Planetary System

A star (and indeed, other bodies such as stellar remnants and sub-stellar objects) can host a **planetary system**. Planetary systems form from the protoplanetary disks that surround a protostar. Alternatively, they can form from the "fallback matter" of a supernova and can thus be found around neutron stars and black holes.

Planetary systems can exist around multiple-star systems.

## Stellar Parameters

There are a number of parameters that shape a planetary system. These parameters are all determined by a star's mass and/or luminosity.

Every planetary system has planetary limits. Within the inner boundary, the planet is disintegrated by the star's gravity. Beyond the outer boundary, the planet is ejected into space. The inner boundary is the Roche Limit of the two bodies (the primary being the star and the secondary being the planet), while the outer limit is the Hill Sphere of the star (with respect to its nearest stellar neighbour). However, these can be approximated (in AU) as:

The habitable zone of a star is the zone in which water exists in its liquid state. Any closer and it evaporates. Any further and it freezes. This zone is thought to be critical to a planet's habitability. It is determined as:

The frost line of a star system is the point beyond which "volatiles" such as water, methane, ammonia, carbon dioxide, etc. can condense into solid grains. It is thought that giant planets such as gas giants and ice giants can only form beyond this line. It is determined as:

## Orbits

### Orbital Properties

Every astronomical body orbits another body (either the star or another planet) in an elliptical orbit, which is described by a number of key characteristics, defined as follows:

* **Semi-Major Axis (a)**: The average distance from the planet to the star. When creating the orbit, we usually start by defining this, but if not it can be defined as the average of the periapsis and the apoapsis.
* **Eccentricity (e)**: The shape of the orbit, where e = 0 describes a perfect circle and e = 1 describes a parabola. When calculating your eccentricity, consider the following formula, which can be used as a guide when setting the eccentricities of orbiting bodies. *N* is the number of planets in the system and, as *N* increases, so too does the accuracy of the formula, therefore use this formula as a loose guide, rather than a strict rule.

* **Inclination (i)**: The angle between the star’s plane and the orbital plane of the planet. The intersections of a planet’s and the star’s plane are known as the ascending and descending nodes. Comparable to an aircraft’s pitch. Inclinations are measured in degrees, from 0° to 180°, where values of between 0° and 90° indicate prograde orbits and values of between 90° and 180° indicate retrograde ones.
* **Longitude of the Ascending Node (Ω)**: The angle between the ascending node and an arbitrary reference point parallel to the star’s plane, measured counter-clockwise. Comparable to an aircraft’s yaw.

### Guide to Stable Orbits

To create stable orbits in a planetary system, we start by placing our largest planet. The largest planet is usually a giant planet which orbits roughly 1 AU beyond the frost line. Stable orbits for outer planets in the system can be found by multiplying the semi-major axis of the largest planet by a number between 1.4 and 2, and then multiplying the semi-major axis of the new planet by another random number between 1.4 and 2, repeating until the outer planetary boundary (or Hill Sphere radius) is reached. Stable orbits for inner planets can be found in a similar way, but by dividing the semi-major axis of the planet by the number, rather than multiplying it, repeating until the inner planetary boundary (or roche limit, if it is preferred) is reached.

## References

1. ↑ Wikipedia: Planetary System
2. ↑ Wikipedia: Protoplanetary Disk
3. ↑ Artifexian: How to Create a Classical Planetary System
4. ↑ Wikipedia: Circumstellar Habitable Zone
5. ↑ Wikipedia: Frost Line