**Chapter 1 – Invitation to a Greek party.**

Let’s imagine that we receive an invitation to dance, and the theme is an ancient-themed party, but when we receive the invitation we find data that apparently is encrypted. As we are very curious and want to dance, we have to sit down and analyze the data that has been provided to us to solve the mystery of our invitation.

To enter this chapter we will have to use our imagination a little and be prepared to travel through time, do calculations

quick and collect information in each paragraph with jumps back and forth to understand the origin of these questions or concepts and bring them to our time and then prepare to go to our dance party.

One of the most important aspects of science in general, as well as astronomy, is to ask ourselves why things happen. Many questions arise from that invitation which we are going to break down here to later understand the mystery and what that invitation has to do with the desire to go dancing.

What is the day without shadow?; what is the time zone?; And why does the place look like a mathematical operation?

Everything is quite confusing at first, but it is actually easier than it seems, the reality is that all this data has been and is used not only in astronomy, but we make use of it daily without realizing it in our daily lives.

The first thing to know is that time is a unit of measurement that humanity has designed to record what happens from event A to event B, but all of this is based on observation. Time is born from the observation and recording of the movement of the Sun, Moon, planets and stars in the times of the Sumerians and Babylonians, long before the Greeks and Romans.

If we talk about time then “Whoever invented the clock, how did he know what time it was? A funny question if you will, because to invent humanity’s first clock a stick was simply buried in the ground and lines began to be drawn as the sun moved in the sky. But with this, something much more important was discovered.

A sundial records the moment of sunrise on the Eastern horizon while the shadow is projected towards the West, as the movement of the Sun progresses in the sky (Caused by the rotation of the Earth) it rises until reach its highest point, at that moment, the shadow goes from being long in the morning to being very short at the moment of maximum solar altitude, then the Sun begins to move until it hides in the west and again lengthening the shadow this time towards East.

But for every day that passes and depending on where we are on the planet, the shadow can be longer or shorter and there may even be no shadow at all! at the moment the sun reaches its maximum altitude. This “disappearance” of the shadow at noon is known as zenithal noon and usually happens in places that are within the famous lines of the tropics, which as we know are two, the northern one called “Tropic of Cancer” and the southern one called “Tropic of Capricorn” Who named them and where exactly are they located? To answer that,

We are going to make our first trip in the

time of our imagination and

going into this article.

We are in the era of

ancient Greek astronomers, more

specifically around the year 400 before

Christ, and one of our characters is

Aristotle, an astronomer, philosopher, scholar,

mathematician, etc. who in one of his

writings, called “Meteorological”, explained the behavior of the winds, reporting that the Sun moved with the winds in the direction of the northern bears (bears major and minor) to the “tropos” of Cancer and then went south to the Capricorn “tropes.”

The word “Tropos” means “Return” or “return” and it was understood that the Sun therefore had a maximum displacement north and one towards the South, and the names of Cancer and Capricorn refer to the constellations in which the Sun was located. Sun on these dates, however, we are about 2000 years in the past, so if we wanted to make that measurement today, we would be off by a lot of degrees in the sky.

So at the moment when the observer noticed the Sun at its highest point, objects located on the ground lost their shadow for a few minutes. This phenomenon was recorded directly around the years 300 BC by the Greek astronomer Eratosthenes of Cyrene, who when comparing the moment when the Sun was at the Tropic of Cancer, an obelisk located in Alexandria projected a very short shadow, but about 5000 stadia to the South, (formerly used unit of measurement equivalent to 900km

approximately) in the province of Siena (today Aswan, in Egypt) the bottom of a well was illuminated directly by the Sun that only time in the year. Of course, he did not know it instantly, but rather through visiting one location and another over a period of approximately 5 years to

be able to do those check the phenomenon

and perform your calculations.

In those days, it was very

popular “Pythagorization” of things,

quoting Pythagoras who in the year

500 BC he made his famous little triangles,

became quite an “influencer”, he determined

fundamental mathematics through its theorems with which you can calculate distances, heights, navigate and build among many other things. So the entire Greek empire then had the habit of making triangles for everything.

Pythagoras had a student named Philolaus, an avid observer of the sky who thought that the Earth, the Sun and the Planets orbited around a “central fire” found in the cosmos, he also stated in his observations that the earth was spherical and that It rotated on an imaginary axis, so these concepts were well known as the years went by. Aristotle later discarded the idea of the central fire and placed the Earth at the center of the universe, giving rise to the geocentric model.

