Astronomy Principles and Practice Fourth Edition.pdf

434 Practical projects
Figure 24.22. Estimation of the fraction of the lunar disc that is illuminated and the variation of this fraction with
time.
24.6 The Moon’s orbit: practical projects
It is possible, without having accurate astronomical instruments, to take observations over a few months
that enable values of the Moon’s orbital elements to be deduced. Observations are made of the Moon’s
phase, its sidereal position and its angular size.
The phase measurements are the easiest to make. If the diameter of the Moon’s disc is divided into
eighths, then it is possible with the naked eye to obtain fairly accurately the number of eighths of the
diameter at right angles to the line joining the cusps that are illuminated. For example, in figure 24.22
the phase would be noted as six. The date and time of the observation is also noted. If observations
are made in this fashion over some months and plotted against time, an accurate value for the synodic
period, S, can be found.
By using a sky map such as Norton’s Star Atlas, the Moon’s sidereal positions on those nights
when stars and Moon are visible may be plotted on the map. The Moon’s right ascension and
declination (read off from the star charts) and the time and date are recorded. As the months pass,
it will be seen that not only does the Moon make circuits of the heavens, crossing from one side of the
ecliptic to the other but the ascending and the descending nodes regress. The nodes are the points on
the ecliptic at which the Moon is seen to cross that plane, the ascending and descending nodes being,
respectively, where the Moon crosses the ecliptic from south to north and from north to south. After
six months, the nodes will have regressed by almost 10 degrees. From a track on the map, or from a
graph of right ascension against date and time, the value for the Moon’s sidereal period, T ,maybe
found.
Changes in the Moon’s angular size are more difficult to detect by the naked eye. The Moon’s
orbital eccentricity has a value of the order of 1/20, so that the ratio of minimum to maximum angular
semi-diameter is about 9/10.
With some relatively simple manufactured equipment, however, the
variations of the apparent angular diameter of the Moon can be measured with sufficient accuracy
to allow determination of the Moon’s orbital eccentricity.
The type of equipment required is a long, graduated rod (AB in figure 24.23). Two metre sticks
attached end-to-end are suitable. A small piece of wood that can be slid along the rod is also required.
A pencil stub attached to the metre sticks with an elastic band is good enough.
The rod is pointed in the direction of the Moon. By trial and error, a position is found for the piece
of wood where its angular size equals that of the Moon. Let this position be distance, d, from the eye.
Then if α° and R° are the semi-diameter and radius of the Moon respectively, while 2r is the