



BARKER'S TABLES
Available on this Web site are a number of computergenerated
Barker's tables
(all at intervals of 5" in the true anomaly f):
 Watson's convention (C = 75).
This is an extended version of the table published by Watson [1], which sets the righthand side of Barker's equation
H=100 for f=90°. Entries are dimensionless.
To use this table, divide the time from perihelion passage (tT_{0}, in any system of units) by the perigee distance
to the 3/2 power (q^{3/2}). Multiply by K = 75√(GM/2) in consistent units, and find the result in the table.
The corresponding angle gives f. The constant K for heliocentric orbits for different sets of units is:
 t in days, q in AU: K = 0.9122791
 t in days, q in miles: K = 8.176030E11
 t in days, q in km: K = 1.669229E12
 t in seconds, q in meters: K = 6.109450E11
 t in seconds, q in cm: K = 6.109450E14
 Oppolzer's convention (C = √2/k).
This is an extended version of the table published by Oppolzer [2], which uses
astronomical units and assumes the Sun as the central body (k is
the Gaussian gravitational constant = 0.01720209895). To use this table, divide the time from perihelion passage (tT_{0}, in days) by the perigee distance
(in AU) to the 3/2 power (q^{3/2}). Find the result in the table. The corresponding angle gives f.
 Unity convention (C = 1).
This is a new tabulation that can be used for any central body and any system of units. Entries are dimensionless.
To use this table, divide the time from perihelion passage (tT_{0}, in any system of units) by the perigee distance
to the 3/2 power (q^{3/2}). Multiply by K = √(GM/2) in consistent units, and find the result in the table.
The corresponding angle gives f. The constant K for heliocentric orbits for different sets of units is:
 t in days, q in AU: K = 0.01216372
 t in days, q in miles: K = 1.090137E10
 t in days, q in km: K = 2.225638E10
 t in seconds, q in meters: K = 8.145933E09
 t in seconds, q in cm: K = 8.145933E12
 SI convention (C = √(2/GM), for Sun, SI units).
This is a new tabulation, intended for use with calculations in SI units and the Sun as the central body. Entries have units of s/m^{3/2}.
To use this table, divide the time from perihelion passage (tT_{0}, in seconds) by the perigee distance
(in meters) to the 3/2 power (q^{3/2}). Find the result in the table. The corresponding angle gives f.
 CGS convention (C = √(2/GM), for Sun, CGS units).
This is a new tabulation, intended for use with calculations in CGS units and the Sun as the central body. Entries have units of s/cm^{3/2}.
To use this table, divide the time from perihelion passage (tT_{0}, in seconds) by the perigee distance
(in cm) to the 3/2 power (q^{3/2}). Find the result in the table. The corresponding angle gives f.
Example
For example, Comet Barnard (1889 III) has a perihelion distance of 1.102 AU. Find its position 3 years after
perihelion passage, assuming a parabolic orbit.
Solution. Here tT_{0} is 1095.75 days. Dividing this by (1.102 AU)^{3/2} gives
947.1943. Looking this up in Oppolzer's version of Barker's tables gives roughly f = 142° 33' 55".
References
^{[1]} J.C. Watson. Theoretical Astronomy, Table VI. Lippincott, 1868.
^{[2]} T.R. Oppolzer. Lehrbuch zur Bahnbestimmung der Kometen und Planeten I, Tafel IV. Leipzig, Berlin, 1882.
Contact Information
I may be contacted at:

