|
|
 |
TOWARDS NEWTON'S THEORIES
|
|
|
|
| |
| TOWARDS NEWTON’S THEORIES |
|
Newton was born on the same day of Galileo’s death. This was the
time of great scientific developments. Tycho Brahe’s observations
of planetary motions were used extensively by Johannes Kepler to formulate
the three laws, famously called the Kepler’s laws of planetary
motions. A vivid account of Kepler’s laws is given in the book
- ‘Ideas And Opinions Of Albert Einstein’.
|
|
|
|
The first law says that planets move in elliptical orbit with the Sun at
one of its foci. Well, it is irrelevant to ask why the Sun is only at
that focus and not on other. Symmetry principle allows it to be on any
focus – but not both, except for quantum mechanical probabilities.
The second law says that the line joining the Sun and the planet sweeps
out equal areas in equal intervals of time. It is like a restatement
of the law of conservation of angular momentum. We will see a proof of
the second and the first laws in the next section. The third law states
the relation between time period and distance from the Sun (it is square
of time period of orbit and cube of semi-major axis proportionality relation).
Look at the Exercise for this relation.
|
| |
|
There were other
discoveries during this era and the most important development was
made by Rene Descartes (the
Father of
modern philosophy) and Fermat. Rene devised something known as the
Cartesian coordinate and, it was probably the most important development
in mathematics when it comes to analytical part. Coordinate system
is a very handy tool for studying the nature as it provides us with
the most important tool, the coordinate axis (the only thing, using
which, one can measure something). The pre-existing system of axiomatic
geometry could not be used to study curves.But coordinate system
enabled mathematicians to do so.In analytical system, you have a
well defined
address for a point which is its beautiful feature in contrast to
axiomatic system. More important insights related to vectors and
perpendicularity
are obtained in this |
|
structure.And Mathematics would
becompletely aloof from physics had there not been an analytical system
since in physical law, different
points of space represent different
properties and relativity holds much importance in it. For example, the
inverse square law definition that a point at distance r from gravitational
body faces a force proportional to the inverse of r’s square reflects
the nature of force at this point and its difference from other points.The
present theories on vector calculus could not have existed had it been
only for Projective
(another successful geometry by Desargues) and axiomaitic geometry.
It can be said that it was coordinate geometry which created the modern
physics. This geometry was developed further by Gauss and Riemann (other
mathematicians like Bolyai and Nicholai Lobachevsky developed the axiomatic
form of the same Non-Euclidean geometry which, by no means, could be
used for analytical purpose like development of relativity) into the
world of hyperdimensions where curved spaces played important role.
|
| |
|
|
| |
|
