Afocal = Describing an optical system in which an image is transferred without bringing it to a focus. Afocal photography, for example, involves pointing a camera, focused on infinity, into the eyepice of a telescope whose image also appears at infinity.
Barlow lens = A diverging lens, usually a doublet, placed in front of the focal point of the telescope to multiply the magnification of an eyepiece. A typical Barlow lens effectively doubles the focal length of the telescope and hence doubles the power of any eyepiece used with it. The value can be varied somewhat by altering the distance between the Barlow and the eyepiece. It was invented in 1834 by the English physicist and mathematician Peter Barlow (1776-1862).
Galileo Galilei (1564-1642) = Italian astronomer, physicist and mathematician. In 1609 he heard of the recent invention of the telescope and began to make his own. He made several small refractors, up to 50mm aperture, the highest magnification being about x30. In 1610 he published "Siderius nuncius" (Starry Messenger) outlining his telescopic discoveries, including mountains on the Moon, four satellites of Jupiter (Known as the Gallilean Moons or Satellites) and innumerable stars of the Milky Way. Also in 1610 he observed the phases of Venus and noted the telescopic apperance of Saturn, although he did not recognize the rings' true nature. Galileo's discoveries added to his discontent with Aristotle's world view and he advocated the Copernican system. This lead to conflict with the Church and he was tried for heresy; he lived the rest of his life under house arrest.
Galilean moons = The four largest moons or satellites of Jupiter, namely Io, Europa, Gannymede and Callisto, which were discovered by Galileo in 1610. All four are easily visible in binoculars and small telescopes, and would be bright enough to be visible with naked eye were it not for the glare of Jupiter.
Occultation =The passage of one astronomical body in front of another, usually the obscuration of a star by the Moon; strictly speaking, a solar eclipse, when the Moon passes in front of the Sun, is a special form of occultation. Precise timings of lunar occultations of stars help to refine our knowledge of the Moon's orbit. Stars can be occulted by asteroids or planetary satellites, which can provide improved diameters for the occulting bodies. The Galilean satellites of Jupiter are regularly occulted by the planet. Jupiter's satellites may occult one another when Earth lies close to their orbital plane.
Penumbra = The lighter, outer region of a sunspot, with a temperature of around 5500K. Small spots often do not have penumbra, but in mature sunspots the penumbra is well developed and occupies about 70% of the total area.
Plössl eyepiece = A design / type of eyepiece using a two-element field lens. The design was invented in 1860 by Austrian optician (Georg) Simon Plössl (1794-1868)
Terminator = The dividing line between the sunlit and night portions of a planet or satellite. It is the line of sunrise or sunset. (sorry nothing to do with Arnie)
Umbra = The central, darkest part of a sunspot. It is also the coolest part, with a temperature of about 4200 K.
All definitions are from the "Oxford Dictionary of Astronomy" by Ian Ridpath. Published by Oxford University Press, ISBN 0-19-211596-0