- Venus/Earth
- Jupiter/Saturn
- Saturn/Uranus
- Uranus/Neptune
- Neptune/Pluto
- Other planets
- Resonance groups
- Conclusion

This difference makes the

It takes 243 years (30x the 8-year cycle + 2 meetings) between the planets meet on an almost-same place.

The resonance shape gets little modified occasionally, mostly by perturbations by Jupiter, but is always restores briefly. Hence, the resonance keeps the orbits stable despite of all perturbations.

Note the start of Fibonacci sequence of 5,8,13, that approaches the

The actual difference of the resonance rate from a Golden section is only

The shape, traced by the bary-center of the two planets (by this sub-system), look like these:

The plots are 1 dot per 1 earthday. From the dot density, you can see the speed of the barycenter at various parts of the trajectory. The point moves fast when far from the Sun, and almost stops when it is nearest. This event is a lot dynamical: the barycenter starts approaching Sun in orbital direction, then it stops almost on one place for 2-3 weeks, then it starts receding from Sun and moving in the orbital direction...

When compared with 1/5 round turn after 240 years, the shape almost closes onto its previous version, but not completelly, probably due to disturbances by larger planets, mostly by Jupiter... Yet despite these disturbances, the resonance keeps the orbits more stable (so that the resonance shape restores briefly (within few years) after the perturbations), and on a larger scale, there is no chaos.

The Venus sidereal day (when compared to fixed star background) is -243.0185 ea-days in counter-orbital (retrograde) direction. After the 13 orbits of Venus, when it meets Earth for 5th time during the resonance cycle, it makes almost exactly

The apparent Solar day on Venus is 116.75 days, and it takes almost exactly

One reason for the counter-orbital (retrograde) spin direction seems, that the tidal force is highest, when the planets meet (and are nearest to each other), and in these times, the Earth moves

The difference makes the shape rotate, and close almost after 854 ea-years, which is almost 29 saturn-years and 72 jupiter-years.

Bary-trace | Compared with 2nd | After 854 years | Compared with next step |

Compared with inner planet trajectories | Meet-point distance chart |

Bary-trace | Meet-point distance chart |

Bary-trace | Saturn meets their barycenter | again after 30 years |

No bary-trace is available, since their weight is incomparable and the barycenter between Neptune and Pluto is almost inside the Neptune, same as barycenter between Jupiter and Mars is almost inside the Jupiter...

The mid-point trace (

Barycenter trace | Mid-point trace | 10 succesive Mid-point traces |

Their weight is little comparable, so that trajectory trace little differs from Venus orbital trajectory.

When drawing middle-point between Mercury and Venus (

Mercury orbit is highly excentrical...

Mercury is also one of few planets, that pass through the trajectory of barycenter of its outer neighbours (other one is Saturn), and seems to meet it regularly (only) at some times.

The resonance of

The barycenter trajectory between Earth and Mars seems erratic, probably due to disturbations to Mars by asteroids and Jupiter...

It takes 14.96 earth-years to complete this figure, here compared to trajectories...

Note the Venus trajectory, as it just does not touch the Earth/Mars barycenter trace...

Note, that the figure is little irregular...

The resonance of

The whole shape rotates after 32.9 years by 1/3 of circle, and after 98.7 years by 1 whole circle...

Meet-point distance chart | |||

Trace between 2 meetings | Trace figure closes later | Figure after rotating 1/3 round |

Mercury sometimes meets the barycenter of Venus and Mars, but even at closest approaches it is separated vertically (Z ecliptic coordinate) by at least 3,318,844 km (at 12.9.414 AD)

The resonance of

Their weight is not much comparable, so the bary-center trajectory runs almost in Earth center. The mid-point trajectory (

Midpoint trajectory between Emb and Mercury | 6.593 figures (after 46 years) |

Resonance can be found also between non-neighbouring planets in the outer group:

Ratio between

Ratio between

Ratio between

Jupiter/Uranus 7:1 | Jupiter/Neptune 14:1 | Saturn/Neptune 28:5 |

- Mercury/Venus/Earth/Mars
- Jupiter/Saturn/Uranus/Neptune/Pluto

The perturbations (see Angular momentum article) average in longer-scale cycles, and the planetary motions are stabilized by the resonance.