Frequently Asked Questions

Series #10

Relativity and the GPS

**
Source
of Energy Between the Pole and the Equator. **

**
Let us examine how the principle of energy conservation is
applied to
the two experiments above. In the case of the orbiting
satellite,
it
is well known that the total energy of the satellite is
conserved
because the sum of potential plus kinetic energy everywhere
along the
orbit is equal to zero. There is no exchange of energy
between
the
orbiting satellite and the Earth. **

** However, we have
seen above that when a mass moves from the pole to the rotating
equator, there is a net increase of energy (potential plus
kinetic),
given to that moving clock. Since it requires no external
energy
to
carry a mass slowly between the Earth pole and the equator
(neglecting
friction), some people believe that there is no difference of
energy.
That is an error, as we will see now. Let us
calculate
where that
energy comes from. **

** When a mass is at
the
Earth
pole, its angular momentum around the Earth axis of rotation is
zero.
Let us slowly move the clock away from the Earth pole.
When that
clock, moving along a meridian, gets to an increasing distance
from the
pole, the rotating Earth makes it move faster and faster in a
direction
perpendicular to the meridian. It is the inertia of the
rotating
Earth, which accelerates the moving clock in a transverse
direction,
until the clock reaches the equator and attains the transverse
velocity
of the equator, which is 1670 Km/hr. **

** At the same
time the clock moves away from the Earth pole, another
phenomenon takes
place. Since the equator is further away from the Earth
center, a
radial force is required to maintain the effortless motion of
the clock
along the meridian, which becomes larger near the equator.
That
effortless motion is natural, since the Earth rotation produces
a
centrifugal force away from the pole in the direction of the
equator.
Those two forces compensates naturally. In fact, the exact
shape
of
the Earth is the natural equilibrium between these forces. **

** Let us calculate
first
the total increase of energy DE(clock)
given
to the clock moving from the pole to the equator. It is
equal to the potential energy plus the kinetic energy.**

**
DE(clock)
=
(kinetic
energy) + (potential
energy)
1**

**Taking
into account the flattened shape of the Earth and the
centrifugal
force, it is well known that the potential energy is equal to
the
kinetic energy. Therefore the total increase of energy of
the
clock is:**

** DE(clock)
=2
(kinetic
energy)
2**

** The kinetic energy
of the
clock at the equator is **

** K.E.
(clock)=½mV ^{2}
3**

** References**

**1- Natural Length Contraction Mechanism Due to Kinetic
Energy.
On the web at:**

**newtonphysics.on.ca/kinetic/index.html**

**2- Natural Physical Length Contraction Due to Gravity. On the
Web at:**

**newtonphysics.on.ca/gravity/index.html**

**3 - A Detailed Classical Description of the Advance of the
Perihelion of Mercury. On the web at:**

**newtonphysics.on.ca/mercury/index.html**

**4 – Einstein’s Theory of Relativity Versus Classical Mechanics**

**P. Marmet, Book, (1997) Ed. Newton Physics Books, Ogilvie Rd.
Ottawa, Canada, K1J 7N4**

**On the Web at: **

**newtonphysics.on.ca/einstein/index.html**

---------------------------------------

Paul Marmet, April 4, 2002

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