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By Dr. rer. nat. Oliver Montenbruck, Dipl.-Ing. Thomas Pfleger (auth.)

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Twilight therefore begins or ends, by definition, when the geocentric altitude of the Sun attains one of the values quoted. We now only have to solve the general problem of finding the instant of time at which a celestial body reaches a predetermined altitude. 5) allows us to determine the altitude h, given the geographical latitude cp, the declination 8, and the hour angle T. 8). 11) We can therefore calculate the hour angle of a star when it is observed at an altitude h above the horizon. The equation is not, however, valid for every 48 3.

COCO answers with the appropriate Julian Date and the converted data in the current coordinate system. As in the previous step we chose ecliptic coordinates, we now obtain heliocentric ecliptic coordinates. It will be noted that the distance has changed. =Help): Date (year month day hour) ? 27480675 R = The conversion into ecliptic coordinates can be reversed by selecting option E again, which converts the current (ecliptic) coordinates into equatorial coordinates. 27480675 Let us now recalculate the coordinates for the original equinox of 1950.

57*COS(D-M3); 25 26 2. 0; END; (* SUN200 *) (*-----------------------------------------------------------------------*) The extent of the SUN200 procedure is explained by the fact that the relative motion of the Sun and the Earth cannot be described to the required accuracy by simple elliptical orbits. Apart from the perturbations of the other planets-particularly those of Venus and Jupiter- there is also the monthly oscillation of the centre of the Earth around the barycentre of the EarthMoon system.

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