World Builder's Handbook Feedback

[Geir]

This is comically down the line from the original release, but...

Someone on the discord asked about the Tidal Heating Factor formula for moons, and if they'd done their computation right. In trying to help them, I suggested plugging in the values for Earth's moon and seeing if they matched what was given in the book as a way to test if they were using the right figures.

From the WBH, Page 126:


The formula given in the book is:
(M² * S⁵ * e²)/(3000 * a⁵ * P * m)
Where:

• M is the Primary's Mass (in M⨁)
• S is the World (i.e.: Moon's) size code
• e is the Moon's eccentricity
• a is the Moon's semimajor axis in millions of km
• P is the Moon's orbital period in days
• m is the World (i.e.: Moon's) mass (in M⨁)

For our Moon, those values are: M = 1; S = 2; e = 0.0549; a = 0.384399; P = 27.321661; m = 0.0123
Which when plugged into the equation give us:
(1² * 2⁵ * 0.0549²)/(3000 * 0.384399⁵ * 27.321661 * 0.0123) = (1 * 32 * 0.00301401)/(3000 * 0.00839288448 * 27.321661 * 0.0123) = 0.09644832/8.46144839481 = 0.01139855914

Which is a fair bit off of the given value of 52 for Luna.
Assuming that the formula given in the book as-presented is already incorporating the "divide by 3000" step, we still find a value of ≈ 34.195 and not the 52 given in the text.

I must assume I am doing something wrong, though what exactly I know not.

See the post above. I was being too clever by far...

 

[mando501]

I was wrong about being wrong…

Trying to reconstruct what I did 2+ years ago (with no notes, just spreadsheet scribbles)



Assumption One:

The factors I included for tidal energy change in the following manner: ~M^2*R^5* N* E^2/A^6

M=mass of planet

R = radius of world (or Size in this unitless case)

N = mean angular speed in orbit

E= eccentricity

A = orbital distance



From that, I considered N to be proportional to the circumference of the orbit / orbital period, so that’s proportional to 2*pi*A / P, where A is the orbital distance and P is the period… since the fudge factor to make the temperature work out is going to be a constant added later, we can ignore the 2*pi and we can reduce the power of A in the divisor from 6 to 5.

And this is the total amount of tidal energy.

So, Assumption Two:
The energy is going to be applied to the entire body and the actual temperature increase is therefore going to be proportional to the mass of the body heated – so 1/ Mass = the actual temperature increase on the body from tidal heating. (If you follow my assumption, all that energy goes into the object and it is applied in direct proportion to the mass – this is my weakest assumption, but there it is - I have a hindsight sneaky suspicion that it might be more correct to assume 1/ Mass^(1/4) ) .

So this gives the final formula as written:

~M^2*R^5* E^2/(A^5 * P * Mass of moon)

For Luna the values I plugged in were:

M =1

R = 2.17175 (here is where you’re going to get a difference for sure, since I took the radius of the moon divided by 1600 times 2 rather than just 2.)

E = 0.055 (not sure why I wasn’t so precise here, but at least I wasn’t off a full decimal point)

A= 0.3844

P= 27.322

M = 0.0123

Which should get you 51.81315 which rounds to 52, and then divide by 3000 to get 0.017271.



Is this correct? Don’t know. A real astrophysicist would probably complain a lot about my assumptions (especially the second one), but if you look at the Wikipedia article https://en.wikipedia.org/wiki/Tidal_heating (not my only source, but I never found anything more useful) it talks about things like “the imaginary portion of the second-order Love number)” and nope, I just wanted to get a number that gave a plausible temperature that varied in a plausible way based on values we already had.

Heh, no worries - less concerned about a PhD thesis and more concerned about consistency and reproducibility, and this helps greatly.

Now that I know that you were using diameters to compute size, rather than just use size, the pieces fall in to place, lol.

So to sum up, the disconnect seems to have been a few typos (including the orbital distance), and ambiguity on the actual values used. Perfect, I feel less crazy now

Thanks very much - I really appreciate you taking the time to dust off the cobwebs

 

[Reisender]

Here is a little mnemonic for remembering the sequence of spectral type letters:
Oh Be A Fine Girl Kiss Me

 

[MongooseMatt]

Here is a little mnemonic for remembering the sequence of spectral type letters:
Oh Be A Fine Girl Kiss Me

Or, if you are from a slightly different background, Oh Boy An F Grade Kills Me...

 

[Levi Dash Card]

What is the practical lower limit of MOR (p.76), with regards to a moon's orbit? I have a world with an HSML of 1.997, meaning MOR is -1. A negative MOR has the unique effect of a lower 2D-2 result creating a larger orbit than a higher 2D-2 result. (For my current world, a result of 0 provides orbital distances of 2.0pd (inner), 2.8pd (middle), and 3.5pd (outer); a result of 10 provides orbital distances of 1.8, 2.5, & 3.0, respectively.)

Is it best to conclude that the any HSML of 1.5 to under 4 should use a MOR of 1? Or, would it better to say any 0 or negative MOR is instead 0.5 (even if that would stunt the random effect of the 2D-2)?

 

[Geir]

What is the practical lower limit of MOR (p.76), with regards to a moon's orbit? I have a world with an HSML of 1.997, meaning MOR is -1. A negative MOR has the unique effect of a lower 2D-2 result creating a larger orbit than a higher 2D-2 result. (For my current world, a result of 0 provides orbital distances of 2.0pd (inner), 2.8pd (middle), and 3.5pd (outer); a result of 10 provides orbital distances of 1.8, 2.5, & 3.0, respectively.)

Is it best to conclude that the any HSML of 1.5 to under 4 should use a MOR of 1? Or, would it better to say any 0 or negative MOR is instead 0.5 (even if that would stunt the random effect of the 2D-2)?

I see what you're saying.
First, I think we I need to add a statement saying that any MOR below 0 is equal to 0. This would force the location equations to equal, at worst 2, 3, or 4. And then state any moons above the HSML should be discarded. So if the HSML is equal 2, you could keep that moon, but not any rolled as in the middle (3) or Outer (4) range. If the HSML is less than 1.5, then all moons fail. The only time you run into this condition is with a planet very close to its star, and it's reasonable to assume any moon would either have been pulled away or be pulled down into a ring (or worse - the rules don't say this, but if the HSML was actually less than 0.5 D, then you could imagine the world itself would be breaking up.

One thing not handled at all by these Moon Orbit rules is a Roche World situation (there's a Robert Forward book about basically contact binary worlds around Barnard's Star - doing this from memory, but I think that's right). Anyway, I suppose two bodies of equalish mass could exist in such a relationship, but if it's so close to the sun that the sun is pulling on the planets, (e.g., a very low HSML), then it wouldn't be a stable configuration.

 

[Levi Dash Card]

I see what you're saying.
First, I think we I need to add a statement saying that any MOR below 0 is equal to 0. This would force the location equations to equal, at worst 2, 3, or 4. And then state any moons above the HSML should be discarded. So if the HSML is equal 2, you could keep that moon, but not any rolled as in the middle (3) or Outer (4) range. If the HSML is less than 1.5, then all moons fail. The only time you run into this condition is with a planet very close to its star, and it's reasonable to assume any moon would either have been pulled away or be pulled down into a ring (or worse - the rules don't say this, but if the HSML was actually less than 0.5 D, then you could imagine the world itself would be breaking up.

One thing not handled at all by these Moon Orbit rules is a Roche World situation (there's a Robert Forward book about basically contact binary worlds around Barnard's Star - doing this from memory, but I think that's right). Anyway, I suppose two bodies of equalish mass could exist in such a relationship, but if it's so close to the sun that the sun is pulling on the planets, (e.g., a very low HSML), then it wouldn't be a stable configuration.

Thanks!

Yes, the span of the example system is 0.007, around an M9 V star of 0.093 solar masses. Even at a minimum 1.2x Spread per orbit, it's a tightly-packed system. Only two of my three gas giants had moons, and that totaled 5 between them (with one of those a ring) - three of the four moons went away with that clarification (although, luckily, the largest of them survived). Still managed to get a Hab 4 mainworld out of it.

It looks like my next system (#31 of 237) is going down the same path (M8 V, but only 0.084 solar masses)...

 

[CordwainerFish]

there's a Robert Forward book about basically contact binary worlds around Barnard's Star - doing this from memory, but I think that's right

Yep - Flight of the Dragonfly. Close enough to have enough common atmosphere to fly a plane from one to the other.