Chemosh, divine power of Permanence

Next in the series of divine refactoring, Chemosh.

While not as problematic as Morgion, or, say, Zeboim, Chemosh is still the "baddie" who apparently has nothing else to do in his eternity than torment and depress people.

Undeath is too much a fascinating concept to be left as it is now.

So, for my campaign... what to do with Chemosh?

Constraints

All gods of Krynn must have an active, inspiring contribution and teaching to soul's evolution and learning. This constribution/teaching does not need to be pleasant, but it has to make sense, even in a twisted way.

The corollary is that priests of all gods should have a philosophy/teaching that makes sense, even in a twisted way: No one should become priest of Chemosh by being coerced into it. If one thing, faith should be sincere.

The modified god (here, Chemosh) should remain recognizable, and, perhaps, from casual examination, should appear like the original version. Only when digging deeper will someone (a reader, or a character) would realize the difference.

Inspirations

For our rework of Chemosh, we need to look around to see if there are interesting concepts we could borrow.

Original Chemosh

The wiki entry for Chemosh is quite extensive, but spends a lot of time in stories where he is not shown in his best light, to be fair.

From the Holy Orders of the Stars sourcebook, we have the following attributes for Chemosh:

• Portfolio: Death, the undead, murder, false hope
  
• Worshipers: Crazed cultists, assassins, necromancers
• Domains: Death, Evil, Trickery, Undeath†

The really part I want to work with is that his portfolio/domains include both death and undeath.

Examples not to take inspiration from

Both Pathfinder's Pharasma and Exandria's Raven Queen are not sources of inspiration. These gods strive to maintain some kind of status quo between life and death, and undeath is not their focus (and is usually a problem for them).

In the same way, Death, the Fourth Horseman of the Apocalypse, the Grim Reaper, and Orcus (despite being as Chemosh-y as Tiamat is Takhisis-y) are not sources of inspiration.

The Necromancer Archetype

A necromancer isn't just a practitioner of dark, or demonic magics. A necromancer deals in the magics beyond life and death. While this knowledge is not necessarily "evil" per se, it is clearly violating classical and modern societal taboos about life and death.

This taboo is very interesting, if we can somehow integrate it in the narrative. The ultimate necromancer might be quite active, striving to irrevocably change known and accepted laws of life in the universe, for some reason (power over the dead, desire to mitigate the cruelty of death, etc.).

Partial Conclusion

There aren't a lot of satisfying inspiration.

Chemosh, divine power of Permanence

Chemosh represents the divine power of Permanence. That is, how a soul might resist change induced by external factors, and thus, evolve only in a way it wants, at its convenience.

The Cycle of Souls is imposed by the current law of Krynn's universe, and is, in Chemosh's viewpoint, by design messy and lossy: How many memories are lost to time? How much enlightenment has been cut short by a premature death, and reset to zero?

This cycle is deemed necessary, and even desirable, by most of Krynn's gods. But as far as Chemosh is concerned, it is widely inefficient. And Chemosh believes that, with his own divine power of permanence, he can cheat the process, and foster the souls Chemosh favors into an accelerated ascension.

To mortals learning about the truth of the Cycle of Souls, the mortality of their own identity, their own avatar is the real tragedy, and Chemosh offers a hope to fix that. This is why Chemosh favors necromancers, as they are the only one able to research necromancy, and push its limits beyond. Chemosh hopes that, with the right inspiration, and with the right necromancers, the god might unearth the secret to circumvent the limitations of the Cycle of Souls.

This is clearly the most outrageous violations of the Laws of Krynn, and Chemosh knows the others gods, no matter the pantheon, would not let that happen, for Chemosh would then be all-powerful, dwarfing both Paladine, Takhisis and Gilean.

So the god works slowly, through indirection, and showing less ambition, and more glee at witnessing the antics of the undead puppets shambling their way around Krynn.

Conclusion

I know, the moment I decided I wanted to do something like Death Knights of Krynn in my campaign, I needed more than just "Lord Soth wants to invade Solamnia".

In my humble opinion, the undead are the only "fiends" that matter, the universal creature opposing and/or feeding from life, that were universal in every culture, which automatically increased the importance of Chemosh in my campaign.

