Libration of the Moon, Hevelius's Theory, and its Early Reception in England

Abstract

In first-order approximation, the Moon rotates uniformly in the course of a month, at the same time revolving in her orbit around the Earth with variable angular velocity, according to Kepler's second law. Although the periods of both motions are synchronized, changes in orbital speed cause an observer on Earth to see either the western or the eastern edge of the lunar disk, depending on the conditions. Because of this, the maximum angular shift of surface objects relative to the centre of the Moon is ±7.9°. This is what we call optical libration in longitude. And, moreover, the Moon's rotational axis is not perpendicular to the orbital plane, but tilted away from the normal to the orbital plane by 6°4G, which is the reason why, in the course of the month, we have alternating views of the north and of the south pole of the Moon. This phenomenon, known as optical libration in latitude, leads to the angular shift of surface objects (±6.8° maximum; see Figure 1), in relation to the centre of the Moon. One also needs to consider that observations of the Moon's surface are not conducted from the centre of the Earth, but from its surface, which each day makes one revolution around the Earth's axis. In this way, analogous to the phenomenon of diurnal parallax, we have diurnal libration, also called parallactic libration. Its maximum value is equal to 57'. The three types of libration described here enable us to view not half but 59% of the Moon's surface from the surface of the Earth.1For obvious reasons, the period of libration in longitude is the anomalistic month (the time between successive passages of the Moon through perigee), while in latitude it is the draconic month (the time between successive passages of the Moon through her ascending node). Due to the incongruence of these periods, the manifestations of libration change from month to month. Optical libration in longitude and in latitude can be illustrated as the oscillations of a point on the surface of the Moon that marks the centre of the lunar disk (at perigee, for example), in relation to a line connecting the Earth and the Moon at their centres of mass. In Figure 2, two diagrams based on this model are used to illustrate the variability of optical libration, by showing different paths of the centre of the lunar disc for January 1635 and January 1643. Finally, we need to recognize that optical libration in latitude and longitude has a direct consequence for an observer on the Earth: the changing position of lunar spots relative to the edges of the lunar disk.The First Reports of LibrationAlthough the optical libration of the Moon is a phenomenon that can be seen with the naked eye, its discovery was strictly tied to the development of telescopic observations of the Moon's surface in the first half of the seventeenth century, as well as to the emergence of selenography, a new discipline in the field of celestial cartography2 The oldest preserved source that most likely refers to the phenomenon of libration is a note from December 1611, made by Thomas Harriot (c. 1560-1621) in the course of one of the three lunar observations he made that month. The English mathematician noticed that two features of the Moon's surface (today called Mare Frigoris and Sinus Roris) appeared closer to the edge of the lunar disk than was the case on the map he had drawn sometime earlier (Figure 3).3 Since he did not follow up on his note, we cannot rule out the possibility that he thought his own map to be inaccurate in this respect. Nonetheless, we could consider this to be the first (qualitative) record of libration in latitude. However, the handwritten notes left by Harriot were not discovered until the end of the eighteenth century,4 so most often it is Michael Florentius van Langren (1600-75) and Galileo Galilei (1564-1642) who are given credit for first mentioning lunar libration.The Dutchman van Langren, Royal Cosmographer and Mathematician to King Philip IV of Spain, wanted to create a map of the Moon that could be used to determine terrestrial longitude through the comparison of sunset and sunrise times at defined points corresponding to the surface features of the Moon. …