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|JEphem Ephemeris trail Truncating VSOP87|
The purpose of this page is to find a way to remove terms of VSOP87 in order to have a given geocentric maximal error.
For this, we'll first consider that the position of Earth is considered as exactly known ; the incertitude on the Earth position will then be taken into account.
S : position of the Sun
E : position of the Earth
P : real position of the planet
P' : position of the planet affected of errMax
|In both cases we have :||tg(αMax) = d / EP||(formula 1)|
|Then :||EP = aP(1 - eP) - aE(1 +eE)||(formula 2.1)|
|A similar drawing for an inner planet would lead to :||EP = aE(1 - eE) - aP(1 +eP)||(formula 2.2)|
|For the Earth, the formula is :||ES = aE(1 - eE)||(formula 2.3)|
BuildVSOP87.calcAlphaMax()was written for this purpose.
|The condition to retain a term is then|
|MER VEN EAR MAR||4|