Newton introduced the idea of mass and formulated the universal law of gravitation. Moreover, he defined the weight of a body as the gravitational force that the Earth exerts on a body with a certain mass (there is no distinction between inertial mass and gravitational mass). The gravitational pull exerted between two bodies is inversely proportional to the square root of their distance. Thus, from Newton on a body has a certain mass and a correspondent weight. Each body consist of a certain mass which is unalterable, while its weight changes with its geographical coordinates: latitude, longitude and altitude. If a body was taken from the Earth to the Moon, or the other way around, its mass wouldn’t change, it’s its weight which changes, instead.
After comparing the recalled ideas, we have:
a) the term weight, within the meaning used before Archimedes till the present day, refers to two different concepts; the first one is the amount of substance (unchanging), the second one is the gravity pull (changing);
b) the ancient term weight gravity (once considered unalterable) is linked to the gravitational pull (afterwards considered variable);
c) the ancient term weight gravity, which was used by Galileo in the meaning of gravity but was considered unalterable; from now on in this book I will only use the term weight gravity referring to the scientists prior to Newton.
1.2 Barycentre, Centre of weight gravity, centre of gravity, centre of mass
The barycentre is one among the many centre points of a geometric figure; this is valid at any point of history.
The centre of a falling body, when we refer to ancient times (from Archimedes to Galileo), its definition is slightly different for each author (Archimedes, Pappus, Stevin), is the centre point such that if a body was hanging from it, the body wouldn’t lose balance.
The centre of weight gravity, when we refer to modern and contemporary ages, is the point where the gravitational force (weight) is applied; it is also called barycentre.
The centre of mass, during modern and contemporary times, is the point in which the static moment of every axis passing through it is zero. In this peculiar case in which the distribution of the mass is uniform, the centre of mass corresponds to the geometrical barycentre of the figure considered; thus, the reference axis is called barycentric axis.
During the ancient time, since the weight of bodies was considered unalterable, the centre of weight gravity used to match the geometrical barycentre.
In the peculiar case of uniform mass distribution, it is underlined that the centre of mass matches with what was called centre of weight gravity during ancient times.
During modern and contemporary times, even if it was known that the gravity force (weight) of a body was alterable, how could they name it centre of gravity or “barycentre”? Moreover, how could they believe that the centre of mass corresponded to the centre of gravity?
The centre of mass corresponds to the geometrical barycentre exclusively when the mass distribution is uniform.
If we treat the simple case of uniform mass distribution, also when there is a symmetry, the centre of gravity never matches with the centre of mass. The classical example is the circle in which the centre of mass corresponds to the centre of the circle, but the centre of gravity lies beneath it and therefore cannot be the barycentre.
The rate of distance between the centre of gravity and the centre of mass peaks on the earth’s surface, diminishing with altitude. Moreover, it increases with:
a) mass growth;
b) density reduction;
c) shape, growing from the sphere to the cylinder to the cube.
All of this is the consequence of my scientific discovery: “The shape of solid bodies”.
“The love for the Pursuit of the Truth and Knowledge”, regardless of “The shape of solid bodies”, has led me to new insights about:
a) buoyant bodies;
b) hanging/rotating bodies.
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