http://www.fourmilab.ch/images/3planets/elongation.html

Mercury Chaser's Calculator

To display the date, time, and distance of the maximum elongations of Mercury for a given year, enter the year in the box below and press "Calculate". Depending on the speed of your computer, it may take a while for the results to appear in the text boxes. This page requires your browser to support JavaScript, and that JavaScript be enabled; all computation is done on your own computer so you can, if you wish, save this page in a file and use it even when not connected to the Internet.

Year:

Greatest Elongations of Mercury

The above table lists the maximum elongations of Mercury for the chosen year. Elongations alternate between east and west of the Sun along the ecliptic. Somewhat confusingly, an eastern elongation angle means Mercury will be visible in the western sky after sunset, while for a western elongation Mercury is visible in the eastern sky before dawn. The "Apparition" column helps sort this out. Maximum elongations occur on the indicated Date in universal time (UTC, or Greenwich Mean Time). Depending on the time zone at your observing site (possibly modified by summer time, if in effect), the maximum elongation may occur on an adjacent date at your location. In practice, a day or two makes little difference in the appearance of Mercury near elongation, so there's no need to worry about time zone corrections. The magnitude at maximum elongation is calculated by determining the relative positions of the Earth and Mercury with respect to the Sun, calculating the phase angle (percent illumination) of Mercury and the intensity of light it receives from the Sun at the point along its substantially elliptical orbit it occupies at the moment, and the distance from Mercury to the Earth. These quantities are arguments to G. M¸ller's empirical formula for the magnitude of Mercury (derived from observations made between 1877 and 1891), from which the estimate in the table is derived. Estimating the magnitude of planets by simple formulÊ is problematic, and you may see difference of a few tenths of a magnitude among various tables of planetary phenomena. In practice, such discrepancies are of little import since it's next to impossible to observe such small differences in intensity without a nearby references, especially in the twilight conditions in which Mercury is usually glimpsed.

References

Meeus, Jean. Astronomical Algorithms . Richmond: Willmann-Bell, 1998. ISBN 0-943396-63-8.
This is the essential reference for computational positional astronomy. The calculation of the time of Mercury's greatest elongations is performed using the algorithm given in Chapter 35. The elongation angle and visual magnitude of Mercury are obtained by determining the heliocentric positions of Mercury and Earth using the VSOP87 planetary theory as described in Chapter 32, transforming the position of Mercury into geocentric coordinates using the first method in Chapter 32, then calculating Mercury's phase angle and approximate magnitude using the technique in Chapter 40. The visual magnitude is estimated by the traditional empirical formula of G. M¸ller.

by John Walker
September, MIM

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