Developing a Workflow – Part IV: Yaccatrice and Sky Moon

For most of the worlds in this system, I am only interested in those attributes which might impact on Yaccatrice. I will detail Yaccatrice, itself, to a greater degree. To start with, I figure I need mass, qualitative composition, qualitative atmosphere, radius and albedo to work out the appearance of the planet in Yaccatrice’s sky. This is also the step where I place moons.

Because of my decision to make Yaccatrice the moon of a gas giant, I need a lot of extra detail about that gas giant. I am going to dedicate this post to detailing the gross physical parameters of Yaccatrice and its immediate primary which I will call Sky Moon. I will separate detailing other planets in the system to a later post.

Since the purpose of this mini-project has been to sharpen my understanding of the processes required to properly detail worlds, in preparation for developing my own worldbuilding algorithm, I don’t yet have many of the procedures I need to randomly determine the parameters of my planets.

Currently, I am using worldbuilding procedures derived from GURPS Traveller First-In, GURPS Space(both 2nd and 4th editions which are often very different), 2300 AD, and Tyge Sjöstrand’s excellent World Generation document on an adhoc basis. I may also pull bits from the Accrete program, my researches on Wikipedia and some stuff from my own accumulated notes.

Size

For planet size I am going to use the GURPS Space 4th edition rules, not because I’m convinced this is the best way to do it but because I’ve been confused as hell about it and I think I’ve finally figured it out. I’m going to modify this with parts from  GURPS Traveller First-In and GURPS Space 2nd edition.

Although I’ve previously expressed my doubts about the ability of a moon of a gas giant planet to survive the tidal stresses in the very tight life zone of such a small star, I’ve been trying to sanity test my chosen orbit for Yaccatrice around Sky Moon by figuring out the Roche limits and Hill sphere radius for Sky Moon. The results seem promising, so I am going to make Yaccatrice into a moon. After going out on a tiny bit of a limb with that, though, I’ve decided not even to try giving Yaccatrice its own moon. That would have been kind of cool though…

After reading a bit of Donald Kingsbury, with all of his weights and measures stuff, I’m itching to have a play with some calendar stuff.

The gas giant Yaccatrice orbits is called Sky Moon because, to the primitive people of Yaccatrice, it looks like a moon and fills a fair fraction of the sky.

Using the rules in GURPS Space 4th edition for gas giant size on page 115, I decide that Sky Moon has a mass of 486 Earths and a density of 0.271 Earths(about 1.5 grams per cubic centimeter). The diameter of this body comes to about 12.15 times that of Earth or 155,000 km.

Since Yaccatrice is a moon of Sky Moon that is tidally face-locked to its immediate primary, the sidereal day of Yaccatrice(relative to the “fixed stars”) is the same as its sidereal day. If I’m understanding things correctly, the synodic month, that is the time from one full moon(or Sky Moon) to the next is the same as the Solar Day.

For reasons deriving from my own madness, I’ve decided I want Yaccatrice to orbit Sky Moon about 21.4 times per local year. To make that a little less round I’ll call it 21.37 times. Thus I get a month/day length of 29 hours, 14 minutes and 39.19 seconds. That should be precise enough!

In my calendar for Yaccatrice each day/month has a name. Since I found myself playing with a Tarot deck while thinking about astrological religious rituals, it seemed obvious to use the Major Arcana to name the day/months. The first day/month is named Magician, the second is Priestess, with the following day/months named, in order, Empress, Emperor, Hierophant, Lovers, Chariot, Fortitude, Hermit, Fortune, Justice, The Hanged Man, Mortality, Temperance, The Devil, The Tower, Stars’ Month, Moon’s Month, Sun’s Month, Judgement, World’s Month. Each such month or day is divided into 24 roughly equal local hours or bells of 73 minutes, 6.63 seconds. The conventional way of stating the date and time is to refer to the day name and an ordinal bell number, e.g. 3rd Bell of Fortune or 17th Bell of Priestess. Two out of every five years will have a leap day/month named The Fool.

Given this information and the formula for the orbital period given in  An Explosion of Equations(Orbital Edition), rearranged to (a/aEarth)^3 = (P/PEarth)^2 * (m1/mSol), I can figure out that the orbital radius of Yaccatrice around Sky Moon would be
2.53 x 10-3 a.u.’s or 378900 km.

