GRAVITY CONE
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Pakhomov Serguey,
Ph. D., Izhevsk
Dedicated to the 445th anniversary of
Johannes Kepler
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ABSTRACT
The geometric concept of “gravity cone” is introduced
for the visualization and graphical solution of the Kepler problem
by the method of construction. Stereometric problem of the conical
surface section with following projection on the orbit plane reduces
to a set of rules for constructions in the plane. Combining the
radius vector with the velocity hodograph in one model reveals
the role of two foci in the construction of conical sections.
There
is a stylistic inaccuracy in the formulation of Kepler’s 1st law,
which students often stumble on. We are talking about the words
"at one of" in the statement: "The orbit of every
planet is an ellipse with the Sun at one of its two foci".
This uncertainty raises the question: and what about the other
focus?
And in general, where is the cone whose sections specify the
orbits? Usually in this case, the teachers talk about mathematical
abstraction, but we will show that the answers to these "childish"
questions may be more meaningful.
The purpose of this work is to show a graphical way to solve the
Kepler problem. To do this, an additional virtual dimension is
used. But before proceeding to the construction of something new,
we recall the basic laws of Keplerian orbits.
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To
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