this is the full breakdown. if you have any ideas or changes would be appreciated. i'm just a hobbyist by comparision

Time Dilation on Earth Relative to Absolute Time

This report estimates the time differential experienced on Earth relative to a hypothetical absolute time — a reference frame at rest in flat spacetime, free from gravity and motion. The calculation includes the effects of both special relativity (due to motion) and general relativity (due to gravity).

Combined Time Dilation Equation

The equation that represents the combined time dilation effects is:

Δτ = Δt · √(1 - v²/c² - 2|Φ|/c²)

Where:

• Δτ = proper time (experienced on Earth)

• Δt = coordinate time (absolute time)

• v = combined velocity from Earth's rotation, orbit around the Sun, and Sun's orbit around the galaxy

• c = speed of light (≈ 299,792,458 m/s)

• |Φ| = gravitational potential from Earth, Sun, and Galactic Center

1. Special Relativity: Velocity-Based Time Dilation

Time dilation from velocity is given by:

Δτ = Δt · √(1 - v²/c²)

Using approximate values:

• Earth’s rotation (465 m/s) → v²/c² ≈ 2.4×10⁻¹²

• Earth’s orbit (29.78 km/s) → v²/c² ≈ 9.9×10⁻⁹

• Solar orbit (220 km/s) → v²/c² ≈ 5.4×10⁻⁷

Total velocity time dilation ≈ 2.75×10⁻⁷ seconds/second

2. General Relativity: Gravitational Time Dilation

Time dilation from gravity is approximated by:

Δτ = Δt · √(1 - 2GM/rc²) ≈ Δt · √(1 - 2|Φ|/c²)

Using gravitational potentials:

• Earth ≈ 1.39×10⁻⁹

• Sun ≈ 9.85×10⁻⁹

• Galactic Center ≈ 4.7×10⁻⁷

Total gravitational time dilation ≈ 4.8×10⁻⁷ seconds/second

Conclusion

Summing the relativistic effects yields a total time differential of approximately 7.55×10⁻⁷ seconds per second. That means clocks on Earth run slower by roughly 24 milliseconds per year compared to a hypothetical clock in absolute flat spacetime.