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Astronomy on the Personal Computer by Dr. rer. nat. Oliver Montenbruck, Dipl.-Ing. Thomas Pfleger

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

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6 Rising and Setting Times 47 We have seen that when dealing with rising and setting times, we must use topocentric altitudes. In addition, we also have to take refraction near the horizon into account. Because rising and setting times are always referred to the upper limb of the Sun or the Moon, we also need to make allowance for the apparent radius 8e or 8Moon. 10) Our task now consists of finding, for a given date, the time at which the body being observed reaches an altitude of h = hR/S. Because there is no sense in trying to obtain the times to an accuracy better than a few minutes, we can forgo accurate calculation of 11" and 8 and use average values.

The maximum value of about 34 arc-minutes is attained at the horizon. 2. In order to obtain the observed altitude, R should be added to the calculated topocentric altitude. Atmospheric refraction also depends on the density and temperature of the air. The figures quoted should therefore be taken as average values. Comprehensive tables of normal refraction and numerical approximation formulae can be found in appropriate reference works. 2. 6 Rising and Setting Times 47 We have seen that when dealing with rising and setting times, we must use topocentric altitudes.

Coordinates (RA (h m s) DEC (0 ' ' ' ) equinox (yyyy)? 0 DEC = R)? 00000000 We first want to convert the given position to epoch 2000, and therefore choose option p to calculate the precession. After entering the year, we obtain the position of the vernal equinox for 1950 referred to the new epoch 2000. The precession amounts to slightly more than half a degree. =Help): New equinox (yyyy) ? 00000000 We now need the given equatorial coordinates to be converted into the ecliptic system. We therefore choose option E and obtain the converted coordinates - again in Cartesian and polar forms.

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