Kepler's 1st law: Difference between revisions
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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, ε 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 < ε < 1 ; in the limiting case ε = 0, the orbit is a circle with the Sun at the centre (i.e. where there is zero eccentricity). | |||
== Resources: == | == Resources: == | ||
*[https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#First_law_of_Kepler Kepler's 1st law] | *[https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#First_law_of_Kepler Kepler's 1st law] | ||
== Discussion: == | == Discussion: == | ||
Revision as of 09:45, 13 February 2020
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, ε 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 < ε < 1 ; in the limiting case ε = 0, the orbit is a circle with the Sun at the centre (i.e. where there is zero eccentricity).