Longitude normalization and angular difference
The modular arithmetic needed to prevent errors around 0°/360° and choose the shortest signed separation.
Calculation contract · released 2026-08-18
Definition
Normalized longitude maps any angle to [0°, 360°). Signed angular difference maps a displacement to a declared interval such as (−180°, 180°].
Calculation procedure
Apply modulo arithmetic that handles negative values, normalize before classification, and use a signed shortest-path difference for motion and aspect calculations.
Required inputs
- Raw angular value
- Target interval
- Tie policy at 180°
Maha convention
Maha uses normalized [0°, 360°) longitudes and shortest signed differences for daily motion and angular separation.
Uncertainty and edge cases
Naive subtraction can turn a 0.2° crossing of 0° into a false 359.8° jump and reverse a motion or aspect classification.
What this does not establish
Correct modular arithmetic classifies geometry only; it adds no interpretive evidence.
Authoritative references
These sources establish the calculation vocabulary, data product, or transformation convention. They do not establish astrological interpretation.
- Horizons System Manual
NASA/JPL Solar System Dynamics · 4.98d (2025-11-21)
Solar-system object identifiers, observing centers, time inputs, reference frames, corrections, output quantities, and stated ephemeris limitations.
Boundary: Horizons output is authoritative only with the complete query contract preserved; transformed or rounded values require their own provenance record.