Solar system simulation -- Significant deviation of some Jovian moons

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SUMMARY

The forum discussion centers on the simulation of the solar system, specifically addressing the significant deviations in the orbital velocities of Jupiter's moons, Io and Europa, when compared to NASA's reference values. The user employed identical initial parameters sourced from NASA Horizons but encountered discrepancies in simulated velocities. The primary issue identified was the use of a 24-hour timestep, which is inadequate for accurately simulating the orbits of Io and Europa, given their respective orbital periods of 1.7 days and 3.6 days. A recommendation was made to utilize a smaller timestep to achieve more accurate results.

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madsmh
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I am working on a simulation of the solar system, but I am having problems with the orbits with Europa and Io shown in the image below, the orbits of Jupiter, Ganymede and Callisto are consistent with NASA's simulations. For all bodies I have used identical parameters in generating the initial values (position and velocities) from NASA Horizons, but the simulated velocities deviate significantly from the reference values, see below the image.
jupiter_moons.png


Code: 
Simulated velocities Io
[[ -8614.49286 -21369.57154   -632.93203]
[  9413.68985 -45300.37648  -1230.23422]
[  9386.14932 -44351.41911  -1197.69465]
[  9380.29852 -44091.59352  -1189.38208]
[  9384.20206 -43964.90674  -1185.66855]
[  9392.3708  -43887.48053  -1183.64575]
[  9402.739   -43833.83182  -1182.43573]
[  9414.37123 -43793.50441  -1181.67948]
[  9426.78351 -43761.39524  -1181.20215]
[  9439.70035 -43734.71132  -1180.90818]]
Reference velocities Io
[[ -8.6145e+03  -2.1370e+04  -6.3293e+02]
[  1.4312e+04   3.7050e+03   5.8373e+02]
[  3.2327e+03  -2.8330e+04  -7.1454e+02]
[  5.2868e+02   5.4834e+03   4.5001e+02]
[  1.6449e+04  -2.4527e+04  -3.9360e+02]
[ -1.0069e+04  -3.4329e+03  -1.9295e+01]
[  2.2782e+04  -1.2263e+04   1.3100e+02]
[ -1.0724e+04  -1.7200e+04  -5.2041e+02]
[  1.8110e+04   7.9950e+02   5.2812e+02]
[ -1.1648e+03  -2.7069e+04  -7.3810e+02]]
Simulated velocities Europa
[[ 17409.7477 -17977.8844   -149.1204]
[ 19892.0848  -6577.1288    388.6789]
[ 15345.577   -6005.3129    330.4903]
[ 13644.4897  -6241.7316    288.5844]
[ 12703.5633  -6475.9464    260.4778]
[ 12088.5888  -6670.4873    239.9645]
[ 11648.2814  -6830.9437    224.0745]
[ 11314.4114  -6965.0308    211.2436]
[ 11051.081   -7078.774     200.5634]
[ 10837.3529  -7176.5748    191.4658]]
Reference velocities Europa
[[ 17409.7477 -17977.8844   -149.1204]
[  9657.1567   1697.3447    562.7489]
[ -8209.8182  -9418.8943   -242.2855]
[  6511.8877 -25017.7237   -653.561 ]
[ 18583.2     -7391.2116    327.0779]
[  -703.984     970.8296    340.24  ]
[ -5401.237  -19722.1106   -642.0661]
[ 16113.2379 -19990.1371   -266.1455]
[ 12018.9873    776.3151    558.5457]
[ -7545.2962  -6950.3879   -130.6148]]

These are the first ten velocities in vx, vy, vz-format. The stepsize used is 24 hours.

The physical constants, using in the simulation are
Code: 
NAME,RADIUS,GM, COMMENT,
Sun, 695700e3,1.3271244004193938e20, "Source: NASA/JPL Horizons",
Mercury, 2439.7e3,22032.09e9, "Source: NASA/JPL Horizons",
Venus, 6051.8e3,324858.63e9, "Source: NASA/JPL Horizons",
Earth, 6371.0e3,398600.440e9, "Source: NASA/JPL Horizons",
Mars, 3389.5e3,42828.3e9, "Source: NASA/JPL Horizons",
Jupiter, 69911e3,126686511e9, "Source: NASA/JPL Horizons",
Saturn, 58232e3,37931207.8e9, "Source: NASA/JPL Horizons",
Uranus, 25362e3,5793966e9, "Source: NASA/JPL Horizons",
Neptune, 24622e3,6835107e9, "Source: NASA/JPL Horizons",
Pluto, 1737.4e3,872.4e9, "Source: NASA/JPL Horizons",
Luna, 469.7e3, 4902.801076e9, "Source: JPL, Lunar Constants and Models Document",
Ceres, 469.7e3,62.6284e9, "Source: NASA/JPL Horizons",
Pallas, 272.5e3,14.3e9, "Source: NASA/JPL Horizons",
Vesta, 262.7e3,17.8e9, "Source: NASA/JPL Horizons",
Hygiea, 203.56e3,7e9, "Asteroid. Source: NASA/JPL Horizons",
Ganymede, 2634e3,9887.83e9, "Moon of Jupiter. Source: International Astronomical Union, Icy Bodies of the Solar System",
Titan, 2575.5e3,8978.1356e9, "Moon of Saturn. Source: International Astronomical Union, Icy Bodies of the Solar System",
Callisto, 2410.3e3,7179.29e9, "Moon of Jupiter. Source: International Astronomical Union, Icy Bodies of the Solar System",
Io, 1821.46e3,5959.916e9, "Moon of Jupiter. Source: International Astronomical Union, Icy Bodies of the Solar System",
Europa, 1562.09e3,3202.72e9, "Moon of Jupiter. Source: International Astronomical Union, Icy Bodies of the Solar System",
Any help would be appreciated :)

.. Mads
 
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Io has an orbital period of 1.7 days. With a step size of 1 day, you cannot get a realistic orbit.
Europa has an orbital period of 3.6 days, still too low.
Ganymede has 7 days and Callisto has 17 days, for these moons steps of 1 day can lead to something that looks like an orbit (with a large error, however),
 
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mfb said:
Io has an orbital period of 1.7 days. With a step size of 1 day, you cannot get a realistic orbit.
Europa has an orbital period of 3.6 days, still too low.
Ganymede has 7 days and Callisto has 17 days, for these moons steps of 1 day can lead to something that looks like an orbit (with a large error, however),

A smaller timestep fixed it, sorry for not looking before posting.
 

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