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Relativity and the GPS( Last checked 2017/01/15 - The estate of Paul Marmet )

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**
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**

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Paul Marmet, April 4, 2002

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