MECHANICS OF THE UNIVERSE

GRAVITY MECHANICS

Copyright 1984 to 2002 Allen C Goodrich

1. The total energy of the universe is a constant.
m(2 pi L)^2/t^2 + G(M-m)m/L = a constant M.

2. From this equation, a positive change of
kinetic energy m(2 pi L)^2/t^2 is equal to a
negative change of potential energy -G(M-m)m/L.

3. A kinetic energy change m(2 piL)^2/t^2 =
m(2 pi)^2 g L.

4. Acceleration of gravity g = L/t^2 would be
considered to be a constant in a universe
in which distance L is changing with time,
due to the expansion of the universe.

5. Time t must also be changing with the change
of dimension L.

6.As the universe expands kinetic energy
increases as potential energy decreases.
Time must therefore be changing with the
expansion of the universe.

7. Present values of distance L must be the
sun of all past changes of the value of L.
Integral S of L dL = L^2/2.

8. present time t must be the sum of all
past changes of past time T.
Integral S of T dT = T^2/2.

9. Present time t = T^2/2.

10.The value of present time t relative
to past time T must be a function of
the expansion of the universe.

11.The expansion of the universe is a
function of the change (increase)
of the kinetic energy M(2 pi L)^2/t^2
or (2 pi)^2 mgL and also the decrease of
potential energy -G(M-m)m/L.

12.The relationship of present time t
to past time T must be a function of
(pi)^2.

13.The experiment of Figure III shows
2t = (pi)^2.

14.The fundamental equation of the universe
delta m(2 pi)^2 L^2/t^2 = delta -G(M-m)m/L,
for past time m(2 pi)^2 (L_T)^2/T^2 = -G(M-m)m/L_T
m(2 pi)^2/T^2 = -G(M-m)m/(L_T)^3
1/T^2 = -G(M-m)m / m (2 pi)^2(L_T)^3
where (L_t)^3 = g(m-M) t^2/2
1/T^2 = -2G(M-m)m / m (2 pi)^2 G(M-m)T^2 = -1/2 (pi)^2 T^2
T^2 = 2 (pi)^2 T^2
t = T^2/2 = (pi)^2 T^2
and 2t = T^2 = (pi)^2 T^2
when T = 1 : 2t = (pi)^2

15. FIGURE III demonstrates that 2t ( 2 times the time
for the transfer of all of the energy of pendulum m_1
to pendulum m_2) is equal to T (pi)^2 ,where T is the
time for one swing of the pendulum m_1.
The fundamental equation is
L^3/t^2 = G(M-m) = Y,
where Y is the volumetric acceleration of gravity.

EXPERIMENTAL

2


THE MECHANICS OF ENERGY TRANSFER
EXPERIMENTAL ANALOG

M' is the mass of the earth and the
rest of the effective universe.
M-m_1 is the mass ( in 4 parts)of
the pendulum of length L on which three
pendulums m_1, m_1, and m_2 of length L
are suspended.
M is the effective total mass of the
Figure III system.
L is the radius of cvurvature of
m_1 ,m_2 and M-m_1 motion.
L' is the distance from m_1 to the
center of the earth.
T is the time of the pendulum swing.
1/T is its frequency.
2 pi L is the length of the arc of
pendulums m_1, m_2 and M motion.
t is the time for the transfer of
potential energy from m_1 to M.
2t is the time for transfer of
potential energy from m_1 to m_2.
The time 2t was found to equal
a constant x times T.

GRAVITY MECHANICS

GRAVITY is no longer assumed to be an
attractive force between masses.
GRAVITY as defined by gravity mechanics
is assumed to be defined as relative
volumetric acceleration of a mass
mL^3/t^2 equals G(M-m)m as derived by
the fundamental equation of the universe:
mL^2/t^2 + G(M-m)m/L = a constant M.

FIGURE III
ENERGY TRANSFER ANALOG


1. Before the start of the pendulum motion,
the pendulum mass has only potential energy
relative to the earth.
The frequency 1/T of pendulum m_1 is a
function of 1/(L/g)^1/2, where g is the
linear acceleration of the mass m_1 in the
direction of the center of the earth. The
maximum kinetic energy of the pendulum
m_1 is m_1 (2 pi L)^2/T^2 while it swings.