By giving Chemosh, something more than wanting to spawn undead, and seduce Mina, I make it (again, in my humble opinion) a very, very frightening god, worthy of being opposed by heroes, beyond the undead-rising monster of the week.

Morgion, divine power of Ordeal

By now, it might be obvious I'm not a fan of some of the choices done in Dragonlance.

One of them is having gods that serve no purpose but "be there".

In my humble opinion, Morgion is the most egregious on that subject: That god's modus operandi is to contaminate someone with a disease, and then promise them with the disappearance of symptoms if they become a priest of Morgion, and they start contaminating others... in a universe where Mishakal can heal diseases. You might be forgiven if you think such priests might be fools. I know I do.

So, for my campaign... what to do with Morgion?

Constraints

All gods of Krynn must have an active, inspiring contribution and teaching to soul's evolution and learning. This constribution/teaching does not need to be pleasant, but it has to make sense, even in a twisted way.

The corollary is that priests of all gods should have a philosophy/teaching that makes sense, even in a twisted way: No one should become priest of Morgion by being coerced into it. If one thing, faith should be sincere.

The modified god (here, Morgion) should remain recognizable, and, perhaps, from casual examination, should appear like the original version. Only when digging deeper will someone (a reader, or a character) would realize the difference.

Inspirations

For our rework of Morgion, we need to look around to see if there are interesting concepts we could borrow.

Original Morgion

The wiki entry for Morgion is a bit light, but already goes where I don't want to go: Decay and entropy are not "active forces", they are "expected statistical outcome".

From the Holy Orders of the Stars sourcebook, we have the following attributes for Morgion:

• Portfolio: Disease, famine, poison, vermin, suffering, madness
• Worshipers: Crazed cultists, ratcatchers, corrupt druids
• Domains: Destruction, Evil, Madness†, Pestilence
  

Also:

... spreading his unholy message: only the strong will survive, for to survive is to suffer, and to suffer is to know the truth.

-- Holy Orders of the Stars, p102

This makes Morgion someone whose modus operandi is to inflict pain and suffering, for its own sake. Psychological pain, physical pain, it doesn't matter. The question would then be: Why?

Pathfinder's Zon-Kuthon

© 2014, Paizo Inc/Yu Cheng Hong

In Pathfinder's Golarion universe, there's one god that stands out: Zon-Kuthon.

Zon-Kuthon share many similarities with Morgion, actually: Both are considered mad, and both seem to enjoy the pain and suffering of others.

Kuthites [followers of Zon-Kuthon] run the gamut in their origins and motivations for joining the faith, whether they be evil sadists, demented masochists, or those whose spirits are so wounded that only overwhelming pain distracts them from their sorrows. Others who immerse themselves in spiritual darkness often find themselves drawn to his anthracite embrace.

[...]

Clergy tend to take their fervor for pain and agony to higher levels than lay believers, but are also experts at blending in with normal society.

[...]

Temples of Zon-Kuthon are, for all intents and purposes, torture chambers, and often function as such even when not in use for religious ceremonies. Because of the unique and often disapproved-of practices that take place in the church, temporary temples in caves or basements are kept fairly simple with decorations and tools brought in especially for services. The tools are often disguised as farming implements, should the secret cult be exposed. In more remote areas, believers might make impromptu shrines in places where violence and pain have occurred.

[...]

Kuthites are not bookish worshipers, often choosing to experience their faith rather than study it in a text.

-- Source: Pathfinder Wiki, https://pathfinderwiki.com/wiki/Zon-Kuthon

This clearly makes suffering a tool of enlightenment, at least, in the minds of Zon-Kuthon's followers.

Silent Hill

© Konami

The series of video games, Silent Hill, is known to its disturbing horror, self-inflicted psychological pain due to real or imagined guilt.

The first and third installments are all about a cult trying to bring back some kind of (genuine) paradise through inflicting pain and torture.

