Mercury chart symbol Mercury Chaser's Calculator

by John Walker

Mariner 10 composite image of Mercury

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.


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. Müller'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 formulĉ 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.

Horizon Views at Maximum Elongations

Depending on the season and the latitude of your observing site, the elevation of Mercury above the horizon may be more or less favourable for a given angular elongation from the Sun. This is due to the fact that elongation is an angle along the ecliptic (the plane in which the Earth and the other planets orbit, more or less), which is inclined with respect Elongation of Mercury on March 3, 1999
Sunset at 47°N 7°E, March 3, 1999.
to the horizon at an angle which depends both your latitude and the season (as the axis of the Earth's rotation is inclined with respect to the ecliptic). For example, the chart at the left, produced by Your Sky, shows the western sky at sunset on March 3rd, 1999, the date of the first maximum elongation of Mercury that year, as seen from Fourmilab's location of 47° North latitude , 7° East longitude.

Elongation of Mercury on October 24, 1999
Sunset at 47°N 7°E, October 24, 1999.

At that location and date, the ecliptic was steeply inclined with regard to the horizon, so even though the angular elongation at this apparition was a modest 18.2°, Mercury was high in the sky after the sunset (not to mention close to Jupiter and Venus, making it easy to locate).

Compare this to the chart at the right, which shows the sky at the same observing site at sunset on October 24th, 1999, the date of Mercury's final evening elongation of the year. Mercury's elongation from the Sun on this date is 24.3°, much greater than in March, but recall that elongation is measured along the ecliptic. In October at this site the ecliptic is much less steeply inclined to the horizon, so even though Mercury is more distant from the Sun in the sky, its altitude above the horizon at the observing site is much less: only 6.2° compared to 18.2° in March, and consequently it sets much sooner after sunset and is far more likely to be concealed by terrain along the horizon or lost in twilight. Thus, to determine your chances of seeing Mercury and knowing where to look, you need more than a table of elongations; in addition you need a custom chart of the horizon for your own observing site. Fortunately, we'll be happy to make one for you. Introducing our…

Elongation Explorer

The calculations required to compute the appearance of Mercury near maximum elongations are straightforward, if somewhat tedious, but fortunately they've already been done in Your Sky, our planetarium of the Web. Simply enter the latitude and longitude of your observing site (to the nearest degree—that's perfectly adequate for this purpose) in the boxes below, choose the elongation you wish to examine, and press the “View Horizon” button. Your Sky will show a view of the horizon around dawn or sunset on the day of the elongation you've chosen. The steeper the angle of the ecliptic (the red line, labeled in degrees) to the horizon, the more favourable the apparition of Mercury. The elevation of Mercury above the horizon and its azimuth (point of the compass above which it appears) are found in the table at the bottom of the page. (Note that astronomers have eccentric ideas about the reckoning of azimuth. While navigators and cartographers measure azimuth from the North, astronomers consider 0° azimuth to mean South. To convert azimuths in the table to compass bearings, add 180 and subtract 360 from the sum if it exceeds that figure.) You can adjust the time and resubmit the Your Sky request to show the appearance of Mercury at various other times. The horizon view will open in a new browser window which will be reused for subsequent requests.

If you prefer an orrery view of the inner solar system at the time of the elongation, press the “View Orrery“ button and Solar System Live will display one.

Observing Site Elongation Date
Latitude: ° North South
Longitude: ° East West


Click on titles to order books on-line from
Meeus, Jean. Astronomical Algorithms . Richmond: Willmann-Bell, 1998. ISBN 0-943396-61-1.
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. Müller.

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by John Walker
September, MIM
This document is in the public domain and may be used in any manner without permission, restriction, attribution, or compensation. Back links to Mercury Chaser's Calculator are welcome.