Delta-Z Calculator

This tool is provided for scientific and educational purposes. If you use this calculator or source-code in your research, please cite: Visuri et al. (2026). MNRAS, xxxx, xx-xx

Contact: Jaakko Visuri
 jaakko.visuri@ursa.fi
Ursa Astronomical Association
Finland

Source codes

Here you can download the source code for application implementations. Source code is provided in Javascript and Python. These includes atmospheric ISA-model values. You dont have to download them separately.
Javascript
Python (beta-version, debugging)

Obligational input parameters:

Apparent angle (degree)

(Measured from true horizon level, positive above, negative below)

Optional input parameters by default:

Use: Observation site height above sea-level (meters)


Use: Pressure at the observation site (Pascals, 1013,25 mBa = 101325 Pa)


Use: Temperature at the observation site (kelvins)


Use: Refractive index at the sea-level (n-1)


Use: Object/Fireball height above sea-level (meters)


Use: Thickness of the atmospheric layers (m, minimum is 0.01m)


Optional real atmospheric condition:

Override atmospheric parameters by uploading real atmospheric data. (Example of data and format )
Upload weather-file:

Calculate




Parameters
Designation Definition Value
H Apparent angle
H' Full-refraction corrected angle
R Full-refraction
R' True refraction
T True directional angle
Line O->Z Full dZ-correction
Line E->Z dZ-error
Line O->E Absolute dz-correction
Line O->F Object distant-dependent dz-correction
     
Other definitions
Line O->J Direction which we observe
the object to be located
Line O->C Direction which we assume the object to be located
after general refraction correction
Curve B->O Assumed lightcurve of the object through atmosphere
Point A Arbitrary position of the object in the atmosphere
along the curve B->O
OBS! Lines O->C, E->D and Z->B
are all parallel
OBS! Point A is situated both on the line E->D
and the curve B->O.