Truncation of the Series

The series VSOP2013 can be reduced with the elimination of terms less than a level of truncation Ļ such as:

(C2+S2)1/2<Ļ(C^2+S^2)^{1/2}< Ļ

with the following units: au for a, radian for Ī», 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.

TIMEINTERVALS+1890 +2000+0900 +3100+0000 +4000-4000 +8000

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

Last updated