2. The energy of the pendulum m_1
changes from potential energy to kinetic
energy at a frequency 1/T in time T.
Acceleration g = G(M'-m_1)/ L'^2
because g must be equal to the difference
of the acceleration of M' and m_1.
g_M = GM'/L^2 and g_m = Gm_1/L^2.
As the kinetic energy of pendulum increases,
L is the radius of curvature and
2 pi L is the circumference of the
circle about M.

3. The total energy of the pendulums m_1, m_2
and M-m_1 also changes during the experiment
of Figure III. If pendulum m_1 swings, its
energy will be transferred to the pendulum
mass M-m_1 in a period ot time t and from this
to pendulum m_2 in a period of time t. The
value of 2t was found to be a constant x
times T. The value of x was found to be (pi)^2.

4. The total energy of the pendulum m_1 is
the sum of kinetic energy m_1(2 pi L)^2/T^2,
where L is the radius of curvature to M-m_1,
plus the potential energy G(M'-m_1)m_1/L'.
The value of potential energy contains a
value of L' that is quite different form L.
As the value of kinetic energy of m_1 changes,
the value of kinetic energy of M-m_1 changes.
The value of potential energy is small
because of the large value of L' and that
change will be equal to the value of the
change of its kinetic energy.

5. The experiment Figure III differs from
planetary motion in that there is very little
total energy change in planetary motion.
The electron motion and energy change,however,
can be compared with the motion of this
experiment. In this experiment, Figure III,
the kinetic energy change or acceleration
of m_1 is m_1(2 pi L)^2/t^2 and this is
equal to the change of potential energy
of m_1 relative to M'.
This rate of change of energy is not dependent
on the value of M' ( the mass of the effective
earth system) but it is dependent upon a
change of the effective potential energy),
where potential energy is G(M'-m_1)m_1/L'.
A change (decrease) of potential energy of
m_1 becomes a change (increase)
of the kinetic energy of m_1 plus an
equal increase of kinetic energy of M-m_1.
A change of kinetic energy of m_1 becomes
an equal and opposite kinetic energy change
of M-m_1.
There is very little reason for a change of
potential energy of m_1 to effect the kinetic
energy of M-m_1 but there is a definite
reason for the change of kinetic energy of m_1
to effect the kinetic energy of m-m_1,and
therefore this change occurs. This change is
smaller than would be expected if the center
of potential energy change was the center of
curvature,as it is in the case of the electron.
And this is because only a small change of the
value of L'occurs during the swing of
pendulum m_1.

6. During the swing of pendulum m_1, the
change of potential energy of pendulum m_1
relative to mass M'is converted to kinetic
energy relative to mass M-m_1. A part of this
kinetic energy is transferred to pendulum M'-m_1.
The rest continues the swing of pendulum m_1.
A part of the potential energy of pendulum m_1
is transferred to kinetic energy of pendulum
M-m_1 and the height of the swing of m_1
decreases.

7. After a series of swings of pendulum m_1
all of its kinetic energy is transferred to
pendulum M-m_1,which is converted to potential
energy of pendulum M-m_1 relative to earth M'
as this pendulum swings with the same period
or frequency as pendulum m_1.
The potential energy of pendulum M-m_1 will
be transferred to pendulum m_2 by the same
process.It was observed that it took a time
2t = k T for the transfer of energy
from m_1 to m_2.

8. Equilibrium is a state of constant total
energy. A state near equilibrium exists
for the planets of the solar system.
For the atom the equilibrium can be changed
by the transfer of a photon.
For the experiment Figure III we can observe
the transfer of energy from pendulum m_1 to m_2.
These energy transfers involve the same
mechanics of the universe and the fundamental
equation of the universe.

10.A transfer of energy is not so easy for
the planet solar system as it is for the atomic
electron and the experiment of Figure III.
If a mass of the same frequency is present
the transfer is simplified.

11.All of the total energy of pendulum m_1
cannot be transferred to pendulum m_2 in time T.
A factor involving the rest of the effective
universe, such as potential energy relative
to the rest of the universe is involved.This
involves the relationship between the values
of L and L'.The total energy of the universe
is a constant.

12. Another factor is relative acceleration
g which controls the rate of energy transfer.

13.Experiment Figure III is not an exact
analog for atomic electron energy transfer.
However it does provide a means of
understanding the mechanics of the process.