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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