Astronomy 1L (Lab Class) Information
Mercury Orbit Project: Part 1 (supplementary discussion) Link for sharing this page on Facebook
Examining the Declinations of the Sun and Mercury
  If you examine the declinations for the Sun (as shown in the data table for the Mercury Orbit Project), you will find that they start off (in January of 1982) as moderately large negative numbers, meaning that the Sun was well to the south of the Celestial Equator, as we would expect, since it is winter in the Northern Hemisphere at that time of year. As the year progresses, the Sun moves to the north in the sky, and the negative numbers that represent its declination gradually decrease until, in late March, the Sun crosses the Equator at the Vernal Equinox, and its declinations become positive.
  Until the Sun reaches its furthest northern position at the Summer Solstice in late June, its declinations continue to increase, but after that they begin to decrease, going from positive to negative when it crosses the Equator again at the Autumnal Equinox in late September. As it continues its southward motion, the declinations become larger and larger negative numbers, until in late December, when the Sun reaches the Winter Solstice, they are as large as possible. After that the Sun resumes the northward motion that it had at the beginning of the year, and the numbers for the declination change as they did before, until the Sun once again reaches the Summer Solstice, in mid 1983.
  Looking at the values for the Sun's declination, we find that they range from about minus 23 1/2 degrees in late December and early January, to plus 23 1/2 degrees in late June and early July. This means that to have all of the Sun's dots neatly positioned on a graph, that graph should cover a range of declinations from around minus (that is, south) 25 degrees, to around plus (or north) 25 degrees. We could cover only the actual range of solar declinations, but when labeling a graph it is customary to use multiples of 5 or 10, since we are used to counting by 10's, so it feels more normal to have labels extending to 25 degrees, rather than 23 1/2 degrees.
  Of course before we make any final plans, we should make sure that Mercury's motion also falls within this range. Since it is not in the same place as the Sun, it could move east or west and north or south relative to the Sun, and if it happened to be to the north of the Sun when the Sun is in the northern part of its motion, or to the south of the Sun when the Sun is in the southern part of its motion, it could have declinations that fall outside the range just discussed. We therefore need to take a close look at Mercury's declinations as well, before making a final decision about what part of the sky needs to be shown on our graph.
  As in the case of the Sun Mercury starts, in January of 1982, well to the south of Equator, and has a moderately large negative declination. For a while, also as in the case of the Sun, Mercury's declinations gradually become smaller and smaller negative numbers, indicating that like the Sun, it is moving northward in the sky. In fact, Mercury's declinations move northward considerably faster than those of the Sun, so that in late January, when the Sun is at -18 degrees declination, Mercury is already at -13 degrees, nearly 5 degrees to the north of the Sun. However, after that, Mercury turns back to the south, and by February 22, when the Sun is at -10 degrees declination, Mercury had moved back down to -17 degrees, more than 7 1/2 degrees to the south of the Sun. The Sun's declination gradually and steadily increases for half a year, then gradually and steadily decreases for the other half of the year, but Mercury's motion is much more complex, and its declination changes, first one way and then the other, several times during the year.
  In late February, Mercury's motion changes again, and it moves northward again, more and more rapidly, crossing the Equator in early April, and by mid May, it has reached 24 1/2 degrees declination, further north than the Sun ever gets, and is more than 6 degrees to the north of the Sun. Since Mercury seems to be capable of attaining declinations as much as 6 or 7 degrees north or south of the Sun's declination, we can begin to wonder whether the range from plus 25 degrees declination to minus 25 degrees declination will prove sufficient to cover all of Mercury's positions.
  As it turns out, however, after reaching 24 1/2 degrees north declination in mid May, Mercury never again (at least during this year and a half) reaches that same high declination, so taking our graph up to plus 25 degrees declination proves to be quite adequate.
  At the other end of the two objects' motion, however, the situation is not quite so happy. As the two objects move southward in the sky, Mercury continues to move north and south relative to the Sun, and as the Sun approaches its lowest position, in December, Mercury once again dips beneath the Sun's path, and in the process, on four dates, falls below minus 25 degrees declination, meaning, of course, that our graph will also have to extend below that position.
  If, when Mercury dipped below -25 degrees, it went well below that point, we would need to consider taking our graph all the way to 30 degrees south declination. However, the furthest south that it ever gets is only about -25 1/2 degrees, so to a first approximation, the range from -25 to +25 degrees declination will work for both objects, providing we can manage a little extra room at the bottom of the graph for the four dates when Mercury dips just below -25 degrees.
  In other words, to plot all the declinations, we need to cover a range from +25 to just under -25, which is a little over 50 degrees.