note to the Star/data talk page with a link to the document you provided. Thank you for that, it looks interesting.

My only complaint is the columns in the table are not described. I can guess a few of them, especially the ones that seem most relevant.

Teff = effective surface temperature (in Kelvin)
Mbol = the absolute bolometric magnitude of the star (i.e how bright).
R_Rsun = Relative radius to the Sun. used to calculate diameter for Jump / Maneuver drive distances.
Msun = Mass of the star in solar masses

These are the important ones, but the rest are a mystery to me.

 

[G. Kashkanun Anderson]

Where are you getting your formulas and such for this analysis?

I assume in this case you are talking about my descriptions of the interrelationships between stellar Teff, mass, radius, age and metallicity.

They come mostly from tables and spreadsheets that I have compiled from a range of good academic sources on the subject, particularly for Teff and mass in this case. The page that Kakistostrat has mentioned (and linked to) a few times already was, in fact, my main source for Teff estimates by mass (from which I have extrapolated a breakdown into Teffs at 1/100 Solar masses by step above 0.1 Solar mass, and by 1/1000 Solar masses by step below it).

It also served to confirm the relationship between Teff and mass at Solar metallicity with other online academic sources, or at least find the best compromise between those sources, when they conflict.

For stellar aging, I initially used some of the standard formulas, but they tended to break down at different mass levels, and the result was too klugey for my tastes. Ultimately, I ran multiple iterations of a program called EVOLVE ZAMS, which provides extremely detailed results about the condition of stars along a wide range of variables at any given mass for the amount of time you specify, and at several different levels of metallicity. This allowed me to extrapolate detailed tables out of different pieces of the raw data, so that I am basically able give a very good account of what any star should look like at any stage in its evolutionary cycle, from Zero Age Main Sequence to White Dwarf, and at nearly every recorded level of metallicity, as well as a few that are currently theoretical.

And by 'multiple iterations' of the program, I mean MULTIPLE. I have pages and pages of raw data to work with.

As a result, I have four main spreadsheets that I can consult: Stellar Vital Data, Stellar Metallicity, Stellar Evolution, and PMS (for 'Post Main Sequence') Stellar Evolution. PMS Stellar Evolution still needs a few minor tweaks, but the rest are essentially finished.

EDIT: I forgot that there's also Stellar Evolution (0.10-0.35), Ultracool & Brown Dwarf Teff, Radii & Luminosities, Ultracool Dwarfs & Brown Dwarf Aging Table, and Traveller Worlds Vital Data. But they cover different issues than what has been discussed here so far.

 

[G. Kashkanun Anderson]

I added a note to the Star/data talk page with a link to the document you provided. Thank you for that, it looks interesting.

My only complaint is the columns in the table are not described. I can guess a few of them, especially the ones that seem most relevant.

Teff = effective surface temperature (in Kelvin)
Mbol = the absolute bolometric magnitude of the star (i.e how bright).
R_Rsun = Relative radius to the Sun. used to calculate diameter for Jump / Maneuver drive distances.
Msun = Mass of the star in solar masses

These are the important ones, but the rest are a mystery to me.

Bolometric magnitude is the star's energy output on ALL spectrums, visible or not. Absolute magnitude is the measurement of its visible brightness.

LogT and LogL are logarithmic representations of each star's Teff and luminosity in Sols. In other words, the 5.82 LogL for OV3 means that that star is 660,693 times as bright as Sol. Ray-Ban dad joke coming in at 3 ... 2 ...

The other numbers present are, I believe, just different fiddly flavors of spectral analysis, few of which have any real value in upping your SF refereeing game.

 

[G. Kashkanun Anderson]

OK, so. Urakkalan and Vland. Here goes:

I start by taking Vland's given V&V temperature, and converting it into a blackbody temperature. After adjusting by the standard greenhouse rating for the atmosphere (1.1, a little low, in my opinion), and then adjusting for its V&V listed albedo (0.26 -- lower than Mars?!), while also adjusting THAT number by ^1/4, to account for Vland's rotation, I arrive at a blackbody effective temperature of 285.47K.

Since I think that the given albedo is a little low, I also ran the numbers for 0.306 (Terra's most often given number), and arrive at a blackbody of 290.09K. Just to see how that works out.

For the orbital period to work with, I chose the 1.312 standard year number (479.21 standard days), because that number is all over the calendars, and as such has wider impact on the OTU.

To find Vland's orbit location, I used the formula: r = (T^2*GM/4pi^2)^1/3, where T is the orbital period (in seconds), G is the Gravitational Constant, M is Urakkalan's mass (in kilograms), and pi is ... well ... pi.

The number I arrive at is 187,294,723.4km, or 1.2520 AU.

For Urakkalan's effective temperature (Teff), I was initially going to go with three potential numbers (6120, 6150 & 6170), but then I realized that I should do what any good Traveller referee/world builder would do -- play dice with the universe! So I rolled a single d6 for the standard F8 range of 6120-70 (at 10 degrees per pip), and then for extra giggles rolled 2d-2 for the single degrees.

I wound up with a Teff of 6154K (1.0651 Sol), which is actually pretty bog-standard for an F8 star.

Now we can figure things out!

