Wikipedia:Reference desk/Archives/Science/2021 August 31

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August 31

Why do historians believe planets revolve around Earth?

What made them to believe like that? What mathematical formulation did they follow to prove that? Rizosome (talk) 05:59, 31 August 2021 (UTC)

They didn't use any math. They simply believed that where they were (the earth) was the center of everything. See Geocentric model. ←Baseball Bugs ^{What's up, Doc?} carrots→ 06:41, 31 August 2021 (UTC)

"They" used a lot of math, "they" being the Ancient Greeks (as summarised in the Almagest of Ptolemy) and the Christian and Islamic scholars who followed them (I'm a bit puzzled by what "historians" is supposed to mean, "historic people" or something?). The most important idea in the mathematical description were epicycles. --Wrongfilter (talk) 07:01, 31 August 2021 (UTC)

Yes, they used math after-the-fact, to rationalize their ancient and flawed model, which was based strictly on belief. Presumably the OP should have said "did" rather than "do". Or something like that. And it was religious authorities, more than historians, who promoted this belief, to the point where anyone who questioned it was branded a heretic. Anyway, the article lists the two main observations on which their belief was based. And for routine day-to-day life, those geocentric observations work fine. The sun appears to rise and set every day. The stars appear to revolve slowly around us through the year. And the apparent retrograde motion of the planets is just a curiosity. ←Baseball Bugs ^{What's up, Doc?} carrots→ 07:23, 31 August 2021 (UTC)

Speaking of religious authorities...Galileo Galilei died in 1642. Finally, in 1992, Pope John Paul II admitted that the Church had made an error, by accusing him of heresy. Only took 350 years! Tribe of Tiger ^{Let's Purrfect!} 19:45, 2 September 2021 (UTC)

Given their naive assumption that the Earth was a flat and stationary surface (neither moving nor spinning), the conclusion of the earliest astronomers that the Sun and the planets alike orbited around Earth was based on observation rather than belief – the main belief aspect being that the lights that came up in the east were the same celestial bodies as the ones that had sunk to the west half a day before, and not newly created light sources. The naive assumption was, of course, a belief, but (I think) purely because no thought of any other possibility crossed their collective mind. Aristarchus of Samos (c. 310 – c. 230 BCE) was the first of a few rare exceptions, but his ideas were not well received, and it took another century before the idea took hold among astronomers that the Earth was in fact a globe – while sticking to the geocentric model. Moreover, the belief or assumption was that the "fixed stars" were fixed to a revolving celestial sphere, while the "wandering stars" (the planets) were moving about on or near that sphere. The notion of "proving" any of this mathematically is not appropriate, also not for modern astronomical models. The proof of any theory in the natural sciences is based solely on observation.  --Lambiam 08:43, 31 August 2021 (UTC)

I see your point. The true "belief" is that we can trust what we observe. In the realm of science, theories can change when new observations come along. When theocrats and other politicians get involved, it interferes with the scientific process. (That is not exactly a news flash!) ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:56, 31 August 2021 (UTC)

• Counterpoint: planets do revolve around Earth. In the geocentric celestial reference system, that is. Why do you think they do not? What mathematical formulation lead you to the belief that planets revolve around the Sun?

(OK, ellipses are cleaner than pericycles, but once you have Newton’s laws and the formulae for non-inertial reference frames, you can do the calculations just fine.) Tigraan^{Click here for my talk page ("private" contact)} 08:31, 31 August 2021 (UTC)

Why are you muddying the waters? Imagine the effort needed to reconcile this model with the theory of relativity. I doubt you can do the calculations "just fine".  --Lambiam 08:50, 31 August 2021 (UTC)

Calculations in non-inertial reference frames is fairly basic. I studied it towards the end of my first year of physics bachelor. The second paragraph of the lead of Coriolis force is a good plain-language explanation; if you want an exercise in checking that the results are consistent with the inertial frame calculation, I found this textbook in about ten seconds of search.

At any rate, I would not call it a "model" when it really is pure math, just like using cartesian or polar coordinates to describe the equations of motion (one is probably easier than the other depending on what problem you want to solve).

