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Consider projecting a particle from or above the earth surface (at a distance $r$ from center of earth) with velocity $v$. My teacher told me that if $v<v_0$ particle will follow elliptical path, $v=v_0$ circle, $v_e>v>v_0$ ellipse, $v=v_e$ parabola, $v>v_e$ hyperbola.

$v_e=$ escape velocity in that orbit
$v_o=$ orbital velocity in that orbit

I asked my teacher for the reasons for the above miracles. He told me that it is experimentally observed.

But I can't believe how exactly an ellipse could be predicted experimentally without knowing the equation of a conic.

Could someone help me knowing the reasons?

Dodo
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Chesx
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1 Answers1

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But I can't believe how is exactly ellipse predicted with experiments without knowing the equation of conic.

Kepler, who first had the idea of elliptic orbits, used data from several astronomers about night by night positions of Mars in the sky. Also day by day position of the sun. All of this with respect to the fixed stars.

The established theory at the time was to suppose an eccentric circle, what was reasonable, but not so precise as an ellipse.

Of course Kepler knew the properties of the conics, that were known since the Greeks.

The real work is not simple as can be seen in this article.

Claudio Saspinski
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