Pendulum for celestial rhythms

For a given length from the suspension to the center of gravity, a pendulum swings back and forth at a given frequency (frequency per unit time).

Regardless of whether the pendulum swing is wide or small, the frequency of the back-and-forth swing is always the same for a given length.

The longer a pendulum is, the lower the frequency with which it swings back and forth.

The formula for calculating the so-called mathematical pendulum (string pendulum) was discovered by the Italian scientist Galileo Galilei after he observed the movements of the lamps hung there in different lengths in a church.

He recognized the connection of gravitational acceleration (which is 981 centimeters per second squared on the earth's surface), pendulum length and oscillation time.

A quarter of a pendulum length oscillates with twice the frequency !

The pendulum formula

(from the book "Die Kosmische Oktave" by Hans Cousto):

It is

g = 981 cm ^. sec ^-2 = Acceleration due to gravity
L = the length of the pendulum (suspension to the center of mass)
π = 3.14159 Pi
T = Duration of a complete oscillation period (back and forth).

It goes:

T = 2 ^. π ^. √ (l:g)  =  2 ^. π ^. L ^{-0,5 .} g^0,5

In our case, T and g are known, and the length L is the quantity we are looking for, so the equation must be solved for L. To do this, the equation is first squared:

T² = 4 ^. π^{2 .} L ^. g^-1

This equation is now solved for L:

L = T^{2 .} g ^. π^{-2 .} 0.25  =  T^{2 .} g : (4 ^. π²)

Any value for T can now be inserted into this equation, whereby the equation can still be transformed expediently beforehand:

L= T^{2 .} g ^. π^{-2 .} 0.25  =  T^{2 .} 24.85 cm ^. sec^-2

Only the time has to be squared and multiplied by 24.85 cm . sec-2 and the result, the pendulum length, is known. However, one can also divide the number 24.85 cm . sec-2 by the square of the frequency f and likewise obtain the desired pendulum length.

The 16th octave of the synodic solar day corresponds to the time:

T = 86400 sec ^. 2^-16 = 1.31836 sec

and the frequency

f = 86400^{-1 .} 2¹⁶ = 0.7585 Hz

and so the corresponding pendulum length is:

L = 1.31836² sec^{2 .} 24.85 cm ^. sec^-2 = 43.2 cm

L = 24.85 cm ^. sec^{-2 .} 0.7585^-2sec² = 43.2 cm

In the table "Planets - Sounds - Colors — Meters" the pendulum lengths of the different cycles of the earth, the moon, the planets and the sun are listed.

With a quarter of the pendulum length a pendulum swings back and forth with double frequency, with four times the length with half frequency !

Cosmic Pendulum Mass Tape

to print, cut out and glue (on a cardboard or wooden strip):
Download here as PDF