The gravitational constant G

Some pages from the book:

COMPLETE UNIVERSE, DYNAMIC FREE SPACE, WAVE PHENOMENA

Subtitle: How the natural laws and forces are applied. The fundamental concepts for a rational Cosmo­logy (Cosmo­nomy). ISBN 978-618-85170-2-8 ©2021

(Some of the first thoughts of investigation is an attempt to comprehend what the constant G of gravity signifies)

► 13.2. Some proportions hidden within the constant G

By the units, which are found in the dimensional content in the constant G, the result in the formulas is in agreement with physics very simply without the need to make more numerical calculations. The constant G of gravity results from the Kepler's 3rd law*[1]:

G = 4π²·r³ /M·t² (= m³ / kg∙s²)

An example accordingly to the measurements for the Earth and Sun.
4π² · (1.495978 ×10¹¹)³ / (3.155421 ×10⁷)² · 1.99 ×10³⁰ = G

If the distance r is in meters from the central body Μ, the time t is in seconds and the mass M in kg. The central body is the Sun. The distance r is between the Sun and the Earth. The time t is the orbital period of the Earth around the Sun in sec instead of the 24-hour period. Actually, we could not calculate this constant, if the phenomena of mass, gravitational force and distance were not altered according to certain laws, so the one depends on the other in such a way, that they do not violate certain limits. We will understand their relation with an example of the mass M and radius r of our planet Earth.**[2] 

(...)

The gravitational constant G in Newton's formula shows, that the force between two spherical bodies in certain relation with their distance and mass can be altered, but with such proportion so as to an immutable relation results from all together, that we determine it with the physical constant G. In the constant G is found already the answer that we ask. We do not make something else from dissolve mathematically the constant G in order to remains force F or the acceleration a.

If the constant G=Fr²/M1M2 of gravity were a larger number, then the bodies would give higher acceleration, higher speeds and higher traction forces. The astronomical bodies would probably approach each other with a stronger force of attraction between them and at higher speeds. The intensity g of the gravitational field of a body could increase faster, with less mass. If, however, the constant G were a smaller number, this would mean less traction force F. The rates of change of speed would be slower and the intensity g of the gravitational field would be less for the same mass. These relations and ratios are imposed by the gravitational constant G.

If the attractive force F between material bodies is increased in the equation G=Fr²/M1M2 or only the distance r (for the same force) is increased, then the mass M will be increased so that the same constant G is maintained. The product of the masses and the proportional force F could be increased indefinitely without a limit. However, the force F between the bodies is adjusted by the distance r raised to the square. As it is shown by the relation F = GMM / r², the attraction force F between the bodies changes (exponentially) x2 times if x is the change of the distance r in the denominator. That is, if the distance r increased 10 times, then the force F is attenuated 10² = 100 times. This means that the attractive force F appears more reduced (x² times for each x increasing of distance r) in longer distances. Conversely, the attractive force will be exponentially increased x² times if this distance diminishes x times. If, instead of increasing the distance between the bodies, their mass is reduced by the same measure so that the same attractive force F results, then the mass should be reduced x² times. That is, the force F be reduced 100 times, if the product of the masses also is reduced 10² = 100 times (for the same radius r).

The fact that the gravitational constant G is a number of the order of 10^-11 ensures that astronomical bodies can exist with their known masses. It ensures that the force of attraction requires such an increased amount of concentrated matter until it acquires the strong gravitational field that causes thermonuclear reactions. Since this constant G requires a long period of time until the highest velocity is reached from a gravitational acceleration. Smaller accelerations can be caused (at a slower pace), in longer distances and cyclic movements at longer radii, and thus in longer periods and intervals. And as it seems, low accelerations and larger distances need bodies of larger mass (mass / volume, more correctly).

The mass of a body could be increased so much in less radius or within a few meters that the body would be destabilized and transformed into nuclear bomb or a black hole, because of a too strong attraction force. We find in nature instead that the structure of matter allows the concentration of matter and the increase in mass until the formation of bodies in astronomical dimensions. The gravitational force does not exceed the limits of conservation of the structure of matter prior to the merger of a large number of material elements. A large number of material elements may be concentrated in a much larger radius (until they undergo a destabilizing pressure). From this observation alone comes the safe conclusion, that the structure of matter and the microscopic processes are not easily to destabilized by the forces, which we observe amongst the visible bodies.

The gravitational field and the force of attraction begin from the structure of matter, favor the concentration of material elements and allow it with limits (length and strength), which are predetermined by their very structure. These limits, which allow the bodies and attractive forces of astronomical dimensions to exist, indicate that the large concentrated bodies, while they have more mass, are however less stable than their components (material elements). We can easily articulate this finding with the usual vocabulary, but - attention! - it should not be concluded, that the structure of matter is maintained by more powerful forces than the force of gravity. The maintenance of the dynamic structure of matter and the approach of some particles, which repel each other, is not only an issue about the size of a competitive force (provided that energy exchanges are made in certain rhythms and fluctuations). But, although powerful forces may appear within the dynamic structure of matter, the thought of a physicist should not be so poor that it cannot discern, that if the application of a force is periodical and with fluctuations, then it is not necessarily the same phenomenon such as the force that we observe to be applied continuously to a body, when it pushes another. The time interval, in which a force is applied, and how a dynamic process unfolds are also crucial.

