The ecliptic

This article is under revision.

Consider the picture aside. It represents the celestial sphere. The ecliptic is the maximum circle eclitt1 inclined of about 23°27’ on the celestial equator eclitt2. It is the projection of the trajectory of the sun (they say the Earth) on the celestial sphere (we say the dome or the firmament).

eclitt3and  eclitt4are the points where the ecliptic intersects the equator otherwise known as the equinox points.

The angle of 23°27’ is the obliquity of the ecliptic and it is not always constant but it registers in the course of the year some small variation.

In the antiquity astronomers had already understood that the trajectory of the sun in the heavens is inclined.

Before the Iron Age many astronomers were forced to deal with this problem and they were able, at the end, to explain it with a good precision. Below is reported a table with some value measu

 

red by ancient astronomers.As you can notice all values are quite similar.

Ptolomeus is probably the best known Greek astronomer. He wrote the “Almagestus”, that remained for centuries a reference point for astronomers. Ptolomeus believed that the Earth is a sphere in the center of the universe and that the sun turns around it as well as all other planets. He measured the inclination of the ecliptic and  confirmed the value given by Ipparcus of 23.6° , value that  nowadays is not considered  completely correct anymore.

Aside you can see a reconstruction of the instrument used by Ptolomeus to measure the ecliptic. As you can note it was a sort of goniometer aligned with the meridian that gives the higher point of the sun in that place at the solstice’s day. The goniometer evaluates the angle of the casted shadow. Yes, the ecliptic  effect for a given point on the earth can be evaluated  by the observation of the differences in length of a shadow between the two solstices.

But how should all these considerations be applied in the case of an Earth given as flat and immovable? How could the ecliptic be imagined in this case? After a lot of thinking and calculations posted by a lot of people on the net all around the world, the flat Earth community quite unanimously admits that the trajectory of the sun should be a cone. This is the shape that is generally accepted and supported by all sort of calculations and confirmed by all visible effects of the sun on the Earth.

Indeed, since the sun has to run faster when in its Southern position, we have to think that it has to shift lower to warm enough some specific zones of the Earth. Similarly, when considering the consequences of many trigonometric calculations, it is impossible not to imagine that the sun is running in a lower position when moving in the Southern parts of the Earth.

Since the ecliptic is generated by the sun being higher in summer and lower in winter I’m lead to believe that in this cone model the ecliptic is very simply the inclination of the cone.

With Sketch-up I’ve tried to do a representation of this cone in a “correct” scale.

The red lines define the inclination of the ecliptic.

In the past, I’ve given some geometric value to describe this cone (see videos on my Facebook profile)that result  not only from calculation, but also from considerations of the harmony always manifest in the measure numbers of the cosmic  creation inside which we all live.

By controlling now these data and considering that we have to face with this angle, that necessarily exists
and has been measured, I have to correct my numbers. In the image below drawn with Autocad you can see the dimensions of the cone and the inclination of the ecliptic.

The outer diameter that was considered to be 13320Km has to be increased to 14310Km by adding 990Km.

This is a good example to show the big amount of  study in order to arrive to good results in the description of  the Earth.

Appendix.

How to calculate the height of the sun.

How can you arrive to have an idea of the path of the sun?

The best way would be to have a sextant, as the one in the image, and make many measurements of the height of the sun in many days of the year and in many different places of the globe.

To learn to use a sextant and correct the altitude from refraction, aberration and parallax would be very interesting…if you have time and money for it.

But what about, when you do have one?

You could do like me and download an application that gives the height of the sun for every place in the world. So, I’ve downloaded Sun surveyor from Google play.

However, you should be careful since these applications are intended for the use relatively to a globe Earth geometry and data are calculated according to a globe geometry that has never actually been measured. Anyway, when you consider values relating to a single place in the northern hemisphere, experience shows that heights can be used for a first, very approximated calculation.

Let’s suppose to be in Rome. Rome has a latitude of 41°54’. You have to consider that in a globe geometry each degree of latitude corresponds to a 111Km arc.

Rome is distant 41°54’-23°27’=18°27’ (2050km) from the summer tropic and 41°54’+23°27’=65° 21’ (7250km) from the other tropic.

Sun surveyor gives these two eights angles for the solstices at Rome.

Summer solstice 71.5°
Winter solstice 24.7°

Let’s now calculate with these two values the height of the sun in winter and in summer.

H=tg71.5°*2050= 6127km
H=tg24.7°*7250= 3334km

If you consider some other place in the northern hemisphere, you will find values from slightly different to very different orders due to the original  geometry considerations  the software is based upon. However you can have a first impressive idea of the behavior of the sun.

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