Whether you’re a die-hard who insists on measuring the distances between the planets and the Sun yourself (which I’ve shown you how to do here and here), or you are willing to accept what other people tell you about them, it’s interesting to look at the pattern among these distances. They are shown at right, starting with the smallest — Mercury (Me) — and proceeding to Venus (V), Mars (Ma), Jupiter (J), Saturn (S), Uranus (U) and Neptune (N), nearly 100 times further out than Mercury. The inner planets up to Mars are very close together, all bunched within 1.5 times the Earth-Sun distance, whereas the outer planets are much further apart.
Also shown in the figure are the lengths of the planet’s cycles. Remember, a cycle starts when a planet reappears from behind the Sun and ends when a planet again disappears behind the Sun… the moment of “solar conjunction,” or just “conjunction” for short in this post. Some planets have short cycles, others have long ones. Interestingly, now it is the outer planets that all bunch up together, with their cycles just a bit longer than an Earth year, whereas Mercury, Venus and Mars have wildly different cycles ranging from a third of an Earth-year to two Earth-years. In the figure I’m also keeping track of something that I didn’t mention before. As their cycles begin, Mercury and Venus initially move into the evening sky, in the west, setting just after sunset. I’ve indicated that with a “<” Meanwhile Mars, Jupiter and Saturn move into the eastern morning sky, rising just before sunrise, as indicated with a “>”. (Mars, Jupiter and Saturn just reappeared from behind the Sun this winter; that’s why they’re all in the morning sky right now.) This difference is going to prove important in a moment.
Before going on, let me make another version of the same figure, easier to read. This involves making a “logarithmic plot”. Instead of showing the step from 1 to 2 as the same as the step from 0 to 1, as we usually do, we replot the information so that the step along the axis from 1 to 10 is the same as the step from 0.1 to 1. It’s gives exactly the same information as the Figure 1, but now the planet-Sun distances don’t bunch up as much.
Orbits Vs. Cycles
Now, the cycles from one solar conjunction to the next, long beloved of astrologers, are not beloved of astronomers, because they involve a combination of two physically unrelated motions. A solar conjunction happens when a planet disappears behind the Sun from Earth’s perspective, so the time between one conjunction and the next combines:
- the orbital motion of the planet around the Sun;
- the yearly rotation of the line between the Sun and the Earth. (So far, we haven’t found evidence as to whether the Sun moves around the Earth or the Earth moves around the Sun — and we’ll remain agnostic about that today.)
So what astronomers want to know is the orbital period of each planet — it’s own year. That is, how long does it takes each planet to orbit the Sun, from the planet’s perspective, or from the Sun’s perspective. This is the time that an observer on the Sun would see for the planet to complete a circle relative to the fixed stars, and vice versa. (Remember we gathered evidence that the stars are fixed, or extremely slowly drifting from the perspective of the Earth, using a gyroscope, whereas either or both the Sun or the Earth are rotating relative to one another by about one degree per day. We also know the stars are much further than the Sun from our two measurements of the Moon’s radius.)
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