Method 3: Out from the Center
For this method, we start with the calculated Innermost Stable Orbit (IS or Oi), add rand[0.1, 0.5] AU, and then proceed to add planets at intervals of rand[1.4, 2.0] AU, out to the limit of Neptune’s orbit, or 40 AU, whichever is greater.
So, for IS = 0.276, adding the maximum of 0.05 AU reveals that the first orbital distance would be 0.310 AU. Using the random sequence:
{1.4, 1.6, 2.0, 2.0, 1.4, 1.7, 2.0, 1.5, 1.9, 1.4}
We simply multiply from left-to-right, arriving at the orbital sequence:
{0.310, 0.434, 0.694, 1.389, 2.778, 3.889, 6.611, 13.221, 19.832, 37.681, 52.753}
And we arrive at the following table:
{1.4, 1.6, 2.0, 2.0, 1.4, 1.7, 2.0, 1.5, 1.9, 1.4}
We simply multiply from left-to-right, arriving at the orbital sequence:
{0.310, 0.434, 0.694, 1.389, 2.778, 3.889, 6.611, 13.221, 19.832, 37.681, 52.753}
And we arrive at the following table:
… we obtain an orbital sequence not drastically unlike those resulting from the other two methods. Again, by randomizing the orbital intervals to 2 or 3 decimal places, we could produce more precise intervals and more “natural” seeming orbits.
Because this system uses the Innermost Stable Orbit of the star (or the Innermost Stable Orbit of a binary system) as its starting point, there is never a concern of an orbit falling too close to the star(s), nor of the first orbit falling unrealistically beyond the closest safe orbit.
The example above is for the fictional star, Nysheryn, which we specified in the previous blog to have a luminosity of 2.76⊙ and thus an Innermost Stable Orbit of 0.276 AU.
Let's try this method out on the also fictional star Anra (also described in the previous blog), with a luminosity of 0.76⊙ and an Innermost Stable Orbit of 0.093 AU.
First, we define the closest orbit to be some value greater than 0.093 AU by adding rand[0.01, 0.05] AU; let's say it comes out to 0.11 AU.
We then generate a random sequence of 10 intervals in the range rand[1.40, 2.00]:
{1.77, 1.87, 1.59, 1.92, 1.95, 1.41, 1.53, 1.98, 1.67, 1.74}
Starting from 0.11, we multiply from left to right: 0.11 AU ⨉ 1.77 = 1.95 AU, etc., to produce the following table of orbits:
Because this system uses the Innermost Stable Orbit of the star (or the Innermost Stable Orbit of a binary system) as its starting point, there is never a concern of an orbit falling too close to the star(s), nor of the first orbit falling unrealistically beyond the closest safe orbit.
The example above is for the fictional star, Nysheryn, which we specified in the previous blog to have a luminosity of 2.76⊙ and thus an Innermost Stable Orbit of 0.276 AU.
Let's try this method out on the also fictional star Anra (also described in the previous blog), with a luminosity of 0.76⊙ and an Innermost Stable Orbit of 0.093 AU.
First, we define the closest orbit to be some value greater than 0.093 AU by adding rand[0.01, 0.05] AU; let's say it comes out to 0.11 AU.
We then generate a random sequence of 10 intervals in the range rand[1.40, 2.00]:
{1.77, 1.87, 1.59, 1.92, 1.95, 1.41, 1.53, 1.98, 1.67, 1.74}
Starting from 0.11, we multiply from left to right: 0.11 AU ⨉ 1.77 = 1.95 AU, etc., to produce the following table of orbits:
... which seem quite reasonable and realistic.
- The nearest planet is just beyond the Innermost Stable Orbit;
- The farthest planet is well within the 35-40 AU "limit";
- The orbital intervals are within the range found in the Solar System;
- The orbital gaps tend to grow as distance from the star increases, again in keeping with observed phenomena.
Conclusion
This is a good, robust way of calculating planetary orbits around fictional stars, especially when the Worldbuilder already has a specific luminosity in mind for the star.
This system shares with the previous ones the potential problem of no planet falling at precisely 1.0 AU, and thus, the need to create specialized time-keeping methods and processes.
This system shares with the previous ones the potential problem of no planet falling at precisely 1.0 AU, and thus, the need to create specialized time-keeping methods and processes.
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