# Consistency checks

Orbital mechanics is rather permissive in what situation it covers - we can happily run a simulation close to a black hole for example. Other physics aspects might be less permissive though - there might be constraints in a defined situation that are not readily obvious but make the setup implausible to impossible.

Consistency checks are a simple way of discovering some of these situations. Their result should not be taken as absolute truth, frequently they utilize pocket formulae and estimates which may be off by as much as an order of magnitude - but the check results are pointers towards issues that might need to be understood better.

The block keyword checks is used to define all checks that should be run. The config file example27.cfg provides a setup which has such issues with the orbital setup.

## Orbiting too close - the Roche limit

Orbital mechanics deals with point masses, and point masses may approach each other as closely as they like. However, real planets, moons and stars are not points, so the periapsis of an orbit cannot be arbitrarily small. An obvious limit is hit when it grows smaller than the sum of the radii, because then a collision happens.

However, even before that another limit might become relevant: Gravity becomes weaker with distance, so the force pulling on the planet-facing side of a moon is larger than that on the opposite side. That means the situation can be understood as a large mean force pulling the moon center (and keeping it on its orbit) and a smaller (differential) force pulling it apart. That smaller force is countered by the moon's own gravity that tries to pull all mass toward the center. If the differential force exceeds the self-gravity, then the moon would likely break apart. This point is known as the Roche Limit.

The Roche limit isn't an exact statement, because internal structure (beyond self-gravity) might stabilize a body, on the other hand if the body is deformable because it is liquid, it might elongate and thus increase the differential force, but generally it is a good indication that the situation is likely not stable, and moons (or planets) orbiting inside the Roch radius will likely disintegrate.

In the simulation, using

 checks roche_limit true

checks for the Roche limit, and in the provided example27.cfg the check returns the report

 Consistency checks for Roche limit: Infernus orbits Inferno-A at 466.977 Roche radii. The situation is plausible. Infernus orbits Inferno-B at 359.733 Roche radii. The situation is plausible. Inferno-A orbits Inferno-B inside the Roche radius for liquid objects. It might be pulled apart by tidal forces. Inferno orbits Infernus at 137.008 Roche radii. The situation is plausible.

indicating that the two stars are orbiting each other too closely (a star is well modeled as a liquid object) and so can't exist at their positions.

## Orbiting too far away - the Hill sphere

When a moon orbits a planet - when does it actually orbit the planet? Clearly there is a distance at which the gravity of the central star becomes more important than that of the planet and beyond that distance it can no longer be argued to actually orbit the planet. This is known as the Hill sphere - if a larger body orbits a star, a satellite of that larger body needs to be within its Hill sphere to actually orbit it, and conversely orbits beyond the Hill sphere are not stable.

If you place a body too far out, the orbital simulation will actually show that there is no proper orbit, but as has been argued before, it is not a particularly suitable tool to investigate long-term stability of multi-body orbits, so a quick Hill sphere check might be of value.

Running the check for the provided example file uses

 checks orbital_stability true

and results in

 Consistency checks for 3-body orbital stability: Orbit of Inferno around Infernus is possibly long-term unstable at 0.566083 R_Hill.

so the moon in this example is placed too far away from the planet to be gravitationally bound in the long term.

## To spin or not to spin - tidal locking

Some time before the Roche limit bites, the tidal forces of differential gravity will make themselves felt in a different way - they will synchronize the rotation of a body around its axis (its spin) to its orbit. This is known as tidal locking. Tidal locking often implies that always the same side of the locked body faces the major body (1:1 resonance), but this isn't necessarily so, also other spin-orbit resonances are possible such as Mercury's 3:2 resonence, especially when there is eccentricity in the orbit.

There is a pocket formula to estimate the time it takes to change the initial spin of a world into a resonance, and if that timescale results in a value of less than a hundred million years, the situation is considered implausible to be not locked.

The check can be initiated using

 checks tidal_locking true

(the provided example file has no tidal locking issues).

## Too cold an atmosphere - phase constraings

The collection of gases which can be used to define an atmosphere is largely chosen based on the fact that the substances are common in known atmospheres and/or gaseous at Earth temperatures. However, a planet may be significantly colder, which means that a particular substance may actually be liquid (or even solid).

To assess the phase of a substance at different pressure as well, the full phase diagram needs to be used. Simplified parametrized phase diagrams for most gases are included in the data sets coming with the simulation, and it is possible to check a defined atmosphere against these. This can be done via

 checks atmosphere_phase true

and for Earth this results in

 Atmosphere gases phase check: At 1.000 atm pressure and 283.5 K apoapsis temperature: O2 is gaseous CO2 is gaseous N2 is gaseous H2 is gaseous Ar is gaseous H2O is liquid CH4 is gaseous O3 is not implemented

Note that water is (correctly) marked as liquid without generating a warning, an issue is flagged whenever a major component (> 5%) is liquid or solid at periapsis temperatures. Minor components may well be primarily liquid but yet yield small contributions to the atmosphere (pretty much like water vapour does on Earth).

Also note that the simulation does not try to run a full thermal evolution to determine the actually coldest spots that develop on the planteary surface - the check is just a quick test using the average radiative equilibrium temperature at periapsis, and actual temperatures may well be lower in places. Generally the dynamics of when and how an atmosphere freezes out under these conditions is complicated, and we will defer a discussion of that to a later stage.

Continue with Non-planar orbits.

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