# Non-planar orbits

So far, even in complex systems with multiple stars and moons, we have assumed that all objects orbit in the same plane. Although for planets that were created from the same accretion disc, that tends to be approximately true, there are many known exoplanet systems where it is not. For instance, close encounters with sufficiently heavy gravitating bodies can change the orbital plane of a planet or even star.

When an orbit is tilted with respect to another reference orbit, two new orbital parameters become relevant. One of them is tha actual tilt angle between the orbital planes, the orbital inclination. The other is relevant if the reference orbit is not circular - the longitude of the ascending node describes where the tilt axis, relative to that reference point, actually lies. The ascending node is defined as the point where an orbit reaches above a reference plane (a third parameter, the argument of the periapsis, describes where the periapsis of the tilted orbit lies with respect to the node, but that is relevant in planar geometry as well and we introduced it already).

Tilting orbits with respect to each other does comparatively little in terms of thermal properties of planets, there are no genuinely new phenomena to observe that do not in principle also appear when axis tilts are studied, but a realistic distribution of orbital inclination reduces eclipses quite a lot and alters the simulated worlds in detail.

If we use the orbit of the planet around the star (or system CoG) as reference plane, then in the context of the simulation one can tilt a) the orbit of a star around the companion or b) the orbit of the star around the binary and c) the orbit of the moon around the planet.

## The Aquablue system

The following config file example28.cfg introduces the Aquablue system. The smaller star Thetis orbits the heavier companion Thalassa. In orbit around Thetis is the gas giant Charybdis, which in turn is orbited by the moon Aquablue.

The orbit of Thetis around Thalassa is slightly eccenntric and tilted by 30 degrees, whereas the orbit of Aquablue around Charybdis is significantly tilted by 70 degrees.

 config orbital_sim_timestep 30.0 apoapsis_init false star mass 0.65 T_surf 3900.0 name Thetis companion mass 2.7 T_surf 11500.0 name Thalassa apsis_angle 0 retrograde false planet name Charybdis mass 516.3 radius 12.9 semimajor_au 0.45 eccentricity 0.1 semimajor_longyear_au 19.21 eccentricity_longyear 0.25 inclination_longyear -30.0 lon_asc_node_longyear 15.0 axis_tilt 0.0 dec_offset 0.0 rot_period_h 12.7 moon name Aquablue mass 0.7 radius 0.9 semimajor_au 0.0062 eccentricity 0.004 inclination_planet 70.0 lan_planet 0.0 axis_tilt 0.0 dec_offset 0.0 rot_period_d 2.52303 end

The relevant keywords to achieve the tilts are inclination_longyear (the angle between star/companion and planet/star orbital planes) and lon_asc_node_longyear (the location of the tilting axis relative to the planet/star periapsis), inclination_planet (the angle between moon/planet and planet/star orbital planes) and lan_planet (synonymous to lon_asc_node_planet, the location of the tilting axis).

As with other orbital elements of binary or companion, the declaration of the parameters happens in the planet block, whereas the orbital parameters of the moon with respect to the planet happen in the moon block.

If a binary star were declared, the relevant keywords would be inclination_binary and lan_binary.

(Note that as in the case of the relative periapsis angles before, the rotation parameters aren't necessarily the actual longitude of the ascending node but a rotation angle that should be adjusted to the desired results using visualization).

## Visualizing orbits

The instructions to plot non-planar orbits do not differ from planar orbits, but in the case of non-planar orbits the output format is no longer (x,y) but (x,y,z) and so a 3d plot-capable program has to be used to visualize the results.

The following block

 plot_orbit body Thetis relative_to Thalassa file thetis_orbit.dat npoints 10000 timeframe_a 1.0

(note that instad of moon or companion, also the names of the objects can be used) creates this output:

 Orbits of Thetis and Aquablue with respect to Thalassa.

We see a part of Thetis' 46 year long orbit around Thalassa on a rising segment, around this track Charybdis describes a helix and this helix has a wobbly small-scale structure when one actually follows the motion of Aquablue around its planet.

Once non-planar orbits are declared, the simulation takes care of all other aspects (different irradiation pattern, eclipse finding, combining the effects of axis and orbital tilts,...) on its own.

Continue with Tropical storms.

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