The second is actually a self-inflicted hell, by people who have, consciously or not, committed real (or imagined) crimes, and whose guilt (real, or imagined) is now torturing them. There's nothing binary there, only gray areas. In a way similar to Ravenloft's Dark Powers, Silent Hill seems to twist reality to trap its victims, amplifying their pain.

Then, there's the body horror, and the monsters. All you have to do is to google "silent hill monsters" (warning, explicit/disturbing content: https://www.google.com/search?tbm=isch&safe=off&q=silent%20hill%20monsters), and you'll find the horrific, disturbing, and yet fascinating creations of Team Silent, the original developers of Silent Hill. (Also, the music... seriously).

Resident Evil

Despite what one may think, Resident Evil is about mutation. The "undead" zombies are a byproduct of a contamination with the T-virus or one of its variants. But the most important effects of these viruses and parasites are the exceptional and obscene mutations of some of the host bodies, turning them into a great variety of monsters, depending on circumstances.

You can find examples of these grotesque monsters in the following link (warning, explicit/disturbing content): https://www.google.com/search?q=resident+evil+monsters&tbm=isch&oq=resident+evil+monsters&safe=off

Unlike the other inspiration sources, the Resident Evil monsters are there only to provide a roster of creatures.

The Tzimisce Vampires

Vicissitude, by John Cobb

Created by White Wolf for their Vampire: The Masquerade role-playing games, the Tzimisce are demented, monstrous deviants, dealing with torture and body horror.

Their main power, Vicissitude, is all about body modification, both of the self, and others. And Tzimisce do enjoy experimenting on others, finding there some kind of crazy spirituality.

Tzimisce are the stuff of nightmares, even for other vampires (who are far from being angels themselves). One would rightly prefer Final Death to falling into the hand of a Tzimisce, and those unlucky to find themselves the subject of Tzimisce's experimentations (or art creation!) sometimes come out "whole", even if joining their torturers in their cruelty and spiritual beliefs.

Other Sources of Inspiration?

There are other potential sources of inspiration, but they all fall back into one of the examples above. For example, the Cenobites from the Hellraiser movies, which are, arguably similar to Zon-Kuthon, above.

Partial conclusion

All these inspirations lead us to a variant of Morgion, which (hopefully) is more "active" and has a clear motivation beyond ruining everyone's day.

Morgion, divine power of Ordeal

Morgion represents the divine power of ordeal: Only through pain and suffering can one soul find true enlightenment.

Any kind of suffering will do: disease, madness, physical and psychological torture. And it is best when self-inflicted, even if unwilling subjects can still profit from a fraction of their "beneficial" effects.

Mercy is, in the disturbing mind of Morgion or his followers, an empty lie, leading to a stagnation of the soul. It is much better to foster its growth and self-understanding by pushing its limits beyond what it can tolerate. Some will never recover from the ordeal, falling into catatonia that won't really protect them from further abuse. But others will ascend into a higher understanding of the soul, and will become true paragons of Morgion's philosophy.

A victim of Morgion's acts might search for Mishakal for relief... or might become so damaged mentally they now embrace their suffering. A sadist might find in Morgion's teaching some kind of moral excuse to indulge in their urges. A torturer or executioner might find solace in "knowing" their victims will grow spiritually under their "care". Truth is, Morgion doesn't really care about the original motivations: Both the tormenter and the tormented will learn from the ordeal.

Of course, from the outside, Morgion's small cult of followers are best described as a group of cruel, sadistic and masochistic creatures, enjoying inflicting pain on themselves, as well on others. There are also rumors of monstrous, aberrant creatures flesh-sculpted from victims (or even leaders?) of the cult.

Conclusion

Followers of Morgion are not anymore coerced into having faith. They are not unwilling victims (at least, not anymore). They are active believers in some kind of deviant spirituality that is pushed into extremes, that leads to horrific acts, all in the name of spiritual enlightenment and ascension.

In the end, instead of dumb cultists to oppose our heroes, we can now have a wide range of either gory or sophisticated cultists, both primal and civilized, all hell-bent into sharing their vision of enlightenment with others, with of without their consent.

I sincerely believe this version of Morgion is more "believable" than the original one.