I don’t really know if a planet is likely to hold onto a moon at this distance against the tidal forces exerted by Cintilla, but I do want to sanity check this against the Hill radius which is the distance beyond which the stellar gravity dominates over the planetary gravity. The formula for this, neglecting eccentricity is:

With m as 486 Earth masses and M as 0.3 Solar masses and all necessary conversions worked out, I get a radius of a little over 2 million kilometers or over 5 times the orbital radius of Yaccatrice. I’ll call that good, though I suspect tidal perturbations will make the Yaccatrene calendar somewhat less predictable than we might be used to here on Earth. Between days named for cards in the major arcana of the Tarot and a certain amount of chaotic variability in that day length I can see the primitive descendants of Yaccatrice’s poorly-prepared settlers coming up with a lively little astrological religion. Cool… I also made sure both that Sky Moon itself was far enough out that it would not be broken up by the tidal forces of Cintilla and that Yaccatrice was far enough to survive the tidal forces of Sky Moon. This Roche limit is:

Where d is the minimum distance from the center of the larger body to the smaller body at which the smaller body can be held together by its own gravity, R is the radius of the larger body, rho_M is the density of the larger body and rho_m is the density of the smaller body. This assumes a perfectly rigid body. To determine the Roche limit for a fluid deformable body, I’ll just multiply that by 2.44 as explained in the Wikipedia article on the Roche limit. Calculating the Roche limit for the survival of Sky Moon against the tidal force of Cintilla, this comes to a minimum safe distance of 245,113 km(598,076 km for a fluid body), much less than the 0.1151 a.u. distance of Sky Moon from Cintilla. For a roughly earthlike body(density of 5.5 gm/cm3), I get a distance from Sky Moon of 126,643 km(309,011km for a fluid satellite), which is less than Yaccatrice’s orbit of 378900 km from Sky Moon.

I use a variation on that formula to try to determine the distance within which Sky Moon definitely could not retain Yaccatrice in its orbit due to tidal effects.

Where r is the radius of Yaccatrice’s orbit around Sky Moon, M is the mass of Cintilla and m is the mass of the Sky Moon/Yaccatrice system, which we will assume to be the same as the mass of Sky Moon. Given these conditions, I calculated that Sky Moon should be able to retain Yaccatrice so long as it is more than 2.8 million km(0.018 a.u.) away from Cintilla for a rigid system or 6.8 million km(0.045 a.u.) for a fluid deformable system. Yaccatrice seems to  survive all of my obvious sanity checks. Short of running the whole mess through a few million years of orbital simulation(doesn’t exactly say mini project, does it?)

Using the GURPS Space 4th edition rules for sizing Yaccatrice will require me to determine the blackbody temperaturefor the planet, or more precisely, its orbital distance around the star. Now I could go to the effort of figuring out the black body temperature using the following formula:

Where Teff is the blackbody temperature, L is the luminosity of the star in, for instance, Watts per square meter, σ is the Stefan-Boltzmann constant

and D is the distance from the planet to the star.

Since this is a mini-project and not some final polished project, I’ll just use the formula from GURPS Space 4th edition.

B = 278 x (fourth root of L/Lo) / (square root of R/R0)

Where L/L0 is the luminosity of the star in Solar units, R/R0 is the distance of the planet to the star in a.u.’s, and B is the black body temperature of the planet.

The black body temperature comes out to 283 K. I’ve already decided this is going to be a habitable(-ish) world, so it should be either Standard or Large size class. Since I don’t want to stretch the point of Sky Moon having an Earth-size moon too far, I’ll restrict myself to standard size. Using the Large Iron Core column, I get a density of  0.9, which I decide to vary down to 0.88. This comes to a real world measurement of 4.86 gm/cm2.

Using black body temperature and this density, I multiply the square root of the ratio of blackbody temperature over the planet’s density in Earth units, by the minimum and maximum values given in the Size Constraints Table on page 85 of GURPS Space 4th ed.(if you’re following along). This results in a range of 0.538 to 1.166 times the radius of Earth. The radius of Yaccatrice comes to 0.873 of Earth. GURPS Space uses the diameter in miles, which comes, according to their calculation, to 6,921 miles. I use metric, mostly, and prefer to use the radius, which comes to a radius of 0.873 times 6,378 km or 5,566 km.

Gravity in Earth units is density in Earth units times radius or diameter in Earth units. For Yaccatrice, this comes to 0.768 g(7.53 m/s2).

