Truncation of the Series
The series VSOP2013 can be reduced with the elimination of terms less than a level of truncation ρ such as:
with the following units: au for a, radian for λ, without unit for the other variables k, h, q, p.
This table gives the largest differences, on the planetary heliocentric longitudes (L) in arcseconds, between a computation using the complete series and a computation with reduced series for 4 levels of truncation and 4 different time intervals.
MERCURY
Truncation
10-08
0.67721"10-01
0.75801"10-01
0.17037"10
Truncation
10-10
0.15743"10-02
0.17826"10-02
0.38273"10-02
Truncation
10-12
0.48047"10-04
0.44625"10-04
0.14062"10-03
Truncation
10-14
0.81680"10-06
0.33789"10-05
0.10122"10-04
VENUS
Truncation
10-08
0.53251"10-01
0.70522"10-01
0.12720"10
Truncation
10-10
0.14642"10-02
0.16925"10-02
0.46000"10-02
Truncation
10-12
0.41051"10-04
0.41504"10-04
0.16087"10-03
Truncation
10-14
0.19316"10-06
0.20458"10-05
0.79408"10-05
EMB
Truncation
10-08
0.65292"10-01
0.70898"10-01
0.15865"10
Truncation
10-10
0.19588"10-02
0.19376"10-02
0.62822"10-02
Truncation
10-12
0.56497"10-04
0.63936"10-04
0.23802"10-03
Truncation
10-14
0.24503"10-07
0.34754"10-06
0.97589"10-05
MARS
Truncation
10-08
0.97685"10-01
0.14296"10
00
Truncation
10-10
0.24870"10-02
0.35107"10-02
0.11166"10-01
Truncation
10-12
0.85882"10-04
0.89968"10-04
0.43410"10-03
Truncation
10-14
0.27480"10-09
0.94669"10-07
0.36979"10-06
JUPITER
Truncation
10-08
0.72111"10-01
0.98043"10-01
0.43798"10
Truncation
10-10
0.23149"10-02
0.41402"10-02
0.18410"10-01
Truncation
10-12
0.52419"10-04
0.77432"10-04
0.95349"10-03
Truncation
10-14
0.18091"10-08
0.67189"10-07
0.12293"10-04
SATURN
Truncation
10-08
0.85180"10-01
0.13503"10
00
Truncation
10-10
0.44443"10-02
0.40293"10-02
0.36953"10-01
Truncation
10-12
0.58705"10-04
0.11242"10-03
0.99838"10-03
Truncation
10-14
0.68700"10-09
0.30549"10-07
0.15439"10-04
URANUS
Truncation
10-08
0.12999"10
00
0.16070"10
Truncation
10-10
0.28179"10-02
0.46278"10-02
0.15507"10-01
Truncation
10-12
0.56458"10-04
0.86700"10-04
0.54348"10-03
Truncation
10-14
0.15780"10-08
0.30961"10-07
0.29137"10-05
NEPTUNE
Truncation
10-08
0.11042"10
00
0.12789"10
Truncation
10-10
0.24840"10-02
0.32288"10-02
0.91847"10-02
Truncation
10-12
0.60694"10-04
0.69311"10-04
0.44163"10-03
Truncation
10-14
0.86562"10-08
0.22378"10-06
0.99586"10-05
PLUTO
Truncation
10-08
0.25573"10
00
0.29364"10
Truncation
10-10
0.26349"10-02
0.40748"10-02
0.27407"10
Truncation
10-12
0.12252"10-04
0.30712"10-04
0.78821"10-02
Truncation
10-14
0.45800"10-09
0.15325"10-06
0.19191"10-03
Unit: arcsecond
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