Astrological Dynamics · astrologicaldynamics.com

◈ VOL. I · THE MATHEMATICS OF THE MOVING SKY

Astrological Dynamics

The sky does not approximate. The planets move at computable velocities,
form measurable angles, and produce verifiable effects on measurable biometric fields.
This is the science of it.

◈ I. ORBITAL MECHANICS

T = 2π√(a³/GM)

Kepler's third law. The orbital period of any body. a = semi-major axis. This equation produced every planetary position in the Swiss Ephemeris — the same dataset that powers AstroTeks to 0.2 arcminute accuracy.

v = √(GM/r)

Circular orbital velocity. Planets nearer the Sun move faster. Mercury at 47.4 km/s. Neptune at 5.4 km/s. Transit duration is inversely proportional to this velocity. An outer planet transit can hold an aspect for months.

◈ II. ASPECT GEOMETRY

θ = |λ₁ − λ₂| mod 360°

The angular separation between two planets as seen from Earth. When this angle matches a harmonic fraction of 360° — 0° (conjunction), 60° (sextile), 90° (square), 120° (trine), 180° (opposition) — the aspect is exact.

ω = |dθ/dt|

The rate at which the aspect angle is changing. When ω approaches zero, the aspect is at its peak. Transiting planets slow, station, and turn retrograde — creating moments of maximum intensity in the field.

◈ III. FREQUENCY CONVERSION (HANS COUSTO)

f = 1/T × 2ⁿ

Any orbital period T (in seconds) transposed up by n octaves until it falls in the audible range (20–20,000 Hz). The Sun's period yields 126.22 Hz. Jupiter: 183.58 Hz. These are real acoustic frequencies, not symbols.

ASPECT	ANGLE	HARMONIC	INTERVAL	FIELD QUALITY
Conjunction	0°	1st	Unison	Fusion. The two energies merge. Amplification of both — for better or worse depending on the planets.
Sextile	60°	6th	Major 3rd	Opportunity that requires action. The door opens; you still have to walk through.
Square	90°	4th	Minor 7th	Friction. The most productive dissonance. Growth under pressure. The aspect of becoming.
Trine	120°	3rd	Perfect 5th	Flow without friction. The most harmonious major aspect. Sometimes too easy — the gift that goes unused.
Opposition	180°	2nd	Octave	The mirror. What you project onto others. Tension that resolves when you own both poles.
Quincunx	150°	—	Major 7th	Adjustment. Incongruent energies that require ongoing recalibration. Never fully resolves. The aspect of perpetual refinement.

AstroTeks computes this in real time

Every equation on this page runs inside AstroTeks — the iOS + Apple Watch app built by KenshoTek. Swiss Ephemeris accurate to 0.2 arcminutes. Your natal chart against live transit positions. Biometric coherence from HealthKit fused with the field state. The mathematics of the sky, on your wrist.

astroteks.com → · kenshotek.com →