in geocentric universe motion of the stars is independent of motion of the sun,
Interesting.
Isn't it?
And on heliocentric model, the ratio between a mean solar day and a sidereal day corresponds to one rotation of the Earth around the sun over a year. Which is what we observe.
How does the geocentric model account for this? Coincidence?
If you have no explanation, just say so and I’ll stop asking.
No, this is actually trivial, few years ago i thought i could use this ratio (the difference of one rotation of the Earth around the sun over a year) in favor of geocentricity, and then Alpha2Omega responded with one very entertaining comment :
By simply redefining the length of the day from 24 hours to about 24h 3m 57s, you could achieve that with no need to mess with the rotation period of the Earth or change its orbit. Stars would transit almost 8 minutes earlier each day, and the Sun would transit almost 4 minutes earlier (shifting by about 2° and 1°, respectively each ciklnoon), and there would be 364 cikldays, 365 (now obsolete) solar days, and 366 sidereal days in the year.[nb]Which date should we get rid of? I suggest we remove your birthday from the ciklcalendar; then you'd never have to grow up.[/nb] A real advantage to this is that we could use the same ciklcalendar for three years since common years would be exactly 52 ciklweeks long instead of the current, inconvenient, 52 weeks plus 1 day. While you're at it, you might consider defining the ciklday as 24h 04m 54.851868s and get rid of the need for leap years, too and we could use the same calendar forever. All you have to do is convince the body that oversees civil time to make this little change. It would be kind of inconvenient when the sun transits near midnight, though, so you might find some resistance to the idea.
Accompanying post : https://www.theflatearthsociety.org/forum/index.php?topic=63727.msg1691932#msg1691932
...
Well, it seems that we have to come back to this issue once again!
Alpha said :
By simply redefining the length of the day from 24 hours to about 24h 3m 57s, you could achieve that with no need to mess with the rotation period of the Earth or change its orbit. Stars would transit almost 8 minutes earlier each day, and the Sun would transit almost 4 minutes earlier (shifting by about 2° and 1°, respectively each ciklnoon), and there would be 364 cikldays, 365 (now obsolete) solar days, and 366 sidereal days in the year.[nb]Which date should we get rid of? I suggest we remove your birthday from the ciklcalendar; then you'd never have to grow up.[/nb] A real advantage to this is that we could use the same ciklcalendar for three years since common years would be exactly 52 ciklweeks long instead of the current, inconvenient, 52 weeks plus 1 day. While you're at it, you might consider defining the ciklday as 24h 04m 54.851868s and get rid of the need for leap years, too and we could use the same calendar forever. All you have to do is convince the body that oversees civil time to make this little change. It would be kind of inconvenient when the sun transits near midnight, though, so you might find some resistance to the idea. By simply redefining the length of the day from 24 hours to about 24h 3m 57s???
Alpha, how can you redefine the length of the day from 24 h to about 24 h 3 m 57s, having in mind that one solar day is exactly 24h???
All we are interested about is to pay attention to :
A The Exact length of the sidereal time ("rotational" period of the earth)
B The Exact length of the synodic time (solar day)
Once we determine A and B we have to do this :
365 * 86400 (solar day) = 31 536 000
365 * 86164 (sidereal time) = 31 449 860
31 536 000 - 31 449 860 =
86 140 (24sec less than sidereal time)
Let's say (for the sake of the argument) that rotational period of the Earth were 472 sec less (instead of 236 sec) than one solar day (24 h), then we would have to reckon like this :
365 * 85928 (hypothetical sidereal time) = 31 363 720
31 536 000 - 31 363 720 =
172 280 seconds (48sec less than two sidereal times)
The point is this :
You can't artificially change the length of one solar day because it is determined by the exact time that sun needs to come back to the local meridian!!!So, the difference between one solar year and one sidereal year being almost exactly one sidereal day is far from being just a coincidence, it is not trivial thing after all...
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Let's see how it looks like in Mars' case :
Mars' orbital period : 687 earth days = 59 356 800 seconds
Mars' rotational period : 88 642 seconds
59 356 800 (687 earth's days) : 88 642 =
669,6 rotational periods
Mars's solar day : 88 775 seconds
59 356 800 : 88775 =
668,6 solar days
ONE SOLAR DAY DIFFERENCE?!?!?!?!?
Very interesting!
According to Copernicus : Mars' distance to the sun = 11 110 400 km
According to modern science : Mars' distance to the sun = 228 000 000 km
Tycho obtained precise measurements of the apparent diameters of the fixed stars, determining that a typical first-magnitude star has an apparent diameter of two minutes of arc—one fifteenth the diameter of the Moon or Sun.
In a geocentric universe, fixed stars could lie just beyond Saturn (Figure 2)—a distance of just over 12.5 A.U. Thus
Tycho determined that the physical diameter of the typical first-magnitude star was about 80% that of the Sun—one of the larger bodies in a celestial
assemblage whose smallest member was the Moon and whose largest was the Sun (see Table 1).
But in a Copernican universe, in order for annual parallax to be no more than a minute of arc (just falling under Tycho’s circle of general accuracy, and thus just evading detection),the distance to the fixed stars would have to be almost 7,000 A.U.