Some time later, one of his students, named Aristarchus of Samos, “Pythagorized” his model when he noticed that the Moon in its apparent movement in the

sky, formed a triangle in the sky with it located at the zenith (highest part of the sky) and the Sun on the horizon when it set or dawned. With this, he calculated that the Moon must be “20 times farther from the Earth and the Sun 400 times farther away.” Today we know this premise was valid, but Aristarchus did not have the means to verify these calculations.

Returning to Eratosthenes, in the

year 300 BC and assuming that we

we find at the time of

Summer Solstice in the hemisphere

North, moment in which the Sun sets

stops at the tropic of cancer

we see how he is calculating the

distance from the shadow of the obelisk and

dividing it by the height of the obelisk,

calculating your arcotagent angle

thanks to the knowledge of

Pythagoras and multiplying everything by the

distance between Siena and Alexandria, distance measured in those visits made in those 5 years, resulting not only in the fact that the earth is truly spherical as Philolaus indicated but also that it measures around 40,000 Kilometers. Eratosthenes, in 300 BC, calculated the circumference of the Earth. In a project that can be carried out in schools called precisely “Eratosthenes”.

With this experiment we can determine the time without a shadow and answer one of the unknowns of our invitation to the astronomical dance, but another thing that was discovered with this experiment is that the Latitude can also be determined with the shadow of the stick. of the place, that is, the geographical position in which a person, object or city, etc., is located.

Aristotle said that the planets, the Sun and the Moon revolved around the Earth in perfect circles, since the circle was the figure of the gods and a symbol of perfection. Given this, we could quote this time Euclid, who around the year 350 BC was in charge of studying geometric figures, circles and triangles, calculating angles and dimensions and indicating that a circle measures 360°, a number that will become one of the most important for the humanity.

He also determined that the sum of the interior angles of a triangle or circle

It is 180°, therefore, if a circle is divided into 2 we would form two arcs whose central part or maximum height would be 90° on one side and the other.

What we are seeing then is a representation of our planet as a circle, where the

horizon is the line that divides the planet into two arcs and

The maximum height that we call zenith measures 90° high,

However, if we combine this information with the axis

rotation imaginary proposed by Filolao, we know in

What position is our “inclined” position then?

planet, and if we observe the rotation of the stars we

We find the direction of Aristotle’s Bears and the famous Polar Star, which coincidentally is the indicator of the planet’s axis of rotation. All of the above complements the premise that if we measure the shadow produced by the pole or obelisk at solar noon we can determine the Latitude or angular distance that exists between a point 0° and 90° of the Earth’s axis of rotation. , so if our invitation says “LAT -13.5068285” as it has a negative symbol, it tells us that it is towards the South of point 0°. On the other hand, returning to Euclid and the number 360°, we know that this number is composed of its 24 divisors and was ideal for calculations, so, if it is divided we make 24 lines from north to south on that sphere and we calculate 360° divided by 24 would result in 15 and precisely 15° is what separates each divisor of that sphere. These lines will have

The name Longitude and corresponds to the angular distance given between a 0° meridian and its displacements in the East and West direction. Our invitation says LON -71.9865281 so again I have to check the map to find out where said dance will be. A no less important fact is that if we count the “meridians” or parallel lines of our zero point, we will see that they are -5, we have therefore found the Time Zone.

The year 300 BC was an important year, not

only by the discoveries of Eratosthenes

but also the works that from that year on

They built the structure of astronomy studies in ancient Greece, the first catalogs of stars, for example, were published in those years by Timochares of Alexandria, since in those times the sky was probably everything

a spectacle without equal, Timochares also captured the movement of the stars and 150 years later it would be Hipparcos of Nicaea who would take those catalogs and comparing them with his observations would lead to the discovery of the movement of the Precession of the equinoxes and the proper movement of the stars, He classified its brightness by magnitudes as well as proposing the idea of heliocentrism (the Sun at the center of the Solar System), however, at that time, the idea of perfect circles still prevailed, so he abandoned these ideas.

However, much of the knowledge of Hipparchus of Nicaea was compiled by Claudius Ptolemy, who as an encyclopedia published the “Almagest” with many of the concepts expressed in this article as well as his own, which included the model Ptolemaic of planetary movement, and with foreign ideas he tried to explain the reason for the retrogradation of Venus and Mercury and the other planets, he kept the Earth at the center of the Solar System and the model of perfect circles.

The Almagest, published in the 2nd century after Christ, was one of the last scientific records or compilations published by Greek astronomy. It became the closing of a door of knowledge that was imposed for almost 2000 years, preventing the development and advancement of new ideas, due to the emergence and expansion of religion and other empires.

This is how, thanks to the knowledge of the ancient Greeks, we can know where and when our themed dance party will be, and if we don’t know how to dance at least we will know what to talk about.