on the Earth–Moon distance.
There are two parts to any shadow produced by an extended light source like the Sun. The umbra is the zone of total shadow, from within which no part of the Sun can be seen. If the tip of the umbral shadow cone reaches the Earth, those within the small region where it falls will see a total eclipse. Outside the umbra but within the penumbra, the light is not completely cut off by the Moon, and an observer on the Earth sees some part of the Sun, experiencing a partial eclipse. A total eclipse is the most interesting type. For an observer within the umbra, the faint corona surrounding the Sun can be seen if the sky is clear of cloud. The corona is a very thin gas, mostly hydrogen, forming the outer atmosphere of the Sun, which appears as a halo during a total eclipse – it is in fact the most distinguishing characteristic of a total eclipse. A partial eclipse can also be seen when only the penumbra strikes the Earth. None of the special characteristics of totality such as the corona are seen during a partial eclipse.
Figure 1.5. Types of solar eclipse: total (a), partial (b) and annular (c).
In an annular eclipse, the Moon is aligned in front of the Sun but does not completely cover the Sun’s disk because the umbra does not quite reach the Earth. It is still a striking visual effect, with sunlight streaming out from a ring around the Moon’s outer rim. This gives the eclipse its name: annular means ‘ring-like’. As in a partial eclipse, the faint solar corona is not seen in an annular eclipse, for it is overwhelmed by the bright direct sunlight from the annular ring. An annular eclipse can be demonstrated by a slight variation in the DIY demonstration. Align the penny as before, just covering the coaster, then move the penny away from your eye slightly. You will see a ring of the coaster appear around the penny. Voilà – an annular eclipse!
The fact that a central alignment can cause either a total eclipse or an annular eclipse implies that the Earth–Moon distance varies. The Moon is not always close enough to the Earth to obscure the entire face of the Sun. In fact, both the Earth–Moon distance and the Earth–Sun distance change continuously as the Earth and Moon trace out their orbits. The values given in Table 1A for these distances are averages: at a given moment their orbital distances can be more or less than these values. Consequently, the Moon is sometimes not close enough to eclipse the Sun totally, even when perfectly aligned, and an annular eclipse happens instead.
The variation of the Earth–Moon and Earth–Sun distances is due to the non-circularity of their orbits. This is a characteristic of all orbiting bodies, and was one of the discoveries made by the German astronomer Johannes Kepler (1571–1630) early in the seventeenth century. Kepler had proposed a set of laws for planetary motion which were completely at odds with contemporary theories. The first law stated that all the planets, including the Earth, move in orbits around the Sun which are elongated circles called ellipses. Furthermore, said Kepler, the Sun is not at the centre of the planet’s orbit, but sits at one of two points on each side of the centre, each called a focus.
Kepler’s second law proposed another revolutionary idea: that the planets do not move uniformly, but continuously slow down when moving away from the Sun, and speed up when moving towards the Sun. A planet moves fastest at the point in its elliptical orbit where it makes its closest approach to the Sun, called perihelion. It moves slowest at the other end of the orbit, when farthest from the Sun, at the point called aphelion. These extreme points of the orbits are indicated by two prefixes, peri- meaning ‘near’, and ap- meaning ‘away from’; -helion is from the Greek word for the Sun, helios. Figure 1.6 shows the elliptical orbit of the Earth, with the Sun slightly off-centre (the shape of the ellipse is exaggerated a little for clarity). The arrows on the orbital path indicate the speeding up of the Earth as it approaches the Sun and the slowing down as it recedes from the Sun.
Figure 1.6. The Earth’s orbit, showing the variation of the Earth–Sun distance.
Figure 1.7. The Moon’s orbit, showing the variation of the Earth–Moon distance.
The same thing happens with the Moon. In 1687 Isaac Newton (1642–1727) published his theory of gravitation which showed that Kepler’s laws were quite general: any body orbiting another attracting body will obey Kepler’s laws. So the Moon also moves in an elliptical orbit around the Earth, which lies at one focus of the ellipse. The Moon’s orbit around the Earth is shown in Figure 1.7. Again, arrows indicate the speeding up and slowing down of the Moon in its orbit (and again, the ellipse is exaggerated). At the ends of the Moon’s orbit there are equivalent points of closest and farthest approach to the Earth, called perigee, ‘near the Earth’, and apogee, ‘away from the Earth’.
In Newton’s theory of gravitation the attracting gravitational force between two bodies increases as the distance between them increases. It is this variation of the gravitational pull of the attracting body, the Sun pulling on the Earth and the Earth pulling on the Moon, which causes the speeding up and slowing down of the Earth and the Moon in their orbits.
The distances of closest and farthest approach of the Earth and the Moon are indicated in Figures 1.6 and 1.7. From these distances, the percentage change can be computed. The Earth’s orbit is nearly circular, and its distance to the Sun varies only by about 3 per cent. However, the Moon’s orbit is more elongated, and the Earth–Moon distance varies by 12 per cent over the course of each monthly cycle. As a result, an observer on the Earth will see the diameter of the Sun change by 2 per cent around its average value, and the angular diameter of the Moon by 8 per cent. Figure 1.8 shows tracings of photographs taken with the same telescope and lens of the full Moon at perigee and apogee. The effect of the orbital variation on the size of the Moon’s image as seen from the Earth is clear. Optimum conditions for a solar eclipse are summarised in Table IB.
Figure 1.8. Tracings of photographs of the full Moon at perigee and apogee. The same 100 mm f/10 refracting telescope was used for both photographs (based on Harrington 1997).
after Phillip S. Harrington
Table 1B. Orbital conditions of Earth and Moon for solar eclipses.
| Position of Earth | Position of Moon | Type of solar eclipse |
| Aphelion | Perigee | Total |
| (maximum distance from Sun)Sun’s image maximum | (minimum distance from Earth)Moon’s image minimum | |
| Perihelion | Apogee | Annular |
| (minimum distance from Sun)Sun’s image maximum | (minimum distance from Earth)Moon’s image minimum |
THE