Stellar radius we can derive from the formula: r = (T^2*2R)/Teff^2. Luminosity is Teff^4*Radius^2. I can extrapolate Urakkalan's stellar age from my personal tables, as well as adjust for metallicity (A 1.14 Sol star is typically about 6080K at Solar metallicity, so the Fe/H needs to be dropped down a hair to adjust the temperature upwards).

First, Urakkalan's stats for the closest thing to canonical information available -- V&V's world temperature and albedo:

Teff: 6154K​

Mass: 1.14 Sol​

Radius: 806,031.9km (1.1586 Sol)​

Luminosity: 1.7275 Sol​

Age: 1.719 billion years​

Metallicity: -0.06 Fe/H (87% Solar Metallicity)​

​

That's not really bad at all! Pretty decent, even. At under two billion years (less than half of Sol's 4.603 billion years), though, Urrakalan does seem a little young, particularly when you consider that Vland, at about 140+% Terra's mass, will take at least that much longer for its interior to cool down.

I wouldn't mind Urakkalan being a little older, then, to perhaps allow Vland to be a bit less of a potentially shakey, volcanoey, sulfury/carbon dioxidey environment, as well as to give the local life forms a little more time to evolve; but one must also remember that Urakkalan has only 6.1 billion years of main sequence life to work with in the first place, due to its larger mass.

Now, Urakkalan's stats at V&V's world temperature, but with a Terra-like albedo:

Teff: 6154K (1.0651 Sol, F8V)​

Mass: 1.14 Sol​

Radius: 832,332.4km (1.1964 Sol)​

Luminosity: 1.8421 Sol​

Age: 2.322 billion years​

Metallicity: -0.06 Fe/H (87% Solar Metallicity)​

A bit better, age wise; almost approaching middle age already.

Now, since I have always rather liked the idea of Vland being something of a hothouse -- though still habitable -- world, I thought I would see what Urakkalan might look like under a regime where Vland's world temperature was the same as Terra's during its most recent hothouse phase: the Paleocene-Eocene Thermal Maximum (about 55.5Ma before present), when Terra's temperature reached 29.7C (302.85K)!

Urakkalan (at V&V albedo and 302.85K Vland Temperature/296.84 Vland Blackbody):

Teff: 6154K (1.0651 Sol, F8V)​

Mass: 1.14 Sol​

Radius: 871,517.5km (1.2527 Sol)​

Luminosity: 2.0196 Sol​

Age: 2.720 billion years​

Metallicity: -0.06 Fe/H (87% Solar Metallicity)​

Urakkalan (at Terra albedo and 302.85 Vland Temperature/301.64 Vland Blackbody)

Teff: 6154 (1.0651 Sol, F8V)​

Mass: 1.14K Sol​

Radius: 899,930.8km (1.2935 Sol)​

Luminosity: 2.1532 Sol​

Age: 3.872 billion years​

Metallicity: -0.06 Fe/H (87% Solar Metallicity)​

Those numbers speak enough for themselves. In the latter, Urakkalan/Vland is almost as old as Sol/Terra, though geologically speaking, Vland is likely more like Terra was about 1.9-2 billion years ago.

So, anyway, that's the analysis. Comments and helpful critiques, corrections or suggestions are appreciated!

 

[Kakistocrat]

For the orbital period to work with, I chose the 1.312 standard year number (479.21 standard days), because that number is all over the calendars, and as such has wider impact on the OTU.

To find Vland’s orbit location, I used the formula: r = (T^2*GM/4pi^2)^1/3, where T is the orbital period (in seconds), G is the Gravitational Constant, M is Urakkalan’s mass (in kilograms), and pi is ... well ... pi.

The number I arrive at is 187,294,723.4km, or 1.2520 AU.

Thanks for your findings, and for the sanity check! On comparing your calculation to mine, I found that I was using the wrong M for Urakkalan. When I corrected M and used the 479.21 standard day orbital period, my calculation was quite close to yours: 187,288,880.048 km = 1.2519488 au.

Using the hzinput.py script (based upon two papers by Kopparapu et al.) to determine the extents of the habitable zones around Urakkalan in your four models returned the following results:

Effective temperature	Luminosity	Conservative habitable zone	Optimistic habitable zone
6154 K	1.7275 Sol	1.22–2.13 au	0.96–2.25 au
6154 K	1.8421 Sol	1.26–2.20 au	1.00–2.32 au
6154 K	2.0196 Sol	1.32–2.31 au	1.04–2.43 au
6154 K	2.1532 Sol	1.36–2.38 au	1.08–2.51 au

The inner edge of the conservative habitable zone is determined by the “moist greenhouse effect”, in which the stratosphere becomes water-dominated, leading to a rapid escape of hydrogen into space. At a distance of 1.252 au from Urakkalan, Vland is comfortably habitable* with an orbit of 479.21 standard days only in the first model above.

* — presuming that UV radiation from Urakkalan is tolerable near the inner edge of the conservative habitable zone

 

[tjoneslo]

Using the hzinput.py script (based upon two papers by Kopparapu et al.)

Ooh, more data to update in the wiki. This is great. Now do decide if I need to convert the python to a spreadsheet, or update the python to output a CSV...