The values from the SSC file that I think may be needed are:
- EllipticalOrbit.Eccentricity
- EllipticalOrbit.Inclination
- EllipticalOrbit.AscendingNode
- EllipticalOrbit.LongOfPericenter
- EllipticalOrbit.MeanLongitude (probably not needed for an analemma diagram but may be needed for equation of time as a function of time T)
- Obliquity
- EquatorAscendingNode
- Axial tilt of the planet (equal to Obliquity if EllipticalOrbit.Inclination is zero)
- Equator ascending Node in relation to orbit of planet (equal to EquatorAscendingNode if EllipticalOrbit.Inclination is zero)
Code: Select all
Axial tilt = arccos(cos(AscendingNode)*sin(Inclination)*cos(EquatorAscendingNode)*sin(Obliquity) + sin(AscendingNode)*sin(Inclination)*sin(EquatorAscendingNode)*sin(Obliquity) + cos(Inclination)*cos(Obliquity))
(The above formula is the dot product of the vectors described by these two pairs of angles.)
We will need to derive the following formulae:
- Equation of time
- Declination of the sun (or star) in relation to the equator of the planet
From Meeus, I have the following formula for equation of time E:
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E = y sin 2L0 - 2e sin M + 4ey sin M cos 2L0 - (1/2)y^2 sin 4L0 - (5/4) e^2 sin 2M
- E = equation of time
- y = tan^2 (axial tilt/2)
- L0 = Sun's mean longitude
- e = eccentricity
- M = sun's mean anomaly