The rotation of Mercury
Published on Mar 14, 2006 at 7:10 pm.
No Comments.
Filed under Mercury, planets.
A couple days ago, in my post on Enceladus, I mentioned the rotation of Mercury as having a 3:2 spin-orbit coupling. I thought that I might say more on the subject.
Spin orbit coupling occurs when tidal forces on a planet or moon cause either speed up or slow down the rotation to match the orbital period. The usual case is 1:1 spin-orbit coupling, such as Earth’s Moon. Tidal forces between Earth and the Moon work on both bodies to slow the rotation to match the orbit. The Earth is bigger, so its work is done first. The Moon, however, is still acting on Earth gradually slowing its rotation rate. Fossil records indicate that millions of years ago, there were about 400 days in a year. That isn’t because the year was longer. Instead, the days were shorter, so the Earth turned more in the course of a year. Without the effects of the Moon, Earth might have a day only a five or six hours long.
As early as the 19th Century, physicists understood tidal dynamics enough to explain the 1:1 spin-orbit coupling of the Moon, and to even predict that tidal forces are also causing the Moon to recede from the Earth. Reflectors left on the Moon by the Apollo astronauts, together with a powerful laser at McDonald Observatory in west Texas, showed that the Moon recedes from the Earth an average of almost 4 centimeters per year. It was also entirely conceivable that a planet orbiting close to the Sun would experience similar forces as a moon around a planet. So, it was not at all a surprise when the astronomer Giovanni Shiaparelli declared that Mercury had a 1:1 spin-orbit coupling to the Sun (not quite correct, as we shall see).
Mercury is very close to the Sun in the sky, so it is always very hard to see. Mercury’s the most elliptical of the major planets (Pluto’s is slightly more, but Pluto isn’t really major!). The best time to observe Mercury is when it is at its farthest from the Sun, a point in the orbit called its aphelion. Since Mercury’s orbit is 88 days long, this happens about every three months. So, Schiaparelli observed Mercury, and he believed that he saw vague fuzzy markings on it (an amazing observation, given his equipment!). The next time Mercury was at aphelion, though, it was lined up with the Sun as seen from Earth, so he had to wait until the next aphelion after that. He then was able to observe Mercury again, but seen from the opposite side of the Sun as before. Then, the next aphelion, Mercury was again hidden in the glare of the Sun, but Shiaparelli was able to see the aphelion after that one. He was now seeing the planet from the same vantage point as before. Two aphelia later, he again saw the planet. He kept this up for several years until the alignments were not so ideal. His observations seemed to show the same fuzzy patches each time that he looked at Mercury from the same vantage point. He was seeing Mercury exactly two orbits later, and it seemed to have the same side lit up. So, from knowing that the Moon had a 1:1 spin-orbit coupling, he just assumed that so did Mercury. After all, if every time that you look you see the same side lit, what else would you expect? You’d just assume that it was spinning at the same rate as its orbit, so it would always keep one side towards the Sun.
This was the standard model for Mercury. Even when I went to school, textbooks said that Mercury always kept the same side towards the Sun (pre-college textbooks are notoriously out of date when it comes to the latest scientific news). The big shock, though, came in 1965 when astronomers using the powerful radio transmitter at the Arecibo radio telescope bounced radar signals off of Mercury. The radar bounced back, but Doppler shifted. A Doppler shift is a change in frequency of a wave reflected off of a moving object. As Mercury rotated, one side was approaching us, and the other was receding. This resulted in a Doppler shift on each side, but in opposite directions. Analyzing the spread of the Doppler shifts, astronomers were able to accurately measure the rotational rate of the planet. I often have my students do an exercise where they analyze this data to measure the rotational rate of Mercury. What was found, though, in 1965 was that Mercury did not rotate in 88 days as everyone expected. Instead, it rotated in a bit over 58.6 days. This was exactly 2/3 of the orbital period. Mercury has a 3:2 spin-orbit coupling. So, that means that Mercury rotates exactly 3 times every two orbits. So, Shiaparelli was correct in thinking that he was always seeing the same side of the planet. He was looking every two orbits. He simply came to a wrong, though perfectly understandable, conclusion from his observations.
So, how does this sort of strange 3:2 coupling occur? Well, it is simple. Mercury’s orbit is very elliptical. It’s aphelion (farthest from the Sun) is almost 50% farther than its perihelion (closest to the Sun). Thus, the tidal forces that would lock the planet are far stronger at perihelion than at aphelion. So, what has happened is that the Sun has locked the perihelion rotational rate to very near the orbital rate. However, elliptical orbits speed up and slow down, moving fastest at perihelion. So, Mercury is locked to the faster portion of its orbit. This also means that the aphelion is going to have the same side illuminated every second orbit. It is just dumb luck that Earth’s orbit is such that we only get to get a good view of Mercury every two Mercury orbits!
Anyway, another piece of astronomy history trivia.
-Astroprof
