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CODES OF SECULAR RESONANCES
Codes of divisors (secular resonances) in the analytic theory.
Note that divisors 3 and 6 cannot give rise to a secular resonances.
g and s are asteroid frequencies of perihelion and node respectively,
while planetary frequencies are labeled with the corresponding number
(5 = Jupiter; 6 = Saturn; 7 = Uranus; 8=Neptune).
- '1'=g-g5
- '2'=g-g6
- c this one cannot give rise to a resonance
- '3'=g5-g6
- '4'=s-s7
- '5'=s-s6
- c this one cannot give rise to a resonance
- '6'=s7-s6
- '7'=g+s-s7-g5
- '8'=g+s-s7-g6
- '9'=g+s-s6-g5
- '10'=g+s-s6-g6
- '11'=2*g-2*s
- '12'=g-2*g5+g6
- '13'=g+g5-2*g6
- '14'=2*g-g5-g6
- '15'=-g+s+g5-s7
- '16'=-g+s+g6-s7
- '17'=-g+s+g5-s6
- '18'=-g+s+g6-s6
- '19'=g-g5+s7-s6
- '20'=g-g5-s7+s6
- '21'=g-g6+s7-s6
- '22'=g-g6-s7+s6
- '23'=2*g-s-s7
- '24'=2*g-s-s6
- '25'=-g+2*s-g5
- '26'=-g+2*s-g6
- '27'=2*g-2*s7
- '28'=2*g-2*s6
- '29'=2*g-s7-s6
- '30'=g-s+g5-s7
- '31'=g-s+g5-s6
- '32'=g-s+g6-s7
- '33'=g-s+g6-s6
- '34'=g+g5-2*s7
- '35'=g+g6-2*s7
- '36'=g+g5-2*s6
- '37'=g+g6-2*s6
- '38'=g+g5-s7-s6
- '39'=g+g6-s7-s6
- '40'=s-2*s7+s6
- '41'=s+s7-2*s6
- '42'=2*s-s7-s6
- '43'=s+g5-g6-s7
- '44'=s-g5+g6-s7
- '45'=s+g5-g6-s6
- '46'=s-g5+g6-s6
- '47'=2*s-2*g5
- '48'=2*s-2*g6
- '49'=2*s-g5-g6
- '50'=s-2*g5+s7
- '51'=s-2*g5+s6
- '52'=s-2*g6+s7
- '53'=s-2*g6+s6
- '54'=s-g5-g6+s7
- '55'=s-g5-g6+s6
- '56'=2*g-2*g5
- '57'=2*g-2*g6
- '58'=2*s-2*s7
- '59'=2*s-2*s6
- c divisors appearing only in forced terms
- '60'=g-2*g6+g7
- '61'=g-3*g6+2*g5
- c degree six divisor z2
- '62'=2*(g-g6)+(s-s6)
- c other nonlinear forced terms
- '63'=g+g5-g6-g7
- '64'=g-g5-g6+g7
- '65'=g+g5-2*g6-s6+s7
- Fundamental frequencies of major planets in arcsec/yr
- g5=4.25749319
- g6=28.24552984
- g7=3.08675577
- g8=0.67255084
- s5=0
- s6 -26.34496354
- s7=-2.99266093
- s8=-0.69251386