Observing Project 7B Dichotomy of Venus and Mercury

In this project, we will use our telescopes to judge the time at which Venus and Mercury reach dichotomy or precisely half-illuminated. For Venus, this will come almost exactly on the day of greatest elongation when Venus is at the corner of a right angle involving itself, Earth and the Sun. For Mercury though, this can come several days before or after the day of greatest elongation. The principle reason is due to the elongated nature of Mercury's orbit as opposed to the nearly circular orbit of Venus.

An inferior planet always shows its one-half phase when it reached that position at the corner of that right angle. If the orbit of the planet is perfectly circular or nearly so, then that will also be the time of greatest elongation. Venus' orbit is the closest to a perfect circle in the entire solar system so it is very likely that dichotomy and greatest elongation will always occur close to the same time. For Mercury, however, its orbit is one of the most eccentric of any major body in the entire solar system. Only that of Pluto is more elongated. This can cause Mercury to reach greatest elongation early simply because it may be several million miles farther from the Sun and thus reach greatest elongation while still gibbous. Or if it is near perihelion, the planet may reach half-illuminated on perihelion day, then continue to climb away from the Sun as it pulls away in its orbit. This will happen very quickly because Mercury's orbital speed is double at perihelion what it is at aphelion. A few days difference therefore can mean several million kilometers difference in Mercury's distance from the Sun.

Study Mercury and Venus carefully as they swing around the Sun towards their half-illuminated phase. Know when the date of greatest elongation is for the planet and make a careful estimate of how much of the planet's surface is illuminated on that date. For Venus, it is a good bet that the planet will be half-lit on the day of greatest elongation, or fairly close to it. For Mercury, the only time that dichotomy and greatest elongation will occur on the same day is if the planet is also at perihelion or aphelion on or about that exact date. Remember also for Mercury that the planet's brightness will also vary dramatically on the day of greatest elongation depending upon what its phase is. If the planet is less than half-illuminated it will likely be fainter than zero magnitude while if it is gibbous, then it will likely be brighter than zero magnitude. Mercury's distance from Earth will also be a factor in determining how bright the planet will appear at any given time. Watch Mercury carefully from apparition to apparition and see how its behavior changes each time it comes around the Sun.

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