diff --git a/doc/model.md b/doc/model.md index 6c2a1fde..0cbec399 100644 --- a/doc/model.md +++ b/doc/model.md @@ -32,6 +32,30 @@ Some elements of the sim might be hidden before the user first interactions. Her The [numerical engine](https://github.com/phetsims/my-solar-system/blob/d55f4e68c494be3d6f31d64e7085e5ad2ca9c6f6/js/common/model/NumericalEngine.ts) on this sim relies on the Position Extended Forest-Ruth Like algorithm (PEFRL) to compute the motion of the bodies [(Omelyan, Myrglod & Folk, 2001)](https://arxiv.org/abs/cond-mat/0110585). PEFRL is a numerical integration scheme that provides high accuracy and stability for simulations involving many bodies, especially those with periodic or quasi-periodic behavior. It essentially integrates the position and velocity over time in multiple intermediate steps. -## Radii of Bodies -For the purposes of collisions and display, the radii of bodies are modeled somewhat non-proportionally, as spheres with an additional minimum radius. \ No newline at end of file +## Physical Simplifications +### Mass ranges +Typical mass ranges in astronomical bodies can span about 40 orders of magnitude. From the smallest planetesimal or satellite, up to super massive black holes. However, for this simulation, the user accessible mass range is limited from 1027 kg, which is roughly the mass of Jupiter, up to 3x1030 kg, about 1.5 times the mass of the Sun. This is done to avoid numerical instabilities in the simulation, and to keep the simulation manageable for the user. As for the pre-sets, some of them can have initial masses of 1022 kg, close to the biggest moon masses in the Solar System (In model units, that's 0.000001 uM). + +### Distances and Sizes +The bodies sizes are greatly exaggerated, as using the same scale for distances and sizes would render all bodies as invisible points. For example, the real solar radius is about 0.004 AU, but in the sim it is displayed as 0.15 AU. Additionally, typical gravitational systems usually have enormous distances between bodies, even when measured in AUs, but most of the sim pre-sets show them in the same range of ~5AU in size. + +### Radii of Bodies + +For the purposes of collisions and display, the radii of bodies are modeled somewhat non-proportionally, as spheres with an additional minimum radius. + +### Comments to all Pre-Sets +Based on the above innacuracies, the following are the additional comments for each of the pre-sets, to keep in mind what's precise and what's innacurate. For all, as was stated above, body sizes are greatly exaggerated: +- Sun-Planet: Distances, velocities and times are accurate. The planet would be about 100 times as massive as Jupiter, almost a brown dwarf. +- Sun-Planet-Moon: The moon would be about 100 times closer to the planet. Velocities and times are accurate for the given orbit. +- Sun-Planet-Comet: Mostly accurate. But keep in mind that comet's orbits have a wide range of possible orbits. +- Trojan Asteroids: Apart from the 50 times Jupiter's mass, the rest is accurate. +- Ellipses, Hyperbolic, Slingshot and Double Slingshot: Because what's most important is the shape of the trajectory, these are accurate. +- Four Star Ballet: This system would be unlikely to exist in real life, but it's a good example of what a possible semi-stable system would look like. +- Double-Double: These kinds of systems do exist in real life, with binary star systems orbiting each other, for example the Castor stellar system. However, the masses and distances might be innacurate. + +### Collisions +Body impacts are pretty much simplified, when two bodies collide, the smallest ones disappears and adds its momentum to the bigger one. In reality this process is much more complex. + +## Stability of Systems +All gravitational systems with more than 2 bodies are chaotic in nature. That means that small changes in initial conditions can lead to large differences in the final state of the system. Because of this, pre-sets that would exhibit a somewhat stable behaviour in real life will de-stabilize in the sim after a few sim years (i.e. Sun-Planet-Moon, or Double-Double). Also, playing the sim in different speeds will cause the system to de-stabilize in different ways (For Sun-Planet-Moon, at normal speed the moon crashes into the planet, but at fast speed it will escape). \ No newline at end of file