Can I base my system orbits around the habitable zone orbits?
- Design the orbits after the star is designed.
- Design the star based on the orbits.
Lets look at them in turn.
Based On The Star
We specified that Nysheryn had a luminosity of 2.76 times that of the Sun. This would lead to a nucleal habitable zone orbit of:
In the Follow the Giant system, the first gas giant planet is located according to the frost line, and then other orbits are devised by multiplying (for planets farther out) or or dividing (for planets closer in) each generated orbit by a random value in the range [1.4, 2.0] AU.
For this current method, we already know the location of the orbit we want our planet (call it Ardesh) to have: 1.661 AU. So, we can simply calculate other orbits based on that one. As with the Follow the Giant method, we calculate the closer-in orbits using the iterative equation:
Based On A Pre-Selected Orbit
Is the planet's orbit the nominal habitable zone orbit?
If so, then we can calculate the luminosity of the star by squaring the value of the planet's orbit in AU, and proceed with the method outlined above.
If not, then we have yet another couple of decisions to make:
Is the planet orbiting inside or outside the nucleal habitable zone orbit?
If it is inside the HZN, then the apparent brightness of the star will be > 1.0 times that of the Sun, otherwise it will be < 1.0 times that of the Sun. Based on that decision, we have a further choice:
Do we want to choose a nucleal habitable zone or the apparent brightness of the star?
Choosing a value for the HZN means we can determine the system orbits in the same way as putting our planet on the HZN; otherwise,
What apparent brightness do we want our planet's host star to have?
Selecting a value for the absolute brightness will require us to determine the luminosity of the star based on that value and the distance of our planet's orbit.
Option 1: The Planet's Orbit Is At the Nucleal Habitable Zone Distance
Note that because Skelys is at the nucleal habitable zone distance, we automatically know that Raigeld's apparent brightness is 1.0 times that of the Sun.
Option 2: The Planet's Orbit Is Not At the Nucleal Habitable Zone Distance
So, if our planet is orbiting closer than the HZN, we know that the star has to have an apparent brightness greater-than that of the Sun as seen from Earth. That value is still completely up to us—as long as we're allowing the properties of the star to be determined by the orbital characteristics alone.
Let's specify that the apparent brightness of Yheru at Osar's orbit is 1.371 times that of the Sun as seen from Earth. The equation that gives us Yheru's luminosity is the apparent brightness multiplied by the square of the orbital distance:
Some care should be taken at this point—certain combinations of apparent brightnesses and orbital distances may result in luminosities that move the habitable zone limits closer to or farther from the star than the specified planet's orbit.
Note that orbital distance 5 also falls within the optimistic habitable zone limits, so a planet which is (in)habitable could be placed on that orbit.