The Fate of the Ogre

The Irda, by Larry Elmore

As I engrave this last account from the might Ogre Empire, I feel the curse of the gods coursing through my blood.

Let the last of my words warn you, mortals, of the price of hubris.

The Might of the Ogre

We were the First.

The beloved of the gods.

Our might spanned the continent, cowing the lesser races as well as the mighty dragons.

Our cities crowned mountains, floating above clouds.

Our slaves revered our power, and willingly submitted themselves to our superiority.

Our magic was unparalleled.

But none of it equalled our pride.

The Pride of the Ogres

Despite our near perfection, our flaws were apparent to our beloved Emperor.

We were mortals, albeit longer lived than any other soul. Diseases could still bring us down despite our knowledge. Our magic could warp the ground, and raise the seas, and even brighten the skies... But the stars were still out of our reach. As were the Realms of the Gods.

Surely this was our last challenge, set by the gods to weed out the unworthy from the worthy.

And, our beloved Emperor claimed: The Ogre were worthy.

The Test of the Ogre

The first steps were easy. For the challenges were nothing compared to our might and wisdom.

The gods smiled on us. Majestic Paladine, wise Gilean, and magnificent Takhisis.

They acknowledged our claim to Ascension, a celestial sign, a single comet burning through the night skies.

And we rejoiced.

They honored us with more challenges, hardening us, so we could make them proud, for all the multiverse to witness the worth and might of the ogre of Krynn.

And with each step on, with each success, the Comet of Ascension would greet us in the skies.

Nothing would stop us from reaching the gods, bow to them one last time in respect, then join them in herding the clueless mortals we would leave behind.

Or so the Emperor said.

And so we all believed.

Oh... How wrong we were.

The Fall of the Ogre

The Emperor gathered us all in Giant's Hall, our mighty capital of marble and silver and gold.

And as the sun rose on the horizon, and as its light poured on us, we all joined the Emperor. Old and young. Noble and Common. Whispering the words, waving our magic so the power of the sun would become our power.

The sun turned blue, then red as it reached its zenith.

The other races could only witness our greatness, envious of our power, and of our worthiness. The dragons raged, impotent, as we had now outshined them.

Even the stars shined in the daylight, welcoming our ascension. And the Soaring Comet has never been so large and so bright in the sky.

We felt the gaze of the gods upon us, and we smiled in pride.

"We are your creation!" claimed our Emperor. "It is now time the children joined the parents."

Then, as he wove the last strands of magic, stealing the power of the sun, and the divinity of the Comet, the Emperor stuttered.

And the gem cracked.

A blinding light surrounded us.

And when we could see again, the sun was normal, in the sky. The stars were nowhere to be seen. The comet had been dissolved, its power absorbed by the Might Ogre Race.

Or so we thought.

Oh... How wrong we were.

The Truth of the Ogre

The Ascended Ogres dispersed, waiting for the divine magic's effects to manifest.

And manifest it did.

In the next months, a few among the newborn, the first ascended babies, the future of the Ogre.

Our blind faith turned sour.

Instead of divine beings, they were mutated, pitiful monstrosities. The Emperor was silent, as the first two-headed baby was presented to him.

For he knew.

He had known the whole time, he told me. Ever since he had stuttered.

The gods had never welcomed the Ogre among them. The Comet of Ascension had been a warning of our impending destruction. A warning, in our pride, we mistook for an invitation. That fateful day, by unraveling the ritual, the Emperor had avoided the immediate destruction of our race... But the damage had been done.

The Commons whispered that Igraine, the Traitor, had been right.

They revolted against the Nobles, who had misled them. The Nobles revolted against the Emperor, and the Wise counseling him, for having failed. The slaves revolted against us, for being weak.

Our Empire faltered.

The Decay of the Ogre

I've seen the future of the Ogre.

The dread disease is now part of our blood. The mutation cannot be stopped. Our magic is faltering. Our wisdom is decaying. Our perfection is unraveling.

The Ogre will pay for their pride with the annihilation of our civilization and our race.

The Last Witness

My city is burning. The mob had hunted me. Right to my own tomb.

And here, entombed under the rocks of the mountain, I await my death.

The gods' lies has been revealed.

