Eclipses only occur if the satellite of a planet is located within 0.5 degrees of the plane of the ecliptic, on a line that passes through the center of the Sun and Earth. The Moon travels along an orbit inclined by 5 degrees to the ecliptic plane, so there are only two opportunities each month -- when it passes through the plane of the ecliptic -- called the ascending and descending nodes.
These two points connected to the barycenter of the Earth-Moon system (the point around which the objects orbit, in this case roughly Earth's center) define a 'line of nodes.' Eclipses of the Sun and Moon will occur if this line of nodes coincides with the line drawn between the center of Earth and the Sun.
Again, the Moon also has to be within 0.5 degrees of one or the other of the nodes so that the disk of the Sun is partially or totally covered in a solar eclipse. A similar argument explains why lunar eclipses do not happen every full Moon at the node opposite the Sun from Earth.
What happens more often, solar or lunar eclipses?
According to Fred Whipple's book Earth, Moon and Planets, solar eclipses are fairly numerous, about two to five per year, but the area on the ground covered by totality is only a few miles (kilometers) wide.
In any given location on Earth, a total eclipse happens only once every 360 years.
Eclipses of the Moon created by Earth's shadow are actually less numerous than solar eclipses; however, each lunar eclipse covers about half of Earth's surface. At any given location, you can have up to three lunar eclipses per year, but some years there may be none.
In any one calendar year, the maximum number of eclipses is four solar and three lunar.
Do eclipses affect humans?
There is no evidence that eclipses have any physical effect on humans. However, eclipses have always been capable of producing profound psychological effects.
For millennia, solar eclipses have been interpreted as portents of doom by virtually every known civilization. These have stimulated responses that run the gamut from human sacrifices to feelings of awe and bewilderment. Although there are no direct physical effects involving known forces, the consequences of the induced human psychological states have led to physical effects.
What are shadow bands?
Shadow bands are among the most ephemeral phenomena seen by observers during the few minutes before a total solar eclipse. They appear as a multitude of faint bands that can be seen by placing a white sheet of paper several feet square on the ground.
They look like ripples of sunshine at the bottom of a pool, and their visibility varies from eclipse to eclipse. 19th-century observers interpreted them as interference fringes caused by some kind of diffraction phenomenon. The Sun, however, is hardly a 'point source' and the patterns are more random than you might expect from diffraction effects.
The simplest explanation is that they arise from atmospheric turbulence. When light rays pass through eddies in the atmosphere, they get refracted. Unresolved distant sources simply '"twinkle," but for nearby large objects, the incoming light can get split into interfering bundles that recombine on the ground to give mottled patterns of light and dark bands, or portions of bands.
Near totality, the image of the sun is only a thin crescent a few arcseconds wide, which is about the same size as the atmospheric eddies as seen from the ground. Bands are produced because the Sun's image is longer in one direction than another. The bands move, not at the rate you would expect for the eclipse but at a speed determined by the motion of the atmospheric eddies.
Will total eclipses of the Sun always happen?
The Earth-Moon system is unique in the solar system, because only for this system at the present time, does the angular size of the Moon match the angular size of the Sun as seen from Earth's surface. This means that sometime during its orbit, the Moon can exactly cover the Sun, causing an observer to be thrown into an eerie nighttime in the middle of the day!
But, the orbit of the Moon is not stable. Because of tidal friction, the orbit of the Moon is steadily growing larger, so that the angular size of the Moon from Earth is growing smaller.
When we get to the point where the Moon only covers 98 percent of the Sun's disk, enough of the Sun will still be visible at totality so that you will not experience nighttime during a total eclipse.
The Sun has a diameter of 870,000 miles (1.4 million kilometers). At the present time, the Sun's angular diameter varies from 32.7 minutes of arc to 31.6 arcminutes.
The Moon, on the other hand, has a diameter of 2,160 miles (3,476 kilometers), and varies in distance between 221,218 miles (356,000 kilometers) at perigee to 252,288 miles (406,000 kilometers) at apogee. This means its angular size ranges from 33.5 to 29.43 arcminutes.
So, there is plenty of opportunity for the angular sizes of the Moon and Sun to be equal for a total eclipse. But, the Moon's orbit is increasing by about a 0.4 inch (1 centimeter) per year, so that when the Moon drifts about 12,552 miles (20,200 kilometers) farther out from Earth, it will be so far away even at its closest point, that its disk will appear smaller than the Sun's disk. At a generous speed of almost 1 inch (2 centimeters) per year, we have about 1 billion years before the last total eclipse occurs.
A complicating viable is that the size of the Sun itself will grow slightly during this time, which will act to make the time of "no more total eclipses" a bit earlier than 1 billion years hence.
How do computers predict eclipses?
Astronomers first have to work out the orbital mechanics of how Earth and the Moon orbit the Sun under the influences of the gravitational fields of these three bodies. From Newton's laws of motion, they mathematically work out the motions of these bodies in three-dimensional space, taking into account the fact that these bodies have finite size and are not perfect spheres, and that Earth and its moon are not homogeneous bodies.
From careful observation, they then feed into these complex equations the current positions and speeds of Earth and the Moon, and then program the computer to "integrate" these equations forward or backward in time to construct ephemerides of the relative positions of the Moon and Sun as seen from the vantage point of Earth. Eclipses are specific configurations of these bodies that can be identified in the computer runs and captured. Current eclipse forecasts are accurate to less than a minute in time over a time span of hundreds of years.
What is the Saros cycle?
The Saros cycle -- hang on to your brain cells here -- exists because it takes 18 years and 10 days for the entire orbit of the Moon to precess once around in its orbit plane so that the lunar nodes make one complete revolution along the orbit. This "Nordical" period equals nearly an integer number of lunar months (223 x 29.53 days = 6,585.19 days) during each Saros cycle. Because the true length of the Saros cycle is 6,585.32 days, you have to wait three Saros cycles in order for a solar eclipse to repeat at the same spot on Earth.