Общие астрорасчеты

Visual limiting magnitude
Size of Airy disk
Mount Periodic Error
Star trail lengths
Auto Guider rates

Visual Limiting Magnitude

A rough formula for calculating visual limiting magnitude of a telescope is:

VLM = 7.5 + (5 * Log(Aperture [cm]))

The photographic limiting magnitude is approximately two or more magnitudes fainter than visual limiting magnitude.

Size of the Airy Disk

A formula for calculating the size of the Airy disk produced by a telescope is:

D = 2.43932 * l * FR


A = 2 * ArcTan(D / (2 * fl))


D = Diameter of Airy disk in mm
λ = Wavelength of light (in mm here, normally in nm)
FR = Focal Ratio of system
A = Angular diameter of Airy disk in arcsec
fl = Focal length of telescope in mm

Light Colour
Wavelength (nm)
Telescope Diameter (mm)
Imaging system focal ratio
Calculated size of Airy disk (mm)
Calculated angular size of Airy disk

Calculating Mount Periodic Error

To calculate the periodic error of your mount using a CCD or webcam, you will typically put some numeric deviation data into a spreadsheet and create a graph. The data is normally in the form of a pixel offset and a timestamp. To convert this into an error in arc seconds you need to know how many arc seconds per pixel the images were captured, and the declination of the star used. The formula to plug into your spreadsheet is based on:

Error = (D * R) / cos(Dec)


D = Deviation of star from base position in pixels
R = Resolution of the camera in arc seconds per pixel
Dec = Declination of the star

Of course you can remove the requirement to use the declination in the calculation by using a star at (or close to) declination 0 degrees - the celestial equator.

Star Trail Lengths

You can use the calculator to estimate how long (or short) the star trails will be in a fixed camera image of the sky:

Star trail length


F = Focal length of lens scope (trail length in same units as focal length)
E = Exposure length
T = Length of sidereal day in same units as exposure
D = Declination of the star

Or, for the CCD imagers:

Star trail length in pixels

Focal length (mm)
Exposure time (secs)
Pixel size (microns)
Pixel binning
Star trail length

Auto Guider Rates

Calculate how many pixels per second your auto-guider will move when the mount is being guided. Note that this assumes your auto-guiders axes are aligned with RA and Dec directions.

pixels/sec = (str * gr * cos(dec)) / aspp


str = Sidereal Tracking Rate (15.04 arcsecs/second)
gr = Mount Guide Rate (fraction of sidereal)
aspp = Autoguider arcsecs/pixel
dec = Declination of the star

Guide scope focal length (mm)
Mount guide rate (fraction of sidereal)
Declination of guide star
Auto Guider pixel size (microns)
Pixel binning
Guide rate