Friday, September 09, 2005
Movement and Phases of the Moon
Changes in phases of the Moon are observed due to fact that we see one side of the Moon illuminated by the Sun from various angles during the course of its revolution about the Earth.
The period of revolution is the SIDEREAL MONTH and has mean value of 27.32166 days. The SYNODICAL MONTH is the interval of time between two identical phases and has a mean value of 29.53059 days.
The Eastward motion of the Moon against the background of stars has a speed of per mean solar day. Thus time intervals between successive Lunar transits, ie. LUNAR DAYS, have a mean duration of 24hr 51min. The Moon changes its position by approximately , or its own angular diameter, per hour.
The Moon's obstruction of other celestial objects is called occultation. The Moon revolves about its axis with exactly the same period that it revolves about the Earth, ie. in a synchronous orbit --and thus presents the same face towards the Earth.
Librations of the Moon are small oscillations from time to time which allow us to get short glimpses of small portions of the side of the Moon which is normally hidden.
The Moon orbits the Earth in an ellipse (a=384,400 km, e=0.0549). The plane of the lunar orbit intersects the ecliptic at an angle of In consequence of perturbations by the Sun and planets the Moon's orbit has two major motions:
(i) The line of nodes of the lunar orbit (the line of intersection of the plane of the lunar orbit with the plane of the ecliptic) has a retrograde motion ie. rotates towards the West (in the plane of the ecliptic) at a rate of /year ie. with a period of 18.60 years (nutation period). Thus the node, or point at which the Moon's orbit crosses the ecliptic, moves steadily Westward. The interval of time between the passage of the Moon through the same node is called the DRACONITIC MONTH, and is 27.2122 days. The times of the eclipses depend upon these factors.
(ii) Perigee is distance of closest approach, apogee is that of farthest. The line joining these two points (the line of Apsides) has a progressive motion, it advances ie. rotates in space in the plane of the Moon's orbit to the East, ie. direct motion, making one complete revolution in 3232.575 days or about 8.85 years.
Solar and Lunar Eclipses
Conditions for occurrence of an eclipse are determined (largely) by:
the inclination of the lunar orbit to the ecliptic the apparent diameter of the Moon and the Sun (their parallax) and the speed of revolution of the lunar nodes. Eclipses occur when the line of S-M-E or S-E-M coincides with the line of nodes.
Thus Lunar eclipses can only occur at full Moon and Solar eclipses can only occur at new Moon.
Conditions are fulfilled at about 10 days short of 6 monthly intervals--due to motion of lunar nodes--this period of revolution of the lunar nodes relative to the Sun, marking the recurrence of the interval of time during which eclipses are possible is called the period of a SYNODIC REVOLUTION of the NODES or ECLIPSE YEAR (346.62 days).
The SAROS CYCLE. In the course of : the Sun will have passed through the lunar nodes 19 times... 19 x 346.62=6585.78 days,
and the Moon will have performed 223 revolutions...223 x 29.53=6585.19 days.
Thus, after this period the relative positions of the Sun, Earth and Moon repeat themselves. There are about 70 eclipses per Saros roughly in the ratio: 20 solar to 13 lunar.
Unfortunately Roy and Clarke's text on Astronomy: Principles and Practice does NOT deal with the description and explanation of the motion of the Moon, cause of eclipses etc... Many other books do so, including Roy and Clarke's other text: Astronomy : Structure of the Universe
HOWEVER, some freely available accounts are available on the Web. One that I have found at an introductory level and contains some nice diagrams is: Introduction to Astronomy and Astronomy Without a Telescope at http://userzweb.lightspeed.net/~astronomy/nakedeye/nakedeya.html To access these Click here.
The RGO have some leaflets on Eclipses and also the Metonic Cycle and the Saros at http://www.ast.cam.ac.uk/pubinfo/leaflets/
To access these click on Eclipses.
Please let me know if you find any other real or virtual sources with useful information on this topic and I'll add them to this mini-list!
Tue Sep 24 15:09:21 BST 1996