Tracking Error Tolerance Calculator Formula

Understand the math behind the tracking error tolerance calculator. Each variable explained with a worked example.

Use the Tracking Error Tolerance Calculator

Formulas Used

Max Periodic Error

pe_max = pixel_scale * acceptable_drift

Max Drift Rate

drift_rate = pixel_scale * acceptable_drift / worm_period * 60

Variables

VariableDescriptionDefault
pixel_scalePixel Scale(arcsec/px)0.77
acceptable_driftAcceptable Drift(px)2
worm_periodWorm Period(s)480

How It Works

Tracking Error Tolerance

For unguided astrophotography, the mount's periodic error (PE) must be small enough that stars do not trail beyond the pixel scale.

Formula

PE_max = pixel_scale * drift_pixels

  • *pixel_scale* = arcsec/pixel from sensor and focal length
  • *drift_pixels* = acceptable pixel drift (typically 1 to 2 px)

    • The drift rate limit is PE_max divided by the worm-gear period.

    Worked Example

    0.77 arcsec/px scale, 2 px acceptable drift, 480 s worm period.

    pixel_scale = 0.77acceptable_drift = 2worm_period = 480
    1. 01PE_max = 0.77 * 2 = 1.54 arcsec
    2. 02Drift rate = 1.54 / 480 * 60 = 0.1925 arcsec/min

    Frequently Asked Questions

    What is periodic error?

    PE is the back-and-forth tracking error caused by imperfections in the mount's worm gear. It repeats every worm cycle (typically 4 to 10 minutes).

    How can I reduce PE?

    Use periodic error correction (PEC), autoguiding, or a mount with a high-quality worm gear. Belt-driven mounts often have lower PE.

    Is autoguiding always necessary?

    For long focal lengths or multi-minute exposures, usually yes. At short focal lengths (under 200 mm) many mounts track well enough unguided.

    Ready to run the numbers?

    Open Tracking Error Tolerance Calculator