Space Telescopes

1 degree = 60 arcminutes or 3,600 arcseconds (written as 3600”)
1 arcminute = 60 arcseconds
1 radian = 57.295 degrees
Visible Light: 0.39 to 0.75 micrometres
Near Infrared IR: 0.78 to 3 micrometres
Medium Wavelength IR: 3 to 50 micrometres
Long Wavelength IR: 50 to 1000 micrometres
1 inch: 25,400 micrometers
1 cm: 10,000 micrometres
A Microsoft Excel file with the most important equations already laid out is available HERE.
Degrees = ArcSeconds / 3600
Radians = Degrees • ( π / 180)
EXAMPLE: Our Space telescope can resolve down to 0.05 arcseconds. What is this in radians? First, we convert arcseconds to Degrees. 0.05 / 3600 = 1.389E05 degrees Then to Radians 1.389E05 • ( π / 180) = 2.42E07 radians 
δ = 2 • arctan (½ • d / D)
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: Earth's moon has a diameter of about 3,474 km and is about 384,000~ km from Earth. What is its angular size? 2 • arctan (½ • 3,474 / 384,000) = 0.009 radians 
D = d / [ 2 • TAN(δ/2) ]
Where:
δ: Angular Diameter of object in radians
d: Diameter of object
D: Distance between observer and object.
NOTE: d/D must be expressed in the same unit.
EXAMPLE: The Hubble Space Telescope has a visual resolution of 0.1 arcseconds (0.00000048 radians). How far away can it see an object 100 meters in diameter? 100 / [ 2 * TAN(0.00000048/2) ] = 208,333,333.33 meters or 208,333.33 kilometers 
This was based off of empirical studies done by W.R. Dawes. It is for light with a wavelength of about 562 nm.
Resolution = 4.56 / Diameter
Where:
Resolution: Resolution of the telescope in arc seconds
Diameter: Diameter of the Telescope optic in inches.
EXAMPLE: What is the resolution in arc seconds of a 8foot (96inch) diameter optical telescope? 4.56 / 96 = 0.0475 arcseconds 
sin θ = 1.220 * (λ / D)
Where:
θ: Angular resolution of imaging system in radians
λ: Wavelength of observed radiation
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
θ = (λ / D)
Where:
θ: Angular resolution of imaging system in radians
λ: Wavelength of observed radiation
D: Diameter of the lens aperture.
NOTE: Both the lens aperture diameter and the wavelength must use the same measurement units.
θ = (λ / B)
Where:
θ: Angular resolution of imaging system in radians
λ: Wavelength of observed radiation
D: Length of maximum physical separation of telescopes in the array (baseline)
NOTE: Both the baseline and wavelength must use the same measurement units.