I regret nothing, for we were worthy, and the gods feared us.

I'd rather die knowing the gods feared us, than live a coward bowing to them, as Igraine's Chosen must be, at this very moment.

One Last Warning

You, who will read this, long after my death: Heed my warning.

The gods are jealous.

They won't share the power.

But remember: The power isn't theirs.

"So, that is what happened to the ogre," the lich, powerful and terrible, said, his sepulchral voice echoing in the tomb. He crossed his skelettal arms over his chest with a grim satisfaction, the purple light radiating from his empty sockets flashing. "They lost control."

At the entrance of the chambers, the guards witnessed the purple robes examining every inch of the heart of the tomb.

"This ogre is long gone," the ghoul, beautiful and majestic, answered, lowering her hand as her necromancy had failed to summon the long lost soul. She turned away from the large skeletal remains on the ground, and walked back toward the lich. "Its bones still radiate magic, though. Chaos magic."

The lich's gaze turned towards the Ghoul Queen. He hated her. She visibly couldn't care less.

"The gem is at Giant's Hall," he said, turning toward the purple robes. "Copy every sentence, every glyph, every drawing. Somewhere in this tomb is the location of Giant's Hall. Find it."

He saw the Ghoul Queen walk away, silently.

"Where are you going?" he asked, his voice menacing. "Our work here is not finished."

She turned, smiling, and revealing elongated canines as she did.

"The gem is cracked, Ardhalox," Sylvyana reminded the lich, dismissively. "The magical focus is broken, and six thousand years old. You might harvest more magic from these old bones, than from that stone."

She shrugged.

"I am expected at Neraka," she explained, turning away. "I'd rather spend my time there, with the living and the undead, than crawling through tombs, dust and old bones." She stopped, adding: "Please do not hesitate to tell me, should you find the ogre ruins."

Ardhalox, high necromancer of the Purple Robes, eyed the Chemosh's Chosen walk away, flaunting his authority.

Not for very long, if everything went as expected...

"Oh, you'll know..." he whispered, before turning back to his work.

Astrophysics of Krynn, part 3

 In the previous and previous posts, we figured:

• Earth: 6,371.00 km (mean radius)
• Krynn: 2,376.45 km (radius)
• Luna (Earth's moon): 1,737.4 km (mean radius)

... and:

• Solinari (36 days): 460,540 km radius orbit around Krynn
• Lunitari (28 days): 389,498 km radius orbit around Krynn
• Nuitari (8 days): 168,963 km radius orbit around Krynn

In this post, we'll try to deduce the radius of each of the moons of Krynn.

What's the data

There is no data. But we can use the following hints:

• Let's assume that Krynn's sun is of the same size, and same distance as Earth's sun.
• Let's assume that Lunitari is of the same size as Luna

This has interesting consequences:

• Lunitari is able to make a beautiful eclipse, hiding the sun (as Luna hides the sun)
• Solinari will hide more than the sun during an eclipse (i.e. probably no visible corona)
• Nuitari is unable to hide the sun, but will put a black point within the sun during an "eclipse"

Also, I want the following data to be true:

• When Solinari, Lunitari and Nuitari are in conjunction, I want a beautiful "eye" to form in the sky, as below:

In other words, the apparent radius of each moon need to have a specific size in relation to the others. For example, using the drawings I did:

• Solinari: 64 px
• Lunitari: 40 px
• Nuitari: 20 px

Two-moons conjunctions will result the following image in the sky:

For reference, you'll find below the image of each individual moon, with a green circle representing the size of Luna, for comparison's sake:

Also, all the moons are tidally locked with Krynn.

So? Lunitari

Disclaimer: Again, I'll be rounding a lot. In particular, the difference at sea altitude, between Krynn and Earth is negligible, and thus, neglected. Also, the difference between the radius of Krynn, and the radius of any moon's orbit can also be considered as negligible, so distances will be taken from the center of Krynn, not the surface. Last but not least, we'll assume angles are small enough to approximate A, tan(A) and sin(A) as the same values, in radians.

