Telescope apertures to see all Messier objects
Galileans/Refractive: 142mm / 5.79" about 6 inches
Newtonians: 164mm / 6.46" about 7 inches (commercially 8 inches)
Maksutov/Catadioptrics: 174mm / 6.85" about 7 inches (commercially 8 inches)
Apparent magnitudes of stars are exponential. Each magnitude measures a light intensity 100^0.2 times less than the previous magnitude. The average human eye can perceive stars up to magnitude 6. Messier objects have a magnitude of up to 11.5. That means that a telescope must capture at least 100^1.1 = 158.5 the amount of light that human eyes capture. So, the relation between a telescope effective area and the human eye area must be about 158.5.
With perfectly efficient lenses, this implies that the minimum aperture for a telescope to help perceive all Messier objects would be (100^1.1)^0.5 = 12.6 times the aperture of the human eye. [ Because 158 = PI *R1^2/ (PI*R2^2) ]. If the average human eye diameter is 9.6mm (http://www.iovs.org/content/37/7/1396.full.pdf), then the minimum telescope aperture should be 121mm, or 4.76". However, telescopes lenses are not that efficient.
In fact, very good telescopes such as those produced by Meade or Celestron, have an efficiency of 85% in each lens.
Different types of telescopes have different numbers of transmissions (lenses/ or mirrors):
Galilean : 2 transmissions
Newtonian : 3 transmissions
Catadioptric: 4 transmissions
Newtonians and catadioptrics have obstructions of about 10%, so they have an additional factor of 90%.
So, the real efficiency of telescopes with transmissions with efficiencies of 0.85% is :
Galilean : 72%
Newtonian : 54%
Catadioptric: 48%
That is, a Galilean telescope effectively transmits 72% of the light that the primary lens concentrates.
The calculated apertures must take in account the efficiency and type of telescope.
[(158 / efficiency)^.5 * Reye = Rtelescope ]
So for the different types of telescopes, apertures are:
Galilean: 142mm / 5.79"
Newtonian: 164mm / 6.46"
Catadioptric: 174mm / 6.85"
That is, if they have very efficient lenses and obstructions of 10%.
Newtonians: 164mm / 6.46" about 7 inches (commercially 8 inches)
Maksutov/Catadioptrics: 174mm / 6.85" about 7 inches (commercially 8 inches)
Apparent magnitudes of stars are exponential. Each magnitude measures a light intensity 100^0.2 times less than the previous magnitude. The average human eye can perceive stars up to magnitude 6. Messier objects have a magnitude of up to 11.5. That means that a telescope must capture at least 100^1.1 = 158.5 the amount of light that human eyes capture. So, the relation between a telescope effective area and the human eye area must be about 158.5.
With perfectly efficient lenses, this implies that the minimum aperture for a telescope to help perceive all Messier objects would be (100^1.1)^0.5 = 12.6 times the aperture of the human eye. [ Because 158 = PI *R1^2/ (PI*R2^2) ]. If the average human eye diameter is 9.6mm (http://www.iovs.org/content/37/7/1396.full.pdf), then the minimum telescope aperture should be 121mm, or 4.76". However, telescopes lenses are not that efficient.
In fact, very good telescopes such as those produced by Meade or Celestron, have an efficiency of 85% in each lens.
Different types of telescopes have different numbers of transmissions (lenses/ or mirrors):
Galilean : 2 transmissions
Newtonian : 3 transmissions
Catadioptric: 4 transmissions
Newtonians and catadioptrics have obstructions of about 10%, so they have an additional factor of 90%.
So, the real efficiency of telescopes with transmissions with efficiencies of 0.85% is :
Galilean : 72%
Newtonian : 54%
Catadioptric: 48%
That is, a Galilean telescope effectively transmits 72% of the light that the primary lens concentrates.
The calculated apertures must take in account the efficiency and type of telescope.
[(158 / efficiency)^.5 * Reye = Rtelescope ]
So for the different types of telescopes, apertures are:
Galilean: 142mm / 5.79"
Newtonian: 164mm / 6.46"
Catadioptric: 174mm / 6.85"
That is, if they have very efficient lenses and obstructions of 10%.
posted by Gralfca at 6:43 PM
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