On the other hand, involving relativity, Lorentz transformations etc. for stuff that can be well-approximated by classical mechanics does muddy the waters quite a lot, both as a matter of physical hypotheses and as a matter of calculations to work through. Tigraan^{Click here for my talk page ("private" contact)} 15:11, 31 August 2021 (UTC)

I used "model" in the sense of "mathematical model", a description of a real-world system in the form of a collection of mathematical formulas. And I invoked relativity because in that model the speed of material objects can routinely exceed 300,000 km/s, while the speed of light is not constant. But also without invoking relativity, it violates the most basic forms of symmetry, such as the translational invariance of the laws of physics.  --Lambiam 21:05, 31 August 2021 (UTC)

Any particular reference frame is feasible to use, given the amount of mathematics your willing to do to transform measurements in one frame to another. Which reference frames are useful is a different story, and for many reasons, the heliocentric model works well for most applications for anyone who isn't interested in pursuing an advanced physics degree "I learned it in my first year in my physics bachelors" already puts it out of range of 99.99% of the human population, but other simpler models are both a) easier for everyone else to understand and b) correct enough for them to use. --Jayron32 17:33, 31 August 2021 (UTC)

[un-indent] Actually, there was a seemingly good reason why they concluded that the earth was at the center of the universe: their reasoning was that if the earth moved relative to the "fixed stars", then they would likewise seem to move from their places from one night to the next, and since this was decidedly not observed, they concluded that it couldn't possibly be the case! (The reason for their error was, this apparent movement is so tiny -- less than 1 arc second even for the nearest star of all -- that not only is it impossible to see with the naked eye, but even to measure with a mariner's sextant, you need a telescope with at least 60x magnification and high-precision adjusting gear to detect it at all, which was not something available in the ancient world!) 69.181.91.208 (talk) 09:33, 3 September 2021 (UTC)

Distance change between moon and earth per year - strange development

Looking at the numbers given in Lunar distance (astronomy)#Orbital history, the distance between earth and moon has changed per year in the following magnitudes:

Distance	years ago	Distance increase / year (Averagre from then until now)
384.400 km	now	3,8 cm (measured)
383.000 km	80 million years	1.75 cm
332.000 km	2.5 billion years	2.1 cm
24.000 km	4.5 billon years	8 cm

This would mean that the 'speed' of the moon increasing its distance from earth would have gone from some much higher value in the early stages (probably more than 20 cm or maybe even much more) down to ca. 2 cm per year - and has now doubled again within a fairly short time. Does this make sense? Can it be accurate? --KnightMove (talk) 10:43, 31 August 2021 (UTC)

A pretty good bet is that continental drift has changed how ocean tides function over geological timescales, which feeds back into the Moon's recession rate. Lunar distance mentions the current unusual rate and has some links to research papers. 85.76.66.247 (talk) 12:20, 31 August 2021 (UTC)

The tides also get 8 times less powerful for each doubling of distance, they were tsunami height at first. Sagittarian Milky Way (talk) 17:18, 31 August 2021 (UTC)

Well after the first ocean formed. Sagittarian Milky Way (talk) 18:17, 31 August 2021 (UTC)

4.5 billion years ago, there were no oceans with which to have tsunamis, given that a Mars-sized planet had just collided with the Earth. The earliest oceans on Earth would have been no older than 4.28 billion years ago, and a more conservative estimate puts that at no older than 3.8 billion years ago. --Jayron32 17:24, 31 August 2021 (UTC)

I distinctly remember PBS or something saying the tides were still very high when there were already oceans, but yes a big gap in between. Sagittarian Milky Way (talk) 18:17, 31 August 2021 (UTC)

A new model of the formation of the Moon has invoked the presence of a magma ocean at the time of the giant impact, see here. So, after the formation of the Moon there would have been large tides in the magma ocean. Count Iblis (talk) 02:35, 1 September 2021 (UTC)

I have better memories of Blondie's version of the song. --Jayron32 16:03, 1 September 2021 (UTC)