Polar alignment vs. star movement

Calculate star movement during a single exposure from the exact target direction and the altitude/azimuth components of polar-axis error. A conservative maximum is shown alongside the exact result.

Input parameters

Sensor

Custom pixel size

µm

Telescope focal length

Polar altitude error

′

Polar azimuth error

′

Exposure time

Observer latitude

Target altitude

Target azimuth

Maximum acceptable movement

Result

Image scale—arcsec / pixel

Exact movement——

Worst case——

Sensor	Pixel	Image scale	Exact movement	Maximum	Conservative error for limit

Directions: target azimuth is measured from north through east (0° north, 90° east, 180° south, 270° west). A positive polar altitude error means the axis points too high; a positive polar azimuth error means east of true north. The exact result uses all four geometric inputs. The maximum is conservative for the same total axis separation. Stack registration corrects displacement between exposures, but not smearing within a single exposure.

Calculation

pixel scale = 206.265 × pixel size [µm] / focal length [mm]

exact trail = 15.041 arcsec/s × exposure × |(misaligned axis − true axis) × target direction|

maximum trail = 15.041 arcsec/s × exposure × 2 sin(total axis separation / 2)

Effective pixel sizes: IMX585 2.9 µm; IMX462 2.9 µm; OV50Q40 2.4 µm in 2×2 binning mode (1.2 µm native pixels); OS08B10 2.9 µm. Technical sources: Sony IMX585, Sony IMX462, OMNIVISION OS08B10.