Kepler's laws of planetary motion

There are 3 laws:

1. Every planet orbits around the Sun in an elliptical orbit.
2. This concerns the speed of a planet around its orbit, and notes that an imaginary line between the planet and the Sun would sweep out the same area in the same given area.
3. The square of the time a planet takes to go round its orbit is proportional to the cube of the orbits semi-major axis (half the diameter of the planet's orbit).

The first law is relatively easy to convey, we all know that planets orbit the Sun and they effectively "circulate" it, better known as an orbit!!
What is important to understand is that a planet I.E Earth, has 2 key points in its orbit, these are known as the Aphelion and Perihelion.

Aphelion: Furthest from the Sun.

Perihelion: Closest to the Sun.

This effectively means that our orbit is not perfectly spherical and you're probably wondering why do we have these 2 key points??

Gravity pulls things together and in actual fact it wants to combine the Earth and the Sun and if it could it would, but it can't. Why?

The Earth is travelling at too high a velocity (velocity=speed in a given direction).

You may have heard the word FALLING mentioned when people talk about gravity.

Here's a pic to show the orbit:







You can see the 2 key points clearly marked. The Earth is bound to this orbit because of the gravitational pull of our Sun. The word FALLING may be easier to understand if I rotated the pic with the aphelion at the top, I'm not doing that as it would be illogical.

The Earth is travelling at a velocity around the sun which stops it being drawn in, however the gravitational pull of the Sun, results in this orbit. So the Aphelion is the point that Earth gets to when the Sun says "you're going nowhere" and pulls it back. The Perihelion is the point at which the Earth says "you can't have me".

A point to mention here is that the Earths velocity increases the closer it gets to the Sun - that is it is FALLING and everything increases its velocity as it falls. This doesn't mean it spins faster, it means it moves through space at a higher velocity.

You can see from the pic that our Moon has an elliptical orbit too!

Perigee: nearest

Apogee: furthest

Thats the first law.

Here's the second:





Sometimes labelled the law of "equal areas", the main principle to note here is that a planet will be travelling at its fastest when it's closer to the Sun and at it's slowest when it is furthest from the Sun. However, if I was somehow able to draw an imaginary line from the centre of Earth to the centre of the Sun, the line would be equal length at equal times.

Have a look at this picture:





You can see that although the triangles' sides are different, the actual area of each is the same. Please note that there are 12 Earths shown to reflect our 12 calendar months respectively.
The last part to note about the second law is that the short base of the triangles are a reflection that Earth is travelling slower (its further away from the Sun!). Therefore the longer base of the other triangles is a reflection that the Earth is travelling faster (it has travelled further over the course of the month).


Third law!

This is all about comparing the orbits of each planet in our solar system.

Probably a good idea to put this here:










AND THIS:

 

The important factor to establish here is that the closer the planet is to the Sun in general - I.E Mercury is the nearest planet, the faster/quicker its orbit of the Sun. This may seem obvious because it has the shortest distance to travel when compared to the other 7 planets. However, the time taken to orbit the Sun is due to the Sun itself, remember the point that the closer a planet gets to the sun, the more it accelerates. Well, Mercury is accelerating faster than all the other planets because it's the closest.

Here's an everyday example: you have an ice-skater on a rink who is spinning round and round with her arms out in front of her. In order to increase the speed of her spin, she PULLS her arms inwards to her body, the closer together she is - the faster she'll spin.

Planet	Period (s)	Average Dist. (m)	T2/R3 (s2/m3)
Earth	3.156 x 107 s	1.4957 x 1011	2.977 x 10-19
Mars	5.93 x 107 s	2.278 x 1011	2.975 x 10-19

You may wonder why I've put this table here, well it's because mathematics is an important part of the third law. I shan't go too in-depth. The main point is that:

The comparison being made is that the ratio of the squares of the periods to the cubes of their average distances from the sun is the same for every one of the planets.

Planet	Period (yr)	Ave. Dist. (au)	T2/R3 (yr2/au3)
Mercury	0.241	0.39	0.98
Venus	.615	0.72	1.01
Earth	1.00	1.00	1.00
Mars	1.88	1.52	1.01
Jupiter	11.8	5.20	0.99
Saturn	29.5	9.54	1.00
Uranus	84.0	19.18	1.00
Neptune	165	30.06	1.00
Pluto	248	39.44	1.00

The last column is the most important here. You can see that amazingly, each planet has the same T²/R^3.


No matter how long their "year" (orbit) is or how far away they are from the Sun. Kepler was able to devise a calculation that showed that every planets' orbit is the same.

The third law is also known as the LAW OF HARMONIES because every planet is in harmony with each other.

I hope you've enjoyed reading.

Much love, Adam XX.