A guide to reading the velocity, acceleration, and periodicity plots produced by the EarthFrame Calculator — and why these dynamics matter for biology.
The plots show the total non-inertial dynamics of a point on Earth's surface as seen from an approximately inertial solar system frame. This is not an Earth-centered view — it captures everything a mass at your location actually experiences.
Every molecule at that point is simultaneously:
These motions compound. The EarthFrame Calculator makes their combined effect visible.
The top plot shows the combined tangential velocity of your surface point over 24 hours. Three velocity components are composed as vectors in ecliptic coordinates:
| Spin | Tangential velocity from Earth's rotation — latitude-dependent, up to ~465 m/s at the equator. Constant over 24 hours but its direction rotates. |
| Orbital | Earth's velocity around the Sun — ~29,800 m/s. Nearly constant over a single day, but changes direction over months (elliptical orbit, vis-viva equation). |
| Barycentric | Earth's center orbits the Earth-Moon barycenter at ~12.4 m/s with a 27.3-day period. Small in magnitude but significant in periodicity. |
Because the spin and orbital velocity vectors are not aligned (Earth's axis is tilted 23.44° from the orbital normal), their vector sum oscillates over each day. The plot reveals this daily modulation — a rhythm embedded in every Earthbound reference frame.
The middle plot shows the net radial acceleration — the sum of four components:
| Spin centripetal | Constant for a given latitude. Sets the baseline. Directed outward from Earth's spin axis. |
| Orbital centripetal | Centripetal acceleration of Earth around the Sun. Nearly constant over one day. |
| Lunar tidal | The differential gravitational pull of the Moon — the difference between its pull at the surface vs. at Earth's center. Modulated by the Legendre polynomial P₂(cos α), where α is the 3D angle between your location and the Moon in ecliptic coordinates. This creates the classic semi-diurnal (~12-hour) oscillation: stretching when facing toward or away from the Moon, compression at 90°. |
| Barycentric wobble | Earth's center accelerates toward the Earth-Moon barycenter (opposite the Moon's direction), projected onto the radial direction at your surface point. This contributes a slower monthly modulation to the acceleration curve. |
The key feature: the acceleration is never constant. It oscillates with interlocking periods — semi-diurnal, diurnal, and monthly — creating a rich strain cycle that every cell at that location experiences continuously.
Jerk (da/dt) is the rate of change of acceleration. Snap (d²a/dt²) is the rate of change of jerk. These higher-order derivatives reveal where the dynamic environment is changing most rapidly — transitions that molecular systems may be sensitive to.
Jerk peaks occur at the inflection points of the acceleration curve, corresponding to moments when the tidal and barycentric forces are shifting most rapidly. These are not abstract mathematical quantities — they represent real changes in the mechanical environment experienced by every mass at that location.
The bottom panel shows the frequency content of the acceleration time series. Key peaks include:
These periodicities are not imposed — they emerge naturally from the gravitational dynamics. They match known biological rhythms (circadian, circatidal, circalunar), suggesting a physical basis for the timing mechanisms that cells use to organize metabolic processes.
Standard biophysics treats the laboratory frame as inertial — stationary and unaccelerated. But no point on Earth's surface is inertial. Every mass is embedded in a continuously varying field of velocity, acceleration, jerk, and snap, rich with periodicities that span hours to months.
The Copernican Project hypothesizes that these dynamics participate in biological energy exchange at the molecular scale — that cells have evolved not despite Earth's motion, but with it. The EarthFrame Calculator makes these invisible dynamics visible so that researchers can begin to test this hypothesis quantitatively.