# Kepler’s laws of planetary motion

(Extracted in pure ‘hullabaloo-headache-boosting-scientific-language’ from en.wikipedia, and gracefully ‘headache-disipate-translated’ to the average Joe’s language by me).

#### 3. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.

###### Figure 1: Illustration of Kepler’s three laws with two planetary orbits. (1) The orbits are ellipses, with focal pointsƒ1 and ƒ2 for the first planet and ƒ1 and ƒ3for the second planet. The Sun is placed in focal point ƒ1.

(2) The two shaded sectors A1 and A2have the same surface area and the time for planet 1 to cover segment A1 is equal to the time to cover segment A2.

(3) The total orbit times for planet 1 and planet 2 have a ratio [~= are proportional to] of

[semi-major axis for either of the planets to the third power]:

(a1/2)3  and (a2/2)3.’

##### ‘Kepler’s laws improve the model of Copernicus. If the eccentricities of the planetary orbits are taken as zero, then Kepler basically agrees with Copernicus:

(These do not comply with real orbits, because they are elliptic).

1. The planetary orbit is a circle

2. The Sun at the center of the orbit

3. The speed of the planet in the orbit is constant

##### Kepler’s corrections (<- these do comply) are not at all obvious:
1. The planetary orbit is not a circle, but an ellipse.

2. The Sun is not at the center but at a focal point of the elliptical orbit.

3. Neither the linear speed nor the angular speed of the planet in the orbit are constant, but the area speed is constant.’

#### ‘A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.‘

For this I will upload an image of a lemniscata I provided in the ‘Meridiana… post

Analemma or lemniscata

Image extracted from web.romascuola.net

This curve has this form due to the law #2 of Kepler for the planetary movements, which says the areas covered by the planets (considering they sweep the space between two points in their orbits with a line joining themselves and the astro around which they are revolving , just the way we can sweep an area on the sand if we put an astro-pencil, a thread-force, and a planet-pencil, and move the planet-pencil around the astro-pencil describing a sector of swept sand) all along their orbits are swept with the same velocity.

This is so, because when a planet is near the center of attraction has necessarily to move faster in order to counterpart the attraction force, be it magnetic, gravitational, electrostatic, weak or strong nuclear… because if they would not accelerate they would end up crashing against the astro-center for their orbits movements.

If you array the above image on a circumference, you make the same calculi you’ll end up concluding the same Kepler did some centuries ago.

I’ll go on writing about this in the ‘Kepler’s laws of planetary motions (II)’ post, that I’ll write soon (along with the previous series of posts I am writing about).