The planet’s mass is M = K D3 . With M being mass, K being density and D being diameter or radius, all in Earth units. For Yaccatrice, this is 0.585 that of Earth or about 3.5×1024 kg.

The albedo of Yaccatrice will be the reciprocal of the absorption factor given on page 84 of GURPS Space 4th edition raised to the fourth power(albedo = 1 – absorption4). I’ll assume a Hydrographics rating of 20% coverage or less. Albedo thus comes to 0.185.

The atmospheric pressure will come to 0.67 atmospheres or 674 millibars. And, using the GURPS Space 4th ed. rules, I’ve calculated a surface temperature of 306 K(Warm).

My calculation of the solar day as 30.68 hours screws up my whole calendar unless I assume folks use sidereal days. I forgot there’d be one extra rotation to account for orbiting Sky Moon. Me ineptum!

Escape velocity isn’t included in the GURPS Space rules, but I like to know it.

Using this for Yaccatrice I get a velocity to escape from its surface of  9160 m/s.

Related to the escape velocity is dealt with in the GURPS Space book, minimum molecular weight retained. In the book it is defined as

W = B/(60 D2 K), where W is the MMWR, B is the blackbody temperature, D is the diameter or radius relative to Earth and K is the density of the planet, also relative to Earth. For Yaccatrice, it comes to 7.03 gm/ mol, which is consistent with an Earth-like atmosphere.

I’ll assume Yaccatrice is the only moon of Sky Moon. Any other moons that Sky Moon might have had when Yaccatrice was captured billions of years ago were expelled during Yaccatrices wild early days. I’ll assume eccentricities of Sky Moon in it’s orbit about Cintilla and Yaccatrice in its orbit about Sky Moon to be essentially circular. I’m afraid that large eccentricities in the satellite orbit might make it easier for the satellite to be expelled. No real science, just a gut feeling.

Next week, we will continue by detailing the other worlds in the system, hopefully less laboriously, detailing climates and cultures on Yaccatrice, and along the way creating a pretty little map of this harsh little world.

Star name Cintilla
Spectral class M1 V
Mass 0.3 Solar masses ( = 99858 Earth masses, = 5.97×1029 kg )
Luminosity 0.0142 Solar luminosity( = 5.47×1024 W)
Temperature 3,736 K
Radius 0.285 Solar radii ( = 198,245 km )
Density 18.3 gm/cm3 ( = 3.32 Earth density)
Age 8 billion years
Roche limit(body of 1.5 gm/cm3 274,834 km( 701,298 km for fluid satellite )
Planet name Sky Moon
Type Gas giant
Mass 486 Earth masses ( = 2.90×1027 kg )
Radius 77,245 km
Density 1.5 gm/cm3 ( = 0.273 Earth density )
Roche limit(body of 4.83 gm/cm3 65,961 km ( 80,473 km for fluid satellite )
Roche limit for Sky Moon/Yaccatrice sytem(Yaccatrice mass assumed negligible) 1.5 million km ( = 0.010 a.u. )(1.8 million km ( = 0.012 a.u ) for fluid satellite)
Hill radius 2 million km
Orbital radius 0.1151 a.u. ( = 17.2 million km )
Orbital period 0.0713 years ( = 26.0 days)
Satellite name Yaccatrice
Type Terrestrial / Garden
Mass 3.5×1024 kg( = 0.585 Earth masses )
Radius 5,569 km
Density 4.83 gm/cm3
Surface gravity 0.767 g( = 7.52 m/s2 )
Escape Velocity 9152 m/s
Orbital radius 367,498 km
Orbital period 27.933 hours
Blackbody temperature 283 K
Atmosphere mass 0.87
Atmosphere pressure 0.667 atm. ( = 676 mbar )
Surface temperature 306 K
Solar day 29.24 hours
Minimum molecular weight retained 7.03 gm/mol

This data is from the latest update brought in by the Mathematica probe.

Thank you for your attention,

The Astrographer

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This entry was posted in Planetary Stuff, Projects, Science Fiction, Science!, World Building, Yaccatrice Project and tagged , , , , , , , , , , . Bookmark the permalink.

2 Responses to Developing a Workflow – Part IV: Yaccatrice and Sky Moon

  1. Pingback: Developing a Workflow – Interlude: Calendar | Astrographer

  2. Pingback: Eyeball Worlds | Astrographer

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