The good point about the data is that it simplifies some calculations: Luna and Lunitari have the same orbital period, and are at the same distance from their planet, and have the same apparent size, so, they have the same radius: 1,737.4 km

The angular diameter of Lunitari (and Luna) is thus (with rMoon being the radius of the moon, and D being the distance between the center of Krynn and the center of the moon):

δ = 2 arcsin(rMoon / D)

δ = 2 * rMoon / D

For Lunitari, this would be:

δ = 2 * 1,737.4 km / 389,498 km

δ = 0.00892122

Et voilà...

How to calculate the other moons?

The apparent diameter of the other moons is a factor of Lunitari's:

• Solinari = Lunitari * 1.6
• Nuitari = Lunitari / 2

This means the angular diameter of the moons are thus:

• δSolinari = 0.00892122 * 1.6 = 0.01427395
• δLunitari = 0.00892122
• δNuitari = 0.00892122 / 2 = 0.00446061

We can then, knowing their real distance, find their real radius:

δ = 2 * rMoon / D

rMoon = δ * D / 2

... which resolves into:

• rSolinari = 0.01427395 * 460,540 km / 2 = 3,287 km
• rLunitari = 1,737 km
• rNuitari = 0.00446061 * 168,963 km / 2 = 377 km

Et voilà...

Conclusion

We know have the following data:

• Earth: 6,371.00 km (mean radius)
• Krynn: 2,376.45 km (radius)
• Luna (Earth's moon): 1,737.4 km (mean radius)

... and:

• Solinari (36 days): 460,540 km radius orbit around Krynn
• Lunitari (28 days): 389,498 km radius orbit around Krynn
• Nuitari (8 days): 168,963 km radius orbit around Krynn

 ... and:

• Solinari (radius) = 3,287 km
• Lunitari (radius) = 1,737 km
• Nuitari (radius) = 377 km

So... yeah, Solinari is larger than Krynn... That is awkward, but unavoidable because our calculations our correct.

(Remember the cause of all of this is the small size of Krynn)

😁

The good thing is:

• No one will go there to verify (even if this can be deduced, the same way the ancient Greeks deduced the size of Luna when it passed through Earth's shadow)
• Even if one did, it's a fantasy world
• Also, Solinari (and the other moons) might have a very low density to counteract their size
• If we assume all the moons have the same albedo as Luna, then nights on Krynn can be much more luminous than on Earth
  

Astrophysics of Krynn, part 2

In the previous part, we found Krynn was a very small, but very dense planet, compared to Earth, both planets having the same mass, though.

Now, I will be using physics from high school for fun, to prove something that is very interesting, and then get an equation that will give the the orbit radius of all of Krynn's moons.

Disclaimer: I'm doing a lot of careless rounding, here, partly because I forgot half the tricks to do exact calculations with error margins, and partly because I don't really care about exact numbers.

Let's Physics!

Believe it or not, but the characteristics of a stable circular orbit of a moon around its planet depends only on the mass of the planet, and the distance between the moon and the planet.

On one hand, you have the Newtonian: ΣF = m.a

On the other, you have the Newtonian gravitation: F = G.m1.m2 / (r²)

Assuming that the mass of the moon is negligible when compared to the mass of the planet simplify the problems because then, the planet doesn't move, and only the moon moves.

So, for the moon, what you have is:

mMoon.aMoon = G.mPlanet.mMoon / (r²)

Which simplifies into:

aMoon = G.mPlanet / (r²)

So, the distance between the two bodies (here, r), is:

r² = G * mPlanet / aMoon

Fun fact, the centripete acceleration of the moon in a stable circular orbit is a function of its tengent speed, and thus, of its orbital period. Indeed, the equation is:

a = v² / r (with v being the tangential speed)

We also know:

• - v = ω.r (where ω is the angular velocity)
• - ω = 2π / T (where T is the orbital period, i.e. the time to complete ONE orbit)

Dropping the minus sign (because we already know the direction), we can deduce:

v = ω.r = 2π / T * r = 2π * r / T

So, now, we can deduce the acceleration a from the speed v and the orbit radius r:

a = v² / r

a = (2π * r / T)² / r

a = 4π²  * r² / T² / r

a = 4π² * r / T²

As we are studying the acceleration of the moon aMoon:

r² = G * mPlanet / aMoon

r² = aMoon / G / mPlanet

... we can then replace aMoon with 4π² * r / T²:

r² = G * mPlanet / (4π² * r / T²)

r² = G * mPlanet * T² / 4π² / r

r^3 = G * mPlanet * T² / 4π²

As you can see, the orbit's radius of the moon only depends on its orbital period, and on the mass of the planet.

