Visibility of Planetary Phenomena

In addition to the limitations of the eye, the observability of phenomena is determined to some degree by the longitude and latitude of the observer, time of night, time of month, and time of year. Most astronomical phenomena cannot be observed when the Sun is in the sky, eclipses and most lunar phenomena excepted. There are occasions when the brighter planets and even the brightest stars can be seen, even in competition with the full light of the Sun. The daytime visibility of objects is best where the scattered sunlight is least— at a high-altitude site on a clear day. Even under the best conditions, and at large elongations, daytime sightings are difficult, except perhaps for Venus. Thus, the long days of high-latitude summers are unfavorable to observations of objects other than the Sun and Moon. Twilight observations of the brighter planets, Venus and Jupiter, on the other hand, are not particularly difficult at any site or time of year. One measure of the visibility of objects at twilight is the arcus visionis, or arc of vision. It is the sun's altitude below the

13 When a telescope is used, the diameter of the primary mirror (for a reflecting telescope) or objective lens (refracting telescope) is used.

horizon at which an object such as a star or planet can just be seen rising before sunrise (or setting after sunset). van der Waerden (1974, p. 19) states that this is 9° or 10° for bright stars such as Sirius, under favorable weather conditions. For a planet such as Venus moving through inferior conjunction, it can be smaller, and observers have claimed to have seen it as an evening star on one evening and a morning star the next morning. The Maya used an interval of eight days for the invisibility of Venus at inferior conjunction, a mean value with which most modern observers agree. The actual values of this interval of invisibility vary between 1 and 20 days.

The celestial equator rises from the east and west points of the horizon at an angle that depends on the latitude: At the equator, this angle is 90°; at the poles, it is 0°. At low-latitude sites like Yucatan (~20° N), the ecliptic, and planetary paths, may be inclined to the horizon at a large angle, facilitating planetary observations. Mercury can not be seen more than about an hour before sunrise nor more than about an hour after sunset, at the best of sites. The limited ranges of inner planet elongations are due to the apparent size of the orbit as seen from Earth (see Figure 2.24). The ability to account for such phenomena was perhaps the Copernican revolution's greatest triumph.

Mercury is particularly difficult to see at high latitudes because of the generally low arc of the ecliptic with respect to the horizon. Copernicus is supposed never to have seen this planet. One of us has seen Mercury several times, even at high latitude sites (see Figure 3.7), but it is not particularly easy under most circumstances. Clear skies down to a level or sublevel horizon, without fog, but perhaps with some cloud below the horizon to dim the scattered light of the sun and improve contrast could aid the resighting of a planet.

Venus is more easily seen than is Mercury, not only because it is often brighter but because its maximum elongation is greater. As we will see (§§12.7,12.10), however, the Maya recorded the intervals of the Venus synodic cycle quite differently from the actual values, except for the period of invisibility at inferior conjunction. Also among the Maya, it was recognized that there are additional periodicities in the apparent motions of Venus in both its evening and morning forms. An eight-year cycle in the movement of Venus among the stars was incorporated into aspects of the calendar (see §12.7).

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