Astronomical Telescope Help
Several parameters are significant when determining the effectiveness of a telescope for various applications. Here are the most important ones.
The magnification , also called power and symbolized ×, is the extent to which a telescope makes objects look closer. Actually, telescopes increase the observed sizes of distant objects, but they do not look closer in terms of perspective. The magnification is a measure of the factor by which the apparent angular diameter of an object is increased. A 20× telescope makes the Moon, whose disk subtends about 0.5 degrees of arc as observed with the unaided eye, appear 10 degrees of arc in diameter. A 180× telescope makes a crater on the Moon with an angular diameter of only 1 minute of arc (1/60 of a degree) appear 3 degrees across.
Magnification is calculated in terms of the focal lengths of the objective and the eyepiece. If f o is the effective focal length of the objective and f e is the focal length of the eyepiece (in the same units as f o ), then the magnification factor m is given by this formula:
m = f o / f e
For a given eyepiece, as the effective focal length of the objective increases, the magnification of the whole telescope also increases. For a given objective, as the effective focal length of the eyepiece increases, the magnification of the telescope decreases.
The resolution , also called resolving power , is the ability of a telescope to separate two objects that are not in exactly the same place in the sky. It is measured in an angular sense, usually in seconds of arc (units of 1/3,600 of a degree). The smaller the number, the better the resolving power.
The best way to measure a telescope’s resolving power is to scan the sky for known pairs of stars that appear close to each other in the angular sense. Astronomical data charts can determine which pairs of stars to use for this purpose. Another method is to examine the Moon and use a detailed map of the lunar surface to ascertain how much detail the telescope can render.
Resolving power increases with magnification, but only up to a certain point. The greatest image resolution a telescope can provide is directly proportional to the diameter of the objective lens or mirror, up to a certain maximum dictated by atmospheric turbulence. In addition, the resolving power depends on the acuity of the observer’s eyesight (if direct viewing is contemplated) or the coarseness of the grain of the photographic or detecting surface (if an analog or digital camera is used).
The light-gathering area of a telescope is a quantitative measure of its ability to collect light for viewing. It can be defined in centimeters squared (cm 2 ) or meters squared (m 2 ), that is, in terms of the effective surface area of the objective lens or mirror as measured in a plane perpendicular to its axis. Sometimes it is expressed in inches squared (in 2 ).
For a refracting telescope, given an objective radius of r , the light-gathering area A can be calculated according to this formula:
A = π r 2
where π is approximately equal to 3.14159. If r is expressed in centimeters, then A is in centimeters squared; if r is in meters, then A is in meters squared.
For a reflecting telescope, given an objective radius of r , the light-gathering area A can be calculated according to this formula:
A = π r 2 – B
where B is the area obstructed by the secondary mirror assembly. If r is expressed in centimeters and B is expressed in centimeters squared, then A is in centimeters squared; if r is in meters and B is in meters squared, then A is in meters squared.
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