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GRAVITY CONE


Pakhomov Serguey,
Ph. D., Izhevsk

Dedicated to the 445th anniversary of
Johannes Kepler

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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445 лет Иоганну КЕПЛЕРУ

27 декабря 2016 Г. исполняется 445 лет выдающемуся астроному Иоганну Кеплеру.
В Удмуртском государственном университете пройдёт лекция-спектакль "Бокал мартини для господина Кеплера"
и презентация работы С.В.Пахомова "Гравитационный конус".

 

 

 

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