The human eye has a diameter of seven millimetres; a 250 mm
aperture reflecting telescope has 1275 times as much surface area (250
divided by 7, squared), which means that it collects 1275 times as much
light. Celestial objects will therefore appear 1275 times as bright as
with the unaided eye.
Astronomers measure the brightness of stars in terms of a magnitude scale, which is essentially derived from an old classification of stellar brightness as classes 1, 2, 3, and so on. The brightest stars are those of first magnitude and the faintest stars visible with the unaided eye are of magnitude six. There are a number of stars that are brighter than first magnitude; Sirius, the brightest star, shines at magnitude minus 1.4; the planet Venus, at its brightest, shines at around magnitude minus 4. The Sun, being the brightest object in the sky, shines at around magnitude minus 26.
Now, the magnitude scale is a logarithmic one, which basically means that if the brightness is divided by a number x, then 2.5 times log to the base 10 is added to the magnitude. For example, a 250 mm telescope makes celestial objects appear 1275 times brighter, which means it makes them 2.5 xlog1275 which equals 7.8 magnitudes brighter. This means that such an instrument can theoretically extend the observer's visual limit to magnitude 7.8 + 6.0 which equals magnitude 13.8.
In reality however, telescopes do a little better than this calculation suggests; with a 250 mm instrument in good seeing conditions, it is possible to see objects down to a magnitude 14.5. This is due to the fact that a telescope can be focused perfectly, with all the light being captured going straight into the observer's eye. The actual formula to use is 7.5 + 5 x log10 times the telescope aperture in centimetres. So, for the 250 mm telescope, the limiting magnitude is 7.5 + 5log10 x 25, which equals 14.49.
However, reflecting telescopes have a central obstruction caused by the holder of the secondary mirror. This covers around 16 per cent of the total surface area, which costs 0.2 magnitudes. So the limiting magnitude under perfect seeing conditions with a 250 mm reflector will be around 14.3.
Telescopes will brighten point-like objects, such as stars, but not extended objects, like the Moon, the planets, nebulae and galaxies. The reason for this is because the telescope spreads the collected light over a wider area of the eye's retina. This means that the higher the power being used, the dimmer the image becomes. This is a phenomenon that always disappoints those who use a telescope on the night sky for the first time. They expect to see more, but struggle to do so.
However, the telescope is gathering more light than the eye ever can, and an extended object like a galaxy at magnitude 10 will be visible through a telescope, but not as bright as hoped for. This is why astronomers use long exposure photography in order to capture and accumulate all the photons of light coming from extended celestial objects. It is the only way that we can truly appreciate the beauty and the colour of the night sky. Witness the wonderful images obtained by the amateur astronomers from all around the world, and of course by the Hubble Space Telescope.
Astronomers measure the brightness of stars in terms of a magnitude scale, which is essentially derived from an old classification of stellar brightness as classes 1, 2, 3, and so on. The brightest stars are those of first magnitude and the faintest stars visible with the unaided eye are of magnitude six. There are a number of stars that are brighter than first magnitude; Sirius, the brightest star, shines at magnitude minus 1.4; the planet Venus, at its brightest, shines at around magnitude minus 4. The Sun, being the brightest object in the sky, shines at around magnitude minus 26.
Now, the magnitude scale is a logarithmic one, which basically means that if the brightness is divided by a number x, then 2.5 times log to the base 10 is added to the magnitude. For example, a 250 mm telescope makes celestial objects appear 1275 times brighter, which means it makes them 2.5 xlog1275 which equals 7.8 magnitudes brighter. This means that such an instrument can theoretically extend the observer's visual limit to magnitude 7.8 + 6.0 which equals magnitude 13.8.
In reality however, telescopes do a little better than this calculation suggests; with a 250 mm instrument in good seeing conditions, it is possible to see objects down to a magnitude 14.5. This is due to the fact that a telescope can be focused perfectly, with all the light being captured going straight into the observer's eye. The actual formula to use is 7.5 + 5 x log10 times the telescope aperture in centimetres. So, for the 250 mm telescope, the limiting magnitude is 7.5 + 5log10 x 25, which equals 14.49.
However, reflecting telescopes have a central obstruction caused by the holder of the secondary mirror. This covers around 16 per cent of the total surface area, which costs 0.2 magnitudes. So the limiting magnitude under perfect seeing conditions with a 250 mm reflector will be around 14.3.
Telescopes will brighten point-like objects, such as stars, but not extended objects, like the Moon, the planets, nebulae and galaxies. The reason for this is because the telescope spreads the collected light over a wider area of the eye's retina. This means that the higher the power being used, the dimmer the image becomes. This is a phenomenon that always disappoints those who use a telescope on the night sky for the first time. They expect to see more, but struggle to do so.
However, the telescope is gathering more light than the eye ever can, and an extended object like a galaxy at magnitude 10 will be visible through a telescope, but not as bright as hoped for. This is why astronomers use long exposure photography in order to capture and accumulate all the photons of light coming from extended celestial objects. It is the only way that we can truly appreciate the beauty and the colour of the night sky. Witness the wonderful images obtained by the amateur astronomers from all around the world, and of course by the Hubble Space Telescope.
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