# A theory on planets

Planets longitude changes continuously in respect of the fixed stars (the dome). They have their own motion on the celestial sphere. Currently a double reason is given for this particular motion: first planets move around the sun on an almost circular trajectory (according to Kepler laws) and, second , the Earth moves around the sun and thus the visual direction Earth-planet that projects the planet on the celestial sphere is continually changing.

What should be the different consequences when considering a fixed and central Earth?

I’ve found three different models that have seemed to me worth of  examination.

# Eudoxus

The first is the Eudoxus’s one. Wikipedia states about Exodus:

Eudoxus of Cnidus (/ˈjuːdəksəs/; Greek: Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios; c. 390– c. 337 BC) was a Greek astronomer, mathematician, scholar and student of Plato. All of his works are lost, though some fragments are preserved in Hipparchus‘ commentary on Aratus‘s poem on astronomy.[1] Theodosius of Bithynia‘s important work, Sphaerics, may be based on a work of Eudoxus.”

He supposed with a very ingenious idea that the motion of planets could be described with a combination of two  or more spheres, one inside the other , a mechanism able to pull the planet around the Earth. This combination can explain the retrograde motion of planets but doesn’t explain why sometimes planets appear to be nearer to the Earth.

## The eccentric model

The other system  is a model that was conceived in Greece in a period from 330a.C. up to 200a.C. and that  was elaborated by Ptolomeus.

This model has been named in two different ways, the epicyclical model and the eccentric model as shown in the picture. The image represents the epicyclical model: the planet rotates 1) on a small circular trajectory and then 2) it rotates on a bigger trajectory around the Earth. The other model is the eccentric model that considers  the planet rotating on a trajectory not centered on the Earth but slightly eccentric.

From a geometrical and dynamical point of view the two models could be considered just one as being perfectly equivalent.

## Tycho Brahe

Another model is the Tychonic system.

This system has been suggested by the astronomer Tycho Brahe in the late 16th century.

He imagined the sun rotating around the Earth while all the other planets were  rotating around the sun. In the picture you should note  the light blue circle  representing  the trajectory of the sun while the five planets Mercury, Venus, Mars, Jupiter and Saturn are following an orange trajectory all around the sun. The blue circle around is an image of the celestial sphere with the fixed stars.

Heraclides in the 4th century BC  suggested that Mercury and Venus revolve around the Sun, which in turn (along with the other planets) revolves around the Earth, an intuition that was partially anticipating the ideas of Tycho Brahe.

## Elongation of a planet

When talking of planets  we have to consider elongation. The elongation of a planet in longitude  is the difference between the longitudes of the planet and that of the sun. The elongation is the angle between the longitude of the planet and that of the sun .

Planets are divided by astronomers in inferior and superior planets. The inferior planets are Mercury and Venus. They are called inferior because considered nearer to the sun in comparison with the Earth. Superior planets are the ones farther to the sun “on the other side of the Earth”  when considering  an heliocentric system.

There is an important idea to understand:  the maximum elongation of Mercury is 28°, while that of Venus is 47°. All other planets have an elongation that can reach  360°. This means that Mercury and Venus will  always stay quite near to the sun while all other planets are independent from the sun position.  Astronomers explain this phenomenon by saying that Mercury and Venus are interior planets, but in consideration of the three model systems we have just considered , this difference in elongation should be explained having in mind a geocentric system. For example, when watching the  picture presenting the Tychonic system you can note that only two planets, Mercury and Venus,  are near to the sun, while for the others the trajectories pass over the Earth, so reaching an elongation of 360°.

The  Ptolomeic  and the Eudoxus systems  allow a clear description of the retrograde movement of planets that during their activity, periodically seem to go back and forth. But all these systems present  a problem, they are thought keeping in mind a spherical Earth, and sun and planets rotating around it. When regarding Earth as not globular and stationary, then the sun should be imagined as rotating over the Earth and not  in a movement around it. So astronomers have to continue  studying  a new model  in order to define  in the correct way  our cosmic reality.

Planets are probably moving on circular trajectories with epicyclical movements over a non globular stationary Earth. The epicyclical system allows to describe both the retrograde movement and the periodical approaching of planets to the Earth. Surely Eudoxus system is the more elegant and it is worth of a deeper analysis.

I will give here some new data about planets.

 Symbol Planet Orbit radius [Km] Orbit circumference [Km] Mercury 29970 89910 Venus 33300 99900 Mars 36630 109890 Jupiter 39960 119880 Saturn 43290 129870