Lesson 26 Harmony of the Spheres

The heavenly motions are nothing but a continuous song for several voices (perceived by the intellect, not by the ear); a music which, through discordant tensions, through sincopes and cadenzas, as it were (as men employ them in imitation of those natural discords) progresses towards certain pre-designed quasi six-voiced clausuras, and thereby sets landmarks in the immeasurable flow of time. -- The Harmony of the Universe (Harmonice mundi) Johannes Kepler

Heavenly music was an idea that dated back to Pythagoras, and Kepler was the first to record the sounds of the planets in Harmony of the Universe

John Rogers and Willie Ruff of Yale University synthesized Kepler's music which became know as the "Harmony of the Spheres."

The Pythagorean theorem was used to find how fast the moon falls each second, just as the odd numbers add up to the perfect squares.

Studying the musical compositions of the heavens, Europeans developed distinct musical compositions in Europe.

Galileo found that each swing of a pendulum occurs in the same amount of time. This discovery led to keeping perfect time, an undeniably important aspect of music.

Galileo then discovered resonance through the application of a rythmically applied chorus.

Western scholars only made discoveries due to the foundations of science from the Pythagoreans and Greeks that ultimately led to the conclusion that nature is solely based off of mathematics.

Newton's Law F = m a describes all bodies on earth, in the heavens, and throughout the universe. This law united the physics of both earth and space.

All projectiles follow orbits that can be depicted by conic sections due to the fact that F = m a applies to every force in the mechanical universe, and every mass no matter what or where.

F= m a is an equation that relies on derivatives and can describe acceleration, velocity, and position of any projectile ever fired.

Copernicus challenged old theories and needed new mathematics of motion to describe the nature of new discoveries.

Whenever there is no outside force, momentum is constant. Force is the rate of change of momentum. Momentum is conserved and if r x f is 0, angular momentum is constant as long as there is no torque.

Energy is also constant. Work that lifts an object from one height to another becomes potential energy. Work that acclerates a block becomes kinetic energy. The kinetic energy of a falling object is transfered into heat, which leads to the kinetic energy among molecules and atoms.

E = U + K is always constant and determines the orbits of the planets:

e<1 - ellipse
e=1 - parabola
e=0 - circle
e>1 - hyperbola

The harmony of the mechanical universe, containing many mysteries yet to be solved.