A Solar Eclipse occurs when the moon passes in front of the sun.
A Lunar Eclipse occurs about twice a year when a satellite of the sun passes between the sun and moon.
This satellite is called the Shadow Object. Its orbital plane is tilted at an angle of about 5°10' to the sun's orbital plane, making eclipses possible only when the three bodies (Sun, Object, and Moon) are aligned and when the moon is crossing the sun's orbital plane (at a point called the node). Within a given year, considering the orbitals of these celestial bodies, a maximum of three lunar eclipses can occur. Despite the fact that there are more solar than lunar eclipses each year, over time many more lunar eclipses are seen at any single location on earth than solar eclipses. This occurs because a lunar eclipse can be seen from the entire half of the earth beneath the moon at that time, while a solar eclipse is visible only along a narrow path on the earth's surface.
Total lunar eclipses come in clusters. There can be two or three during a period of a year or a year and a half, followed by a lull of two or three years before another round begins. When you add partial eclipses there can be three in a calendar year and again, it's quite possible to have none at all.
The shadow object is never seen because it orbits close to the sun. As the sun's powerful vertical rays hit the atmosphere during the day they will scatter and blot out nearly every single star and celestial body in the sky. We are never given a glimpse of the celestial bodies which appear near the sun during the day - they are completely washed out by the sun's light.
It is estimated that the Shadow Object is around five to ten miles in diameter. Since it is somewhat close to the sun the manifestation of its penumbra upon the moon appears as a magnified projection. This is similar to how during a shadow puppet show your hand's shadow can make a large magnified projection upon your bedroom wall as you move it closer to the flashlight.
Dr. Samuel Birley Rowbotham has provided equations for finding the time, magnitude, and duration of a Lunar Eclipse at the end of Chapter 11 of Earth Not a Globe.
There is also a possibility that the Shadow Object is a known celestial body which orbits the sun; but more study would be needed to track the positions of Mercury, Venus and the sun's asteroid satellites and correlate them with the equations for the lunar eclipse before any conclusion could be drawn.