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It is customary to develop them into periodic series which are a function of time, e.g. (a+bt+ct 2 +...)×cos(p+qt+rt 2 +...) and so forth one for each planetary interaction. The factor a in the preceding formula is the main amplitude, the factor q the main angular velocity, which is directly related to a harmonic of the driving force, that is ...
The times of the rising and the setting of the upper solar limb as given in astronomical almanacs correct for this by using the more general equation cos ω ∘ = sin a − sin ϕ × sin δ cos ϕ × cos δ {\displaystyle \cos \omega _{\circ }={\dfrac {\sin a-\sin \phi \times \sin \delta }{\cos \phi \times \cos \delta }}}
A fundamental ephemeris of the Solar System is a model of the objects of the system in space, with all of their positions and motions accurately represented. It is intended to be a high-precision primary reference for prediction and observation of those positions and motions, and which provides a basis for further refinement of the model.
A numerical model of the Solar System is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time. Attempts to create such a model established the more general field of celestial mechanics.
Files vary in the time periods they cover, ranging from a few hundred years to several thousand, and bodies they include. Data may be based on each planet's geometric center or a planetary-system barycenter. The use of Chebyshev polynomials enables highly precise, efficient calculations for any given point in time.
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Mean solar time, for the same place, would be the time indicated by a steady clock set so that over the year its differences from apparent solar time would have a mean of zero. [ 1 ] The equation of time is the east or west component of the analemma , a curve representing the angular offset of the Sun from its mean position on the celestial ...
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