THE    SOLAR     SYSTEM

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PLANET_ASSEMBLY: This video and its companion "long_view" slides are products of a toy model of the planet accretion process which took place during the formation of the Solar System. Approximately 3000 earth-mass chunks are randomly placed in an annulus surrounding a solar mass "proto-Sun". The annulus extends from 1-6 AU (Astronomical Units - the present distance between Earth and Sun. For reference the radius of Jupiter's orbit is 5.2 AU). Chunks move in orbits which deviate in minor, random ways from being exactly circular. The animation is fully n-body; each chunk feels the gravitational attraction of all it's kin as well as that of the proto-Sun.

Collisions form more massive chunks; disrupting encounters - probably common in actual protoplanetary disks - are not considered. Both mass and momentum are conserved in a collision, and the first one causes a colour change from orange to green. Symbol sizes are also mass-dependent; a close inspection reveals a small mass spread among original chunks. A collision is deemed to occur whenever two or more chunks approach within a specified "collision cross section", CC. In order to speed up the process CC is initially set at 0.02 AU; it slowly increases with chunk mass. The random initial placement of chunks always produces a few which satisfy the collision requirement at the start of the animation. An orange collision counter - top left - keeps track, while the animation frame number appears nearby in white. Frames are separated by two days.

If a newly formed chunk exceeds the mass of Neptune - about 17 times Earth-mass - it is assigned a blue colour. In long animations - hours of run time - a few chunks eventually reach Saturn mass, 95 times greater than Earth; they appear in yellow.

LONG_VIEW SLIDES: Nobody wants to watch a video long enough to produce even one "Saturn"; at least a half-hour would be needed. So, to illustrate what happens over long times, I've assembled a number of snapshots produced by a 12-hour animation, and offer them as a do-it-yourself slide show. By the way, you can calibrate the frame number shown on these slides, and the "planet_assembly" video, in terms of the equivalent physical time using the conversion of 1 frame = 2 days of physical time. Thus frame 10,000 signifies the passage of 20,000 days. By "physical time" I mean the time used in solving Newton's Laws of Motion in order to move the chunks ahead in their paths. The code uses the International System of Units - abbreviated as "SI" - throughout.

JUPITER'S GALILEAN MOONS: A simulation covering about nine and a half days in the lives of the four large moons of Jupiter, discovered by Galileo during the winter of 1609-1610. In order of orbital size they are Io (422,000 km from centre of Jupiter), Europa (671,000 km), Ganymede (1,070,000 km) and Callisto (1,883,000 km). For reference, our own moon averages 384,000 km from Earth's centre; Callisto is about five times farther from Jupiter.

The green horizontal reference axis is 4 million km long to accomodate the orbit of Callisto. The relative sizes of Jupiter and the moons are roughly correct, but at the start of the video the orbital sizes are too small relative to them. The initial zoom out shows all sizes with more realistic proportions. The zoom is needed to compensate for the fact that the Python language used to construct the original animation holds plotted syumbol sizes constant while zooming.

The time in hours from animation start appears at upper left. All moons begin on a line with Jupiter - I haven't tried to position them to simulate realistic locations at any actual time. The orbital periods of Io, Europa, and Ganymede are known to be simple multiples of each other, having ratios 1:2:4, respectively. So for example, after Io completes two orbits Europa will complete a single orbit and those two moons should be back where they began - lined up with Jupiter. After four Io orbits Ganymede should join the initial alignment. Checking the video near hour 170 you will see those three moons pass in front of Jupiter, as predicted. However, Io seems to be slightly ahead of Europa, which in turn slightly preceeds Ganymede; the prediction of an exact alignment seems a bit off. Never fear, the explanation - I think - lies in the way orbital movement is handled. In simulations, jumps between positions take place along straight lines. The curved orbital paths are only approximated, and I suspect the accuracy of the approximation varies with speed and the amount of path curvature. Io moves rapidly and around a highly curved path, Europa less so and Ganymede still less. While not a complete explanation, I believe that at least points along the right "path" to one.

RADIATION BELTS: It's well known by astronomers and those who build and operate planetary space probes that Jupiter's strong magnetic field has created an enormous system of radiation belts roughly aligned with the orbits of the Galilean Satellites. The belts are mapped using their radio emission; all those satellites move in a more or less deadly radiation environment - deadly for living things and for man-made electronics. The jittering blue dots are a reminder of these facts. They very roughly map the space occupied by the Inner Radiation Belt. Think of them as representing high-energy particles zipping around at relativistic speeds. The Europa Clipper and JUICE (Jupiter Icy Moons Explorer) missions will have to contend with them.