**The fundamental error of the contemporary celestial mechanics** is the mathematically prohibited transformation of the reference frames that leads many physicists to a conclusion that in the orbital motion the only force acting on a planet is the gravity force and that the centrifugal force does not exist.

*Proof:*

**The Galilean principle** says that any body tends to continue its rectilinear uniform motion at a constant speed. In the contemporary physics this Galilean principle is called the momentum conservation principle. **The momentum as a vector parameter has a magnitude (the magnitude of motion) and direction.** Therefore the Galilean principle means that every body tends to preserve the parameters of the motion vector: the direction and the magnitude. Each change of any of these parameters by the act of an external force (actio) causes a tendency (reactio) for preservation of the hitherto direction and velocity of motion. Therefore during the deceleration and acceleration acts the inertia force

whereas during the orbital motion acts the centrifugal force which is also an inertia force.

Both forces (1) and (2) result directly from the above Galilean principle. The differences between them are only that:

– (1) is the tendency to preserve the **magnitude of velocity** (a=dv/dt) with a parallel direction of the acting force, “actio”, to the direction of the body’s motion

– (2) is the tendency to preserve the **direction **of motion with the angle of 90° between the vector of the force, “actio”, and the body’s motion vector

A homogenous body with mass m in its rectilinear uniform motion at constant speed v has the momentum equal

The situation becomes complicated in the case of a heterogeneous celestial body. The whole momentum (impulse) of a real existing heterogeneous celestial body needs to be calculated by integration of momentum of all its material points

Therefore the whole momentum p of a real existing heterogeneous celestial body is a vector sum of all moments of all its parts of different densities:

From the (5) a direct conclusion can be drawn that the Galilean principle is distributed on particular parts of a real non-homogenous celestial body proportionally to their densities. Each change of velocity or the motion’s direction of the non-homogenous celestial body causes tensions in its interior and in the case of non-rigid bodies such as terrestrial or gas planets, relative shifts of the parts of different densities. It means that reducing the non-homogenous celestial body from the equation (5) to the case of the body from (3) as a material point is mathematically forbidden as the vector sum of momentum cannot be substituted with an arithmetical sum. It means that transformation of accelerates reference frame to inertial reference frame, where orbital centrifugal force does not exist is mathematically prohibited. Through this transformation the whole information concerning the internal structure of the celestial body and stress in its interior is lost. Each true non-homogenous body during every rotation becomes a centrifuge which means that the so called weightlessness state on the orbit is only an approximation (with the exclusion of density differences). A proof for that are the phenomena observed at the ISS, which are erroneously called a microgravity. In reality they are differences of the orbital centrifugal force caused by differences in densities of particular parts of the station. The proof for that every planet on the orbit around the Sun acts exactly as an ordinary centrifuge are the infrared photographs of Uranus taken in 1994÷2003.

As it results from the above given arguments the theorem stating that the only force acting on a body in orbital motion is the gravity force is fundamentally erroneous. The orbital centrifugal force results directly from the principle of momentum conservation as a vector value and is inseparably connected with the centripetal force. Therefore a fundamental error is a statement that the Earth, Moon or any space object are in freefall in their orbital motion.

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