Copernicus’s Saturn-to-stars “gap of the largest size” would be over 700 times the Sun-to-distance. And the stars themselves, rather than falling within the size range of the other heavenly bodies, would have to be hundreds of times the diameter of the Sun (see Table 2).
What’s more, said
Tycho, what if the parallax turns out to be smaller than that minute of arc? Then the fixed stars would have to be
still larger.
Such immense stars at such immense distances were absurd. (see Blair 1990, 364; Moesgaard 1972, 51 Brahe 1601, 167)
But according to
Christoph Rothmann (~1555~1600), the German Copernican against whom
Tycho leveled this argument, this was not absurd at all. The Creator need not make Creation conform to our notions of reasonableness (Moesgaard 1972, 52). Said Rothmann —
But as far as I am concerned ... why should it seem untrue for the distance from the Sun to Saturn to be contained so many times between Saturn and the remoteness of the fixed Stars? or what is so absurd about a Star of the third Magnitude having size equal to the whole annual orb? What of this is contrary to divine will, or is impossible by divine Nature, or is inadmissible by infinite Nature? These things must be entirely demonstrated by you, if you will wish to infer from here anything of the absurd. These things which common men see as absurd at first glance are not easily charged with absurdity, for in fact divine Sapience and Majesty is far greater than they understand. Grant the Vastness of the Universe and the Sizes of the stars to be as great as you like —these will still bear no proportion to the infinite Creator. It reckons that the greater the King, so much more greater and larger the palace befitting his Majesty. So how great a palace do you reckon is fitting to GOD? [Brahe 1601, 186; Graney 2012]
Rothmann was not the first Copernican to invoke “palace of God” imagery in regards to the enormous stars demanded by the Copernican theory.
Thomas Digges (1546-1595) of England — one of only perhaps fifteen identifiable Copernicans in Tycho’s time, one of even fewer to write publicly on the theory, and the first to write on it in a vernacular language (Danielson 2006, 232; Wernham 1968, 461) — described the stars in supernatural terms (see Figure 3).
Indeed,
Copernicus himself had spoken of the stars in such terms: “
So vast, without any question, is the divine handiwork of the most excellent Almighty [Copernicus 1543, 133].”
However, Tycho was most unreceptive to the use of God to solve the problem of the bigness of stars.
He asks where in nature — where all things are well-ordered in all ways of time, measure, and weight, and there is nothing empty, nothing irrational, nothing disproportionate or inharmonious —do we see the Will of God acting in an irregular or disorderly manner?
It is true,
Tycho says,
that a finite world can bear no proportion to an infinite Creator, but nature does show proportion and symmetry within itself — and as an example he cites the human body illustrated in the work of the artist
Albrecht Dürer.
There is nothing proportional or harmonious or rational, says Tycho, in the Copernican theory’s so distant stars that so dwarf the Sun(Brahe 1601, 191-2).Despite Tycho’s exhortations, Copernicans continued to connect the bigness of stars to the power of God. Several decades after the German Copernican
Rothmann spoke of gigantic stars using the language of the “palace of God”, and well after the advent of the telescope (Figure 4), the Dutch Copernican
Philips Lansbergen (1561–1632) could be found using the same language in his 1629
Considerations on the Diurnal and Annual Rotation of the Earth, as well as on the
True Image of the Visible Heaven; Wherein the Wonderful Works of God are Displayed.
In this widely read and influential book (the first in Europe whose purpose was popularizing the Copernican theory among a non-mathematical audience),
Lansbergen accepts the immense sizes of the stars, as to him these show the divine nature of the heavens.
He determines the heavens to be threefold, owing to a reference in 2 Corinthians 12:2 to a “third heaven”. The first heaven, says
Lansbergen, is that of the planets. The second is that of the fixed stars. It is immense compared to the planetary heaven; each star is indeed the size of Earth’s orbit (as Tycho had said must be the case if Copernicus was right). The light of those stars illuminates the whole of the second heaven, which is therefore full of immense splendor. The purpose of this immense size and splendor is to indicate God’s infinity to humankind. The heavens,
Lansbergen says, echoing the words of
Digges and
Rothmann before him, are like a fore-court in front of God’s palace. The third heaven, that of God, is to the second heaven of the stars as that second heaven is to the first heaven of the planets (Vermij 2007, 124-5).
Thus when
Giovanni Battista Riccioli (1598- 1671) in his 1651 Almagestum Novum reprised Tycho’s argument on the bigness of the fixed stars — now using precise telescopic measurements of their diameters and maximum annual parallax (see Figure 4), but obtaining essentially the same result: that in a geocentric cosmos the sizes of stars were consistent with the Sun, Earth, and planets, while in a heliocentric cosmos they dwarfed the Sun (Graney 2010b) — he also reprised Tycho’s complaint about how Copernicans answered the star bigness problem.
Since nothing is beyond the power of God the Copernican answer was beyond refute in one sense, but, like Tycho, Riccioli rejected that answer to the star bigness problem, stating that “even if this falsehood cannot be refuted, nevertheless it cannot satisfy the more prudent men” (Graney 2012).