General information

Venus total equation double argument
Table type		Venus Total equation double-argument table
Table type definition		Equation table providing directly the total equation combining the effect of the excentricity and epicycle
Intellectual author		Jean-Claude Penin
Bibliography		PEDERSEN O., A survey of the Almagest, ODENSE, 1974. TOOMER G. J., Ptolemy's Almagest, Princeton University Press, 1998. CHABAS J. and GOLDSTEIN B. R., A survey of European astronomical tables in the late middle ages, LEIDEN, BOSTON, 2012.
Author of the record		jpenin

Formula definition definition

Formula definitions are modern mathematical expressions of historical theoretical models, usually geometrically expressed, on which the different types of astronomical tables are based. They are used to suggest values when inputting tables content and to analyse mathematically table content.

Glossary

Formula definition : Venus total equation double argument | Venus: Total equation double-argument table

Table model definition

Explanation

It is the sum of two equations :
1)The equation of the center, noted q, is the angle between the earth and the equant point, seen from the epicycle centre. The function q depends of Cm, the mean center (medium centrum).
2)The equation of argument, noted p, is the angle between the epicycle center and the planet, seen from the earth. The function p depends of Cm and true argument av.
Therefore we have for the total equation double argument Venus :
\(d= q(Cm)+p(Cm,av)\)
In this way, the true longitude of venus is given by the formula :
\(L=Lm+ q(Cm)+p(Cm,av)\)
with Lm the mean longitude of the sun.

Formula

\(RAD=\frac{\pi}{180} DEG=\frac{1}{RAD}\\ q=-DEG\times arctan(\frac{2esin(RAD\times x)}\\ {sqrt(60^2-(esin(RAD\times x))^2) +ecos(RAD\times x)})\\ rho=\{[sqrt(60^2-(esin(RAD\times x))^2)+ecos(RAD\times x)]^2+(2esin(RAD\times x))^2\}\\ p=\frac{1}{RAD}arctan(\frac{r sin(RAD\times y)}{\rho+r cos(RAD\times y)})\\ f(x,y)=p+q\)

Parameters

Eccentricity		e 01 ; 15
Radius of the epicycle		r 43 ; 10

Modern definition

No modern definition

Graphical representation

Venus total equation double argument representation