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To Pioneers
 

5             Relativistic Mass Increase

 

As we know from mass spectrometry, the mass of a moving particle increases with velocity. The mass m_v with velocity v is equal to

   kg.

This is called the relativistic mass. Here, m is the mass of the particle when measured at rest, and g is the Lorentz factor corresponding to the particle's velocity.  

However, if mass refers to the amount of matter, it's a foolish way to speak of the mass of a particle, which would have increased for a stationary observer but not for the observer moving along with the particle. Where does this extra matter come from? It clearly violates the Constitution of Physics (p. 1).

 By saying this, one contributes to the fact that science is still searching for how to understand gravity and what is meant by mass.

We must make a distinction between mass and the amount of matter. Therefore, in the Obstruction Theory, we have introduced a definition for the mass of an object in which the magnitude of the mass is determined not by the quantity of matter, but by the influence this quantity of matter exerts.

Then one can speak of an increased mass of a moving object without the amount of matter having increased. The concept of mass is then related to the property of a quantity of matter to prevent radiation from sources behind it from reaching the observer.

The black spot then becomes the measure of the amount of matter.  

The solid angle of the black spot is found to be equal to    sr 
where the radius of the Einstein ring is  meters and where the radius R₀ of the black hole that can form the mass M  is  meters.

The solid angle subtended by the Einstein ring of a celestial body with velocity v will be g times that of the stationary body. Similarly, for an observer in a spacecraft or on a comet with a velocity v, the solid angle of the Sun will increase because the Sun is also moving relative to these objects (see the proof: T&C p. 127). This will amplify the gravitational acceleration of the Sun on the objects. This applies both when approaching and receding from the Sun.

The acceleration g_rela then increases to:     m/s². 

With Newton's   or 
       we find

     m/s².

We consider the first term to be Newton's well-known law of gravitation, the second term to be a quadratic decreasing term taken to represent a portion of the mass, and the last term

                                                      m/sec²

to be an additional acceleration that deviates from Newton's law of gravitation, namely by being of the 3rd power of the distance r.  

This increase in gravitational acceleration, like the extra gravitational acceleration according to the obstruction theory described in §3, has long been part of traditional theory and is concealed in calculations by assuming that space is curved. We will not discuss this latter increase in the context of the investigation of the orbital motions of the Pioneers and 'Oumuamua.

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