11.1. Investigation of the gravitational field and how it is created

The dimensional content of the constant G (that reflects a regular rate in change of speed in relation to the gravitational force and the distance):

Length³ / Mass × Time² | or in simplified units m³ / kg ∙ sec²

· A single material body itself is surrounded by a field (if not the field is caused by it), which acts invisibly to another body. We call this "gravitational field" or "attractive force". This observation leads us to think of the gravitational field regardless of the approach of a body with other bodies. This is a field surrounding the material things, whether they are next to one another or not. The acceleration g in physics coincides with the intensity of the gravitational field.

· We detect and observe more easily this field in bodies containing a large amount of matter in the unit of volume or mass such as the celestial bodies. The things that we know and we can observe in our daily lives do not reveal this attribute to attract each other, a characteristic which all bodies have. We don't observe any force being applied from one body to another and accelerating the other body, without the physical surface of the one touching the surface of the other. Only in special cases we observe bodies that attract each other such as the phenomenon of magnetism and the electrical charging. But these phenomena are described successfully and are considered to be phenomena different than the gravitational attraction.

· The proportional relation, which is summarized by the formulas g=GM/r² and F=GM1M2/r² are not so clear and well defined relations and cannot be applied with accuracy. It is not so easy to identify which the center (of gravity) of a body is, what size the center has and how much exactly the radius is unto the body surface. It is even more difficult, when the body shape is not perfectly spherical and when its structure is not stable and uniform, which seems to be the norm in the astronomical space.

· Observing the relation G=V²·r/M. When the constant G is given by V²·r/M then the distance r is a radius, the motion is elliptical, the mass is the one of a separate body and the attractive force is centripetal. The mass, the speed of a body and the distance manage to acquire the quantity or size, which is needed, in order to maintain the physical constant G. If the constant G does not ensue, then there no rotational motion occurs, the speed V in the formula M=V² r/G is not one of a periodic motion in an orbit and the time in the formula M·V·2π/T=F is not a period. The constant G ensures the elliptical and circular motion and not generally the motion with the attractive force. When we hear that the bodies attract each other, as Newton observed and expressed quantitatively, then one of the first thoughts is the observation, that celestial bodies do not fall on top of each other. By this attraction the celestial bodies had to be accelerated and to fall immediately on top of one another. The attractive force F (between bodies) increases in proportion to the mass, but it seems that the increase in mass is accompanied by the increase of the possible distance between them, while the radius of a separate body can be reduced. It appears that the presence of this constant is due to a specific "inner" relation of mass with the spatial dimensions and length.

· The intensity of the gravitational field (g=GM/r2) or the attractive force F between the bodies does not depend on the chemical properties of matter.

· Theoretically observing the contrast.

The gravitational field is closely related to the presence of mass. But the presence of mass is also associated with some absence of gravity ... In fact, we find that the gravity of a visible body is not attractive in an unlimited manner and cannot bring all the masses together until disappearance of distances. The mass of a body does not eliminate the extent that it occupies (somewhat organized). The gravitational attraction is so strong that there is a distance amongst the bodies and these bodies exist as separate (and they have an extent). We could say from the outset that mass, distance and expanse begin with such movements, that exceed (or fool) the energy of gravitational attraction and they do not let it "gather" and "produce" work to infinity. The limitation of the gravitational attraction is somehow associated with an opposition that is raised by the energy flow (or fast motion) into the structure of matter, in shorter distances and dimensions. Therefore, we might assume by the first thoughts that the appearance of material bodies (and a limit for the gravitational attraction) depends on the rate and speed of changes, which are repeated, on the amounts of energy which are exchanged in microscopic dimensions and on the rate of change of energy in general (increases, decreases, rhythms and transfers).

By an initial finding of a contrast between the mass and gravity we can easily reach the following conclusion: The mediation of a common base is necessary for the existence of matter, so that matter can have the energy, with which it is maintained despite the external influences. This is, because the motion inside the tiny matter and the stability of its structure cannot be explained by the energy and motion of external (and random) effects. The structural elements of matter are found in large quantities in different conditions and with different things. We should observe different structural elements in the unit of volume. Such a matter maintains its structure and we know that matter exists within the vast distances of astronomical space and over time. This single observation leads to the conclusion that matter, either nearby or far away, is associated with something in common, a common reality and even so, that matter has the same microscopic structure. The common reality, which is needed as a base for the maintenance of matter and has same properties, could be looked for in the realm of metaphysics. This common reality is none other than the space.

Note that here we have not ventured in explaining the structural elements as fluctuations and wave effects by introducing directly the concept of a dynamic space after an assessment of the information of modern research. We conclude that there is a common and simultaneous quantity (energy) and we identify it with the phenomenon of space. We explain the free space itself and thus it is revealed how it is dynamically connected to matter.

*[1] Footnote

Johannes Kepler 1571-1630. The third Law: “The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit”. If we know the period of a planet's orbit (how long it takes the planet to go around the Sun) and its mass, then we can determine the distance of the planet from the Sun.

**[2] Footnote

The example here on this web page is omitted

*** The whole physical interpretation of the structure of the Universe and matter, with all paths of thinking that prepare and facilitate its understanding and answer the questions which are created extends to a large number of pages. The cosmological theory in Greek has divided into three volumes or 3 digital books respectively. The cosmological theory has been translated almost entirely and updated in English.

>>> The answers to questions about the preservation and creation of matter cannot be given without understanding how space as an energy participates in this process. These answers can not be given without such a understanding as above, but quite the contrary human thought is led to dead ends, stupid theories and errors.