Any geocentric world view is not by definition worse than any heliocentric world view. Ptolemy, Copernicus, and Tycho assumed motion along circles, and if you add a sufficient number of circles in just the right way to any one of their models, then you can get results at any desired accuracy, regardless of whether you assume that the Sun revolves around the Earth or the Earth around the Sun, and of whether you assume that the planets revolve around the Sun or around the Earth.
The key difference between the models of Ptolemy/Copernicus/Tycho and that of Kepler is that the older models assume motion along circles, and Kepler assumed motion along ellipses.
Tycho's model, if suitable corrections for elliptical orbits are applied, can work as well as Kepler's model, but the same holds for Copernicus or even Ptolemy. Moreover, "suitable corrections" means, if you want to keep to circular motions, that you have to keep adding more and more circles until the desired accuracy is reached.
For the results it does not matter which point you take to be the origin of the coordinate system (the Sun or the Earth), or (with certain restrictions) what shapes you want to use to describe the orbits, but such choices do affect the length of the calculations and the form of the formulas and how much time it takes to explain it all to someone else.
If you use a model with motion along circles, then you need all kinds of circles on top of circles with each their own period of revolution, diameter, and orientation, without any clear understanding (if you don't know what the real situation is) of why a certain circle needs to have just that period, diameter, and orientation. Besides, certain periods keep coming back in the motion of the same or other planets, without it being clear why this should be so. All in all, a complete description of such a system is very large, with many free parameters (such as the period, diameter, and orientation), that all have certain values that cannot be predicted from the theory and therefore have to be measured separately.
In addition, until the end of the Middle Ages, these kinds of models were not presented as descriptions of the true situation, but merely as mathematical tricks to allow prediction of certain things. People saw no fundamental problem if one model was used to predict the longitude but a completely different model to predict the latitude. I seem to recall having read that Galileo used the excuse that "it was merely a mathematical convenience" to get rid of the Inquisition, though he probably did not believe in that excuse himself.
In general, if there are two models that can each provide predictions to the same accuracy, then the one that has the smaller number of free parameter is preferred. This number is smaller in a heliocentric model than in a geocentric model, because the motion of the Earth around the Sun (from the heliocentric model) is reflected (in a geocentric model) in the apparent motion of all other planets around the Earth (for example, in the occasional retrograde motion of the outer planets), so in a geocentric model some additional free parameters are needed including one for the size of the retrograde loop) of which we now know that they really reflect the motion of the Earth around the Sun. If you don't know that really all planets revolve around the Sun, then you don't know how these additional free parameters are related to one another, so then you have to determine their values each separately from observations.
The switch from the geocentric (Ptolemy) to the heliocentric model (Copernicus) meant that a number of these previously free parameters were no longer free, because they could (if desired) be predicted from a transformation from the heliocentric models. I cannot say how this worked for the model of Tycho, because it depends a lot on whether he assumed that some of these parameters were free, or whether he recognized that they really weren't free at all.
The switch from circles (Ptolemy, Copernicus, Tycho) to ellipses (Kepler) reduced the number of free parameters even more, because instead of a large number of joined circles with each its own position and diameter and orientation (and hence many free parameters), now you needed only a single ellipse. If you know that really an ellipse is appropriate, then you can take the small number of free parameters of the ellipse and calculate from those the positions and diameters and orientations of all of those circles that you can use to make the same predictions, but if you don't know that you're really dealing with an ellipse, then you have to separately deduce each of the characteristics of each of the circles from observations, so then they count as free parameters.
Kepler's ellipses gave a preferred position to the Sun, because the Sun (and not the Earth) must be in one of the foci of each of those elliptical orbits. Kepler also found (in his Harmonic Law) a relationship between the periods of revolution of the planets and their distances from the Sun (and not the Earth), which got rid of some more free parameters (because now you could calculate the period from the distance, or vice versa). These were two good reasons to take the Sun and not the Earth as the center of the Solar System, and hence to reject the model of Tycho.
Today we know not just how but also why the planets move in elliptical orbits, namely because of the Law of Gravity of Isaac Newton. There are now only six free parameters for each planet (the so-called orbital elements), if you ignore the disturbance of one planet's orbit by another planet (which the geocentric models did as well): one for the size of the orbit, one for the shape of the orbit, three for the orientation of the orbit, and one for the position of the planet in the orbit at a given time. This number, six, is far smaller than the number of free parameters that is needed for models with only circular orbits, because each additional circle requires four extra free parameters (one for the size, two for the orientation, and one for the position along the circle).
More Universe Wallpapers in FullHD
Niciun comentariu:
Trimiteți un comentariu