Mercury's Rotation Rate
When, in the mid-1880s, the Italian astronomer Giovanni Schiaparelli (1835-1910) attempted to construct a map of Mercurian features, he found that the shape and relative position of the fuzzy surface features that his telescope could reveal did not change greatly with time. Schiaparelli subsequently reasoned that his observations could be best explained if Mercury kept the same face pointed toward the Sun at all times.
If a planet or a satellite spins on its axis at exactly the same rate that it moves around in its orbit, then it is said to be in synchronous rotation. Our Moon, for example, is in synchronous rotation about Earth, and consequently we always see the same lunar features. Synchronous rotation arises through gravitational interactions, and mathematicians have been able to show that once the spin of an object has been synchronized it remains so in a stable fashion. An alternative way of saying that an object spins in a synchronous manner is to say that is satisfies a 1-to-1 spin-orbit coupling.
Astronomers believed that Mercury was in a 1-to-1 spin-orbit coupling with the Sun until the mid-1960s. The first hint that Mercury might not be in synchronous rotation about the Sun was revealed through Earth-based radar measurements. By analyzing the Doppler shift in the returned radar signals, astronomers were able to show that Mercury did not rotate fast enough to be in a 1-to-1 spin-orbit coupling with the Sun. Rather they found that Mercury's rotation rate is 58.646 days. Since Mercury orbits the Sun once every 87.969 days, the radar measurements indicated that the planet is in a 3-to-2 spin-orbit coupling with the Sun. That is, Mercury spins three times about its axis for every two orbits that it completes about the Sun. The Mercurian day, that is the time from sunrise to sunset is therefore 88 terrestrial days long. From Earth its greatest angular diameter is just 4/1000th of a degree. This angular size translates to a physical diameter of 3,030 mi (4,879 km), making Mercury about 1/3 the size of Earth, or about 1.5 times larger than the Moon.