Special Relativity in GPS

A compact project exploring why GPS satellite clocks require relativistic corrections, and how those corrections emerge from first-principles physics.

Overview

GPS satellites experience two competing effects:

• Special Relativity (SR): orbital speed makes onboard clocks run slower.
• General Relativity (GR): weaker gravity at orbital altitude makes onboard clocks run faster.

For GPS, the net correction is about +38.4 µs/day. Without applying this correction, position error would grow by roughly 11.5 km per day.

Repository Status

This repository currently contains the project structure and source placeholders for derivations and simulations. The physics write-up and implementation scripts are being organized.

Repository Layout

.
├── README.md
├── LICENSE
├── derivations/
│   ├── sr_derivation.py
│   ├── gr_derivation.py
│   └── null_altitude.py
├── simulations/
│   ├── altitude_curve.py
│   ├── gnss_comparison.py
│   └── animation.py
└── references/
    ├── JF2027_GPS_Einstein_ProjectPlan_Urvish.pdf
    ├── JF2027_JWST_ProjectPlan_Urvish.pdf
    ├── Jugend-Forscht 2026.pdf
    ├── Right Hand Rule.jpg
    └── Zur Elektrodynamik bewegter Körper.pdf

Getting Started

git clone https://github.com/devNull-bootloader/special-relativity-in-GPS.git
cd special-relativity-in-GPS

When dependency requirements are finalized, install them with:

pip install -r requirements.txt

Planned Work

• Implement SR, GR, and null-altitude derivation scripts.
• Add reproducible simulation outputs and plots.
• Add verification scripts and expected numeric results.
• Expand documentation with equations, assumptions, and data sources.

References

Primary source materials and project planning documents are in /references.

License

MIT License.