Wikipedia:Reference desk/Archives/Science/2025 August 3

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August 3

philosophy and the planets

I have heard that some early-modern philosopher proved (to his own satisfaction) that there must necessarily be exactly seven planets. Can you name him, or better yet summarize his argument? —Tamfang (talk) 03:07, 3 August 2025 (UTC)[reply]

What kind of philosopher? My first thought was