The recent winter solstice, and reading some stories set in ancient Rome, got me thinking about the geocentric model of the universe and some potential problems with it (yes, I know it’s wrong)
Googling around finds accounts that deal with acknowledged problems of planetary retrograde motion and the varying brightness of planets. But I am also wondering;
How did they account for the differing length of day-light hours over a year? Was the sun’s sphere (alone?) supposed to ‘wobble’?
Also
The model puts the sun farther away from the earth than the moon. Yet the moon orbits once a month while the sun orbits daily. They acknowledge different spheres rotated at different speeds; but did anyone calculate what the speed of the sun would have to be? It would seem to be a phenomenal figure.
The Earth was recognized to rotate. The Sun moved against the background stars once a year, not once a day. (*Everything *in the sky rose and fell once a day; sun, moon and stars.)
The sphere that the Sun is embedded in is at an angle to the rotational axis of the Earth. The perceived warmth of the sun (and thus the seasons) are determined by whether the 20-some-odd degree tilt of the solar sphere made the light hit the Earth more directly or obliquely.
We do well to remember that all motion can be considered relative, so there’s no insurmountable problem in describing the observed motions of every celestial object from a geocentric frame of reference. The value of the heliocentric model lies in how much simpler all the explanations become - no need for angels pushing Mars backward during retrograde motion.
The Earth never rotated in the vast majority of geocentric models. Ptolemy, for instance, had an entirely stationary Earth with everything in the heavens rotating about it once a day or so.
You don’t need angels pushing Mars backward during retrograde motion even in a geocentric frame of reference; as you state, all motion is relative, so even what actually does and doesn’t happen (including the fact that angels aren’t pushing Mars) can be described, and explained, from a geocentric perspective. It just becomes, as you said, easier to describe what happens by switching to a different frame of reference. But it’s not as though one or the other is The True Frame of Reference.
Exactly the same way we do–the length of daylight is determined by the position of the Sun north or south of the celestial equator, and the latitude of the observer.
The only difference was in how the Sun got north or south. We say that the Earth rotates once each day, and revolves around the Sun once per year at an angle of 23.5 degrees relative to the axis of rotation. They said that the Sun revolved around the Earth once per day, and superimposed upon that a secondary revolution, once per year, at an angle of 23.5 degrees relative to the daily revolution.
It might be instructive here to mention the model espoused by Tycho Brahe, one of the great astronomers of history. He recognized the calculative power of the heliocentric models, but was still unwilling to give up the notion of Earth as center. So he put forth a model where the Earth was fixed in place, the Sun goes around the Earth, and then everything else goes around the Sun. I mention this because, to this day, it’s still impossible to disprove Tycho’s model: We reject it solely because it’s more complicated than it need be, and not at all on the basis of evidence. Every measurement one could make in Tycho’s model would give the same result as if it were made in a true heliocentric one.
I’m totally ignorant here, but is Tycho’s model not mathematically equivalent to the now standard one? Is there actually a possibility of falsifying the one in preference to the other?
Acceleration is not relative. You could show the spinning of the earth itself pretty easily (with nothing more than a ball on a string), showing its orbit may be harder, but you could use a pendulum for that too.
Admittedly the finer details of using complex math to avoid the obvious is not my strength, but I seem to recall one attempt, the use of lots and lots of epicycles to explain away the excentricities of planet orbits, failed.
Obviously the Tychonian gravity of Earth would be different from that of the Sun and the planets, or their masses would have to be different or something, but could one really assemble such a theory in a way that explained not only Sun, Moon, Planets and Earth orbits, but also the orbits of Pioneer 10, Cassini, SOHO, Giotto etc.?
No, epicycles do work, provided that you have enough of them. Again, it’s a problem of complication. When thousands of epicycles can do the same job as three or four general physical laws, one prefers the three or four laws.
It’s in the nature of physics that little errors always continue to crop up. All any physical theory can ever do is make approximations. Now, we’ve come up with some pretty good approximations with our theories now, such that the errors which crop up are very small indeed, but they’re still there. And it would take a great many epicycles to get the errors down as small as we’ve been able to get them, but it would be possible.