_{1}

^{*}

In this paper it is proposed that the mass of the bodies has its origin and nature in the reciprocal gravitational interactions between them; and also by some kind of effect over the size of the celestial bodies due to the very big distances in space, as seemed each other at a distance. In a Dynamic Theory of Gravitation [1], it is proved that the fundamental velocity is the escape velocity due to the apparent size of the interacting heavenly bodies, which is the medium used by gravity to transmit its effects like propagating force of Nature [2]. Given that is the greatest speed of the Universe, the celestial bodies interact between them in a reciprocal way [3]. Because of that dynamical process all those bodies have an intrinsic property called mass. Then, the mass of any body is a kind of parameter by means of which a measure of the inertial effects can be obtained. That property is different from weight. It is a consequence of the gravitational interactions between any body and all the rest of the heavenly bodies of the Universe, and also by some deep characteristic of the space that separate them.

It was Galileo who discovered that bodies fall at a rate independent of their mass. He used as a tools an incline plane to slow the fall, a water clock to measure the time, and a pendulum to avoid rolling friction [

The weight of a body is the gravitational force exerted on it by a source of the gravity attraction. Being a force, is a vector whose direction is the direction of the gravity force; that is, toward the center of the source [

Newton’s second law

F = m a , (1)

where F is the applied force, m the mass, and a the acceleration, when is applied to a freely falling body, takes the following form

W = m g . (2)

where both vectors are directed toward the center of the Earth; so that it can therefore write that

W = m g ; (3)

W and g are the magnitudes of the weight and acceleration vectors, respectively.

To keep an object from falling, it has to exert on it an upward force equal in magnitude to W so as to make the net force zero [

The relationship between weight and mass is given by the equation (2). Because g varies from point to point on the Earth, W which is the weight of a body of mass m, is different in different localities. Hence, unlike the mass of a body which is an intrinsic property of the body, the weight depends on its location relative to the center of the Earth. Then, the weight of a body is zero in regions of space where the gravitational field or its effects, are null; although the inertial effects, and hence the mass of the body remains unchanged from those on the Earth [

It takes the same force to accelerate a body in a gravity-free space as it does to accelerate it along a horizontal frictionless surface on the Earth; because its mass is the same in each place; but it takes a greater force to hold the body against to pull of the Earth on the earth’s surface than it does high up in space, because its weight is different in each place.

Often, instead of being given the mass, are given the weight of the body on which the forces are exerted. The acceleration a produced by the force F acting on a body whose weight is W can be obtained combining the Equations (1) and (3). Therefore from F = m a and W = m g it is easy to obtain that

m = W g and F = ( W g ) a , (4)

The quantity W/g plays the role of m in the Equation (1), and is in fact the mass of the body whose weight is W [

If the inertial mass of Newton’s second law were not the same as the gravitational mass in the law of gravitation, it would have to write the Newton’s second law as

F = m i a ; (5)

and write the law of gravitation as

F = m g g ; (6)

where g is the gravity acceleration which is a field depending on position and other masses [

a = ( m g m i ) g ; (7)

and would be different for bodies with different values of the ratio m_{g}/m_{i} . In particular, pendulums of equal length would have periods proportional to (m_{i}/m_{g})^{1/2 }. Newton in experiments with pendulums of equal length but different composition tested that possibility and found no differences in their periods [^{9}. A few years later, a group under R.H. Dicke [^{11} [

In spite of the experimental results by means of which the equality of the gravitational and inertial mass are proved; the question about the real nature of the mass has not an answer. Many teachers and books head of the question assuming that the problem of the mass, as an intrinsic property of the bodies, has already been solved. However, it is clear that the mass is independent of the material, composition, and atomic structure of the bodies; and also is not the same as the weight. So that, even today that problem is centered in the question about the origin and nature of the mass.

In Newton’s Law of Universal Gravitation it is implicit the idea that the gravity force between two celestial bodies is independent of the presence of other heavenly bodies, or the properties of the space between them [

It is possible to assert that the gravitational interactions between the heavenly bodies of the Universe, interact each other in a reciprocal way, and also due to their apparent sizes, as seemed at a distance are the responsible of the intrinsic property of any body known as its mass. That is to say, the gravitational influence is the origin and nature of that important physical property.

From that point of view, as it was said before, perhaps the mass is a kind of parameter by means of which a measure of the inertial effects proper of any body, can be explained.

Also, and this is very important, the reciprocal gravitational interactions play a special role in the structure of the Solar System, the Galaxies, and the Universe itself. In fact, that dynamical process is responsible of the construction of a kind of three-dimensional and complex network by means of lines of gravity force, like those of the magnetic field, which link the heavenly bodies between them as seemed each other at a distance in the space. This is so because the gravity force is always attractive.

In the reciprocal gravitational interactions [

Finally, it is well known that A. Einstein was very impressed with the observed equality of gravitational and inertial mass, and that knowledge it can served him as a signpost towards the Principle of Equivalence [

Palacios, A.F. (2017) About the Mass. Open Access Library Journal, 4: e2835. https://doi.org/10.4236/oalib.1102835