Assuming G and mPlanet never change, we can replace them with their values:

• G = 6.674×10^-11 m^3⋅kg^-1⋅s^-2
• mEarth = 5.97237×10^24 kg

(We use the mass of Earth as we showed previously the mass of Krynn was the same), which means the equation becomes:

r^3 = 6.674×10^-11 m^3⋅kg^-1⋅s^-2 * 5.97237×10^24 kg * T² / 4π²

r^3 = 6.674×10^-11 m^3⋅s^-2 * 5.97237×10^24 * T² / 4π²

T is given in seconds, but I would be more interested in its "days" unit.

So we can deduce that:

T = D * 60 * 60 * 24 s

Where D is the number of days. Thus:

T = D * 60 * 60 * 24 s

T = D * 86400 s

T² = D² * 7,464,960,000 s^2

T² = D² * 7.464,960,000 × 10^9 s^2

Going back to the equation, we get:

r^3 = 6.674×10^-11 m^3.s^-2 * 5.972,37×10^24 * D² * 7.464,960,000 × 10^9 s^2 / 4π²

r^3 = 6.674 m^3 * 5.972,37×10^22 * D² * 7.464,960,000 / 4π²

r^3 = 6.674 * 5.972,37×10^22 * D² * 7.464,960,000 / 4π² m^3

r^3 = 6.674 * 5.972,37 * D² * 7.464,960,000 / 4π² × 10^22 m^3

r^3 = 6.674 * 5.972,37 * 7.464,960,000 / 4π² * 10^22 * D² m^3

r^3 = 297.550 / 4π² * 10^22 * D² m^3

r^3 = 7.537,04 * 10^22 * D² m^3

r^3 = 75.370,4 * 10^21 * D² m^3

r^3 = 4.224,096^3 * (10^7)^3 * D^(2*3/3) m^3

r = 4.224,096 * 10^7 * D^(2/3) m

r = 4.224,096 * 10^4 * D^(2/3) km

... which means we have the equation to calculate the radius r of the orbit of a moon, if we know the moon's period, in days D around a planet of the same mass as Earth, like Krynn.

Wait, are you sure?

To prove I'm not wrong in the details, let's put Luna (Earth's moon) in the equation.

For, the Luna, let's assume that the period is 28 days:

28 ^ (2/3) = 9.220,87

... which means the equation becomes:

r = 4.224,096 * 10^4 * 9.220,87 km

r = 38.949,8 * 10^4 km

r = 389,498 km 

... which is more or less the average between the apogee and perigee of Luna.

So, yeah, my calculations are right...

😉

Back to Krynn: Solinari, Lunitari & Nuitari ?

The periods of each of Krynn's moon is:

• Solinari: 36 days
• Lunitari: 28 days
• Nuitari: 8 days

So, to get the orbital radius of these moons, all we have is to feed the equation with the data:

• Solinari: 36 days => 4.224,096 * 10^4 * 36^(2/3) km
• Lunitari: 28 days => 4.224,096 * 10^4 * 28^(2/3) km
• Nuitari: 8 days => 4.224,096 * 10^4 * 8^(2/3) km

... which gives:

• Solinari: 36 days => 42,240.96 * 10.902,7 km
• Lunitari: 28 days => 42,240.96 * 9.220,87 km
• Nuitari: 8 days => 42,240.96 * 4 km

... which gives the orbital radius (i.e. the distance between the center of the moon, and Krynn):

• Solinari: 36 days => 460,540 km
• Lunitari: 28 days => 389,498 km
• Nuitari: 8 days => 168,963 km

Et voilà...

😉

In the next post, we will calculate the radius of each of Krynn's moons.