Kepler's 1st law

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The orbit of every planet is an ellipse with the Sun at one of the two foci.


Mathematically, an ellipse can be represented by the formula:

$${e r={\frac {p}{1+\varepsilon \,\cos \theta }},}{\displaystyle r={\frac {p}{1+\varepsilon \,\cos \theta }},}$$

where $$p$$ is the semi-latus rectum, ξ is the eccentricity of the ellipse, r is the distance from the Sun to the planet, and θ is the angle to the planet's current position from its closest approach, as seen from the Sun. So (r, θ) are polar coordinates.

For an ellipse 0 < ξ < 1 ; in the limiting case ξ = 0, the orbit is a circle with the Sun at the centre (i.e. where there is zero eccentricity).


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