# What is the formula/logic behind the Orbital Factor table?

The Orbital Factor table appears in MegaTraveller and The New Era, in World Tamer's Handbook, page 84. The numbers appear to be derived from what I can only assume is a formula. It has piqued my curiosity, but so far I've only come across a vague reference on a forum. Which is sort of surprising.

What is the formula behind or the logic involved in these numbers?

• What page of TNE are you looking at, and what is the exact name of the table? There's no table by that exact name in my copy of the rules, and the only one that fits your description is the Orbital Distances tale on page 195. Reposted because there's a bug that only lets you edit your comments for five minutes. Jun 22 '17 at 4:05
• ah, that is the one . . . item #45 Orbital Distances. The table appears to have rounded numbers for the solar system, token world-building. Orbital factor, the subject I was interested in, shows up in World Tamer's Handbook, page 84 ( Orbital Distances is on the preceding page ). Jun 25 '17 at 18:27
• Perhaps the question should be edited to reflect the -exact- topic of interest? Based on the comments I am not sure if the question pertains to Orbital Distances (TNE) or Orbital Factor (World Tamer's Handbook) :) Additionally, have you tried asking this question on the Mongoose Forums? Jul 28 '17 at 19:20

TL;DR: Given a distance in millions of kilometers: $$O = \frac{4574}{\sqrt{D}}$$

That's how you derive it. But for the logic behind it...

The formula from page 84 of the World Tamer's Handbook, $$T=LOEG$$ takes four pieces of information generated from the RPG tables to calculate the fifth, temperature:

• T is the temperature, in kelvin.
• L is the luminosity
• O is the orbital factor, where an 'orbit' means one of the orbits generated in step eleven of orbit generation (on page 192 of TNE core) with the orbital distances defined on step 45 (page 195 of TNE core), following the Titius-Bode law which most space RPGs of the decade used for spacing orbits.
• G is the 'greenhouse effect', which represents atmospheric influence.
• E is the energy absorption factor (i.e., how close to a perfect blackbody the planet is).

Now, outside of the Traveller RPG, in physics, the formula to calculate the radiative equilibrium temperature of a black body is:

$$T = \sqrt[4]{\frac{L(1-ɑ)}{16πσD^2}}$$

(Where σ is the Stefan–Boltzmann constant. This constant maps power per unit area - i.e., luminosity - to temperature. You can find out a lot more information about this formula on the astronomy stackexchange.)

Since we're looking to define O, we can simplify this formula by taking out other aspects of the Traveller formula.

Since the greenhouse effect G has a static effect which is not dependent in any way on L or O or E, we can remove G as effectively being a constant:

$$T = LOE$$

The effective albedo of the planet E is also a static value which is not dependent on L or O, so we can treat it as a constant as well:

$$T = LO$$

With those two terms removed, we can simplify the formula:

$$T = \sqrt[4]{\frac{L}{16πσD^2}}$$

We already know that the orbital factors value includes all the constant scalars to convert real-world physics values into game-table-friendly values, so we can remove the constants for the purpose of simplification:

$$T = \sqrt[4]{\frac{L}{D^2}}$$

Now, can we take this simplification, and use it to turn the orbital factors into a real-world measurement? Yes.

Take any orbital factor on the Orbital Factor table, and look up the distance in millions of kilometers on the Orbital Distances Table on page 195 of the TNE core rulebook. For illustration, let's use orbit 7:

$$D = 1495.9$$

Look up the orbital factor from page 84 of the World Tamer's rulebook.

$$O = 118.277$$

Multiply the orbital factor by the 4th root of square of the distance - which is to say, the square root of the distance. (In this case, the table is in millions of of kilometers.)

$$O \times \sqrt{D} = T$$

$$118.277 \times \sqrt{1495.9} = 4574.58$$

No matter what orbital factor you chose, you get within one of 4574. That is to say... the radiative equilibrium temperature in kelvin that a planet would be if it were some hypothetical ideal atmosphereless planet which was orbiting one million kilometers around a sun with a luminosity equal to Sol's.

• . . . close, but you should clarify you used kilometers. COTI has a similar formula but uses AU and avg earth temp; closer to book numbers. I really like your logic walk-thru. not enough points to close question Personally I think they were trying to show Isolation, but I cannot find when the formula was discovered ( in relation to the books release date ). May 27 '18 at 18:56