Читать книгу Eclipse: The science and history of nature's most spectacular phenomenon - J. McEvoy P. - Страница 14

Figure 1.1 shows the two nodes of the Moon’s orbit, the points where the orbit intersects the ecliptic, the path of the Sun on the celestial sphere. The ascending node is defined as the point where the Moon crosses the ecliptic from below to above, south to north. The other node, the descending node, is the point where the Moon crosses the ecliptic from above to below, north to south.

In Figure 1.9 the celestial sphere model has been redrawn with some added features. So that we can further examine the all-important conditions for eclipses, an imaginary line has been drawn connecting the two nodes on the ecliptic. Not surprisingly, this line is known to astronomers as the ‘line of nodes’. The line of nodes rotates slowly in a direction opposite to the Sun’s motion, taking 18.61 years to complete one rotation. When this line is aligned with the Sun, an eclipse can take place. As there are two nodes, the alignment occurs about twice a year. The period of time either side of an alignment is called an eclipse season because if a new Moon occurs at this time, it will be near a node and a solar eclipse is likely.

Figure 1.9. The celestial sphere, showing the ecliptic limits and the line of nodes of the Moon’s orbit.

The motion of the line of nodes affects the time between eclipse seasons. The Sun appears to move about 1° per day eastward around the ecliptic, making a circuit of the sky in 365.25 days – a solar year. The line of nodes slowly regresses westward, in the opposite direction, at a rate of 18.61 years for one cycle. So an eclipse year, the time it takes the Sun to travel from alignment with one node to alignment with the same node again, will be less than a solar year. The length of the eclipse year can easily be calculated.

The line of nodes makes one rotation in 18.61 years, so it moves at a rate of 360/(365.25 x 18.61) = 0.053° per day westward around the ecliptic (365.25 being the length of the solar year). The Sun moves at a rate of 360/365.25 = 0.986° per day in the opposite direction. To get the combined rate of motion of the line of nodes and the Sun towards each other, add the two together to get 1.039° per day. The length of the eclipse year is therefore 346.62 days (the angular values are given here correct to three decimal places – the precise values do yield 346.62 days). From one node to the next, say the ascending node to the descending node, will take half that time, 173.3 days. These values have important consequences for calculating the frequency at which eclipses take place.