Orbital Resonance

[MKruer]

In my pursuit to make a more believable system, I am running into issues with long terms system stability. I have been reading up on Orbital Resonance and how that long term stability is due to the semi-chaotic nature of the orbital resonance.

http://en.wikipedia.org/wiki/Orbital_resonance

Resonance value
(real) Earth:Venus = 0.61518624
(8:13) Earth:Venus = 0.615384615

Simple division turns this into 0.032% discrepancy; which over 960 years leads Earth:Venus into being 180 degrees or have a 1.5 degree drift every cycle (8 years) or .1875 of a degree per year

Ironically the issues that i am having for my excel spreadsheet is that for the life of me I can not figure out how they got to 1.5 degree from 0.032%. i keep getting around 3100 years for a full cycle not 960 as suggested by the wiki. Can someone school me in this conversion.

Thanks

[Hungry4info]

It might be Jupiter or one of the other inner planets driving the cycle faster. I don't remember any specific examples, but I've read that Jupiter affects Mercury's orbit in various ways.

[selden]

Double precision arithmetic may be inadequate. To follow long term orbital interactions accurately you need to use steps which are small when compared to the smallest orbit involved and extended precision arithmetic.

[MKruer]

For my system it should be sufficient, I am not looking for hyper accurate, just more accurate then what I have now. My original system was to perfect, and ended up throwing out objects with in a few thousands years time. I am trying to figure out some of the mechanics and interactions between object. with the Orbital Resonance in theory, if the configuration reverse itself every now and then, sure the planet might swing out of alignment, but it should be placed back into alignment at the end of the cycle. Thats why I was wondering about this problem.

Resonance value
(real) Earth:Venus = 0.61518624
(8:13) Earth:Venus = 0.615384615

Simple division turns this into 0.032% discrepancy; which over 960 years leads Earth:Venus into being 180 degrees or have a 1.5 degree drift every cycle (8 years) or .1875 of a degree per year

A 1.5 degree offset each cycle (8 years) is very easy to understand. I am just not sure how they got 1.5 degrees from the 0.032% discrepancy. Thats what I am looking for.

[ajtribick]

For an exact 8:13 ratio, after 8 years, Venus has made 13 revolutions.

Actual ratio is 0.61518624, so after 8 years, Venus has made 8/0.61518624 = 13.004192 revolutions

0.004192 * 360 = 1.5 degrees

[MKruer]

OK now I feel foolish.

Thanks BTW

I guess while I has anyone found an orbital resonance for a 4 or 5 body system similar to the Io, Europa, Ganymede 1:2:4 connection. This connection is unique because its self stabilizing one of the few cases where it works. I have been fiddling with some number and came up with this.

Code: Select all

1    0   starting at degrees
2    270 starting at degrees
4    180 starting at degrees
8    90  starting at degrees
16   180 starting at degrees