History. Kepler's laws
The first successful model of the motion of the heavenly bodies was
set up by Ptolomej in the 2nd A.D. with his geocentric
system, which has synthetized most of the knowledge and observations
collected by the Egyptian priests during many centuries. According
to Ptolomej, Earth is stationary and situated in the middle of the
space. The stars circle around the Earth fixed to the solid orbit.
That's why their revolving is uniform. The motion of the planet, the
Sun and the Moon is more complex. To explain it, Ptolomej introduces
the motion along the epicycles: the Sun, the Moon and the planes revolve
uniformly along the circles, whose center is also revolving along
the circle, and in the center of this circle the Earth is situated.
Ptolomej succeeded in explaining the unexpected certainty of the planets'
revolving by the means of combining the revolving along the epicycles.
The geocentric system is the example of the physical model completely
distanced from the physical reality, but still describing exactly
the phenomena in the frame of the achieved exactness of the observation.
The geocentric system stayed the dominant theory on space in the whole
middle ages era just because of the lack of the more concrete observations.
Still, Aristarh has even long before Pltolomej concluded that the
natural motion of the heavenly bodies can be explained even starting
from the opposite point, from the fact that the Earth revolves
around the Sun and around it's ax.
Twenty hundred years later the bishop Nikola Kopernik brings forward
his theory of heliocentric system. Kopernik puts the Sun in the middle
of the space. The Earth and other planets revolve around the Sun in
the concentric circle. The standing stars stay still, but their illusive
motion is the reflex of the daily revolving of the Earth around it's
ax. The extreme importance of the Kopernik's theory was not observed
at that time. From the experimental point of view, for the calculation
of the illusive position of the planets and the Moon on the heavens,
heliocentric Kopernik's system was not at the beginning more useful
than a geocentric one. At that time equal number of scientists agreed
on either of the systems. Tycho Brache, at that time was the only
one to have very precious systematic observations on the motion of
the planet Mars. He later gave his knowledge to his follower Johanes
Kepler, who had enough knowledge to bring up the evidence in favor
of Kopernik's heliocentric system. On the basis of the Brache's data
on successive position of the heavenly bodies Kepler concluded that
motion of the heavenly bodies can not be reached by the combination
of the circular motion. There are three laws that sum their research
done in the period of twenty years. Those laws represent the epiric
basis of the heliocentric system:
- The planet move along the ellipsis, and the Sun is in the radiant
of one of them
- The planets move in manner that straight line connecting the position
of the planets with the Sun covers in the same periods of time same
field, no matter how far is the planet from the Sun (the Law of
- The squares of the time planets need to revolve around the Sun
are the cubic of the average distance to the Sun
One of the most important fact in Kepler's laws was that he rejected
the circle as a perfect model of the heavenly bodies path. Introducing
of non- circular paths into the science of physics made road to Galileo's
The Newton's law of gravitation
On the basis of the Kepler's
laws and his own laws on the motion Newton came to the mathematic
form of the force that causes the revolving of the planets around
the Sun. The Law of gravitation was first published in 1686. in his
main work " Philosophiae Naturalis Principa Mathematica".
Illustration 2. Kepler's law:
picture, page 132.
According to the Second Kepler's law the flat speed of planet revolving
around the Sun is constant, so the value 1v is constant, too. The
value of the revolving of the planet around the Sun is m*v*1, so the
Sencond Kepler's law says that the physical value at the planet moving
is constant. So, the force that works on the planets to turn their
direction along the ellipse must be directed toward the Sun.
The Second Kepler's law, with the help of Newton's mechanics, determines
the direction of the force that works on the planets. We shall call
that force - gravitational force. The value of that force and it's
dependence upon the distance from the Sun will be reached by applying
other Kepler's laws. The Third Kepler's law will mathematically be
like this: T2=kr3, where T is time of revoving, and r is the average
distance to the Sun.
The force that works on the planets, and is directed towards the Sun
is the centripetal force, has the form : picture - page 133.
The Sun is so the center of the force which work on a distance, with
no visible physical relation. Newton generalized the concept of force
by introducing the gravitation force. The gravitation force was up
to that time connected exclusively to action of the bodies in the
close contact. So bodies can work on distance, with no material relation
among them. The principle of acting on distance, in other words existing
of the forces that come from one center, was the most important in
the development of physics in the 18th and the 19th
Newton concluded that every two bodies interactively act by the force
The given formula would in words mean the following:
Each material particle attracts each other with the force that is proportional
to the product of the body mass and contra proportional to the square
of their distances; the magnetizing force acts in the direction of
the adjutage of the particles.
The Newton's gravitation law
is the universal law, that can be applied to all bodies in the Universe
that have a certain mass. Between those two bodies there is the force
G*(m1m2/r2) acting in the direction of their adjutage. The value of
that force depends on the value of the universal constant G. But,
that value was not able to determine from the astronomic measurements.
Experimentally, the value
of the constant G can be determined
in manner to measure the gravitational attraction between the bodies
of the known mass, positioned on the given distance from each other.
The first precise measurement of the constant G was done by Cavendish
in 1798., although the measuring device itself was before designed
by J. Michell. The Cavendish scale consists of two little balls, of
the mass m1 each, positioned on the ends of the light horizontal bar,
hanged on the thin vertical thread. The small mirror on the thread
itself enables the measuring of the torsion angle of the thread. If
we bring two big balls of the mass 2 closely to the mass m1the gravitation
magnetizing will move balls mass m1 and turn the bar and thread. G=6,67*10
The property of the material
called mass can be seen in two different ways. For the gravitation
force among two bodies we say that it is proportional to the product
of their masses. In that sense mass is the property of material by
which each body acts on any other body through the magnetizing force.
That property will be called hard or gravitation mass. On the other
side the 2nd Newton'
law says that we have to force if we want to change the value or the
direction of the speed of a body. That property under which the body
resists to the change in the motion will be called the slow or inertial
mass. It is obvious that the hard mass need not be equal to the slow
mass of any body. The experiment at the same time shows that there
is strict proportion among them , if we need twice bigger the force
to give the body A the same acceleration as the body B, and the gravitation
magnetizing force among bodies A and some body C will be twice as
big as the one among the bodies B and C. The experience shows the
strict proportionality among the two masses, we consider them to be
the same and express them in the same units.
gravitation field. As we have seen earlier , like electric and magnetic forces, the forces
that work on a distance, through the empty space , without the touch
of the bodies. For such kinds of forces it is useful to determine
the concept of the force field.
Observe the gravitation force by which some body acts on another
body. We say that the first body forms around it the gravitation field,
and this field acts on the other body. Of course, the other body acts
by the gravitation field on the first body. So, we can say that the
gravitation field exists in a point where gravitation force acts on
the material particle in that point. We consider that gravitation
field exists in the given point even when in that point there is no
particle that it can act on.