*Can I base my system orbits around the habitable zone orbits?*

I received the above question as a private message through my Facebook page and I'm a bit embarrassed that I hadn't thought of this method, myself—so, here's what I've come up with as an answer.

## Two Approaches

There are two ways this could be handled.

Lets look at them in turn.

- 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

Let's revisit our fictional star, Nysheryn, from the blog "Designing System Orbits, Part 2: Titius-Bode".

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:

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:

… and an innermost stable orbit of:

Assuming we want to put a habitable planet at that orbit, we can use a system similar to the one described in "Designing System Orbits, Part 1: Follow the Giant" to generate potential orbits for the rest of the system.

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:

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:

Until we reach the smallest orbital distance which is larger than the innermost stable orbit distance of 0.1661 AU. Let's say we randomize a set of 8 values from the range [1.400, 2.000], and come up with the list {1.852, 1.625, 1.461, 1.515, 1.786, 1.647, 1.783, 1.462}. This results in the following table:

The values starting with row 6 are below the innermost stable orbit for Nysheryn, so they can be discarded as potential planet orbits. There is no theoretical limit to the number of orbits beyond 1.661 AU are possible (up to the Hill sphere for Nysheryn), but orbits beyond 50 or so AU tend not to be common. A random list of 7 values in the range [1.400, 2.000] produces the list {1.820, 1.687, 1.615, 1.533, 1.861, 1.990, 1.633}, and an orbits table of:

The next outer orbit of 76.358 is greater than 50 AU, so we can safely discard stop with these six additional potential orbits, which produces a final potential orbital table of:

Adding in the fundamental orbital values:

Reveals that there is no orbit with a period of one Earth year (because there is no orbit at exactly 1.0 AU); there is only the one planet (Ardesh) in the habitable zone; the eighth potential orbit would be home to the first gas giant in the Nysheryn system; and, the gap between orbits 6 and 7 is the first one wide enough to house an asteroid belt.

## Based On A Pre-Selected Orbit

This process is more complex: we must first decide on an orbital distance—or an orbital period—we want our planet to have. Then, we have further decisions to make:

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:

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,

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.

**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

Knowing the orbital distance of our planet (let's name it Skelys), orbiting a distance of 0.577 AU from its host star. We can then determine that the luminosity of the star (call it Raigeld) is:

… about one-third that of the Sun, and we can use that value to calculate the other fundamental orbital values.

Let's use the same random sets of intervals from the Nysheryn system, above, to determine the orbits for the Raigeld system. The list for the inner orbits was {1.852, 1.625, 1.461, 1.515, 1.786, 1.647, 1.783, 1.462}, and the list for the outer orbits was {1.820, 1.687, 1.615, 1.533, 1.861, 1.990, 1.633}. Using these values produces the following table of potential orbits.

Potential orbits 1, 2, and 3 are all smaller than the calculated innermost stable orbit of 0.0577, so they can be discarded. Adding in the fundamental orbits and estimated orbital periods results in the following table:

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

Let's say that our planet (Osar) is orbiting at 1.563 AU but that is NOT the nucleal habitable zone orbit. We now have to decide whether the nucleal habitable zone orbit is less-than 1.563 AU or greater-than 1.563 AU. Let's say that the nucleal habitable zone orbit is farther out than Osar's orbit, and let's specify an apparent brightness for our star (Yheru), rather than specifying the HZN for the system. (Taking this route will allow us to work through an example which is different from those above.)

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:

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.

Based on this value for Yheru's luminosity, we can calculate the fundamental orbits for the system:

And—again—reusing the randomized interval values from above, we produce the following system table for Yheru:

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.

## Starting With An Orbital Period Instead Of An Orbital Distance

If we wanted to start with an orbital period instead of an orbital distance, we would just calculate the orbital distance from the orbital period and then follow the steps above. For instance, let's say we've decided we want our planet's orbital period to be 1.618 Earth years. Its period, then—using the simplified equation that doesn't require knowing the masses of the star and planet—is given by the equation:

… and our fictional planet's orbital distance would be:

Using that value, we'd then decide whether that is the HZN, or if the HZN is closer to or farther from the star, and follow the appropriate system from above.

## Conclusion

So, short answer: Yes, you can design your system orbits based on the habitable zone orbits, by specifying certain parameters for your star or your planet's orbit, and calculating the values those parameters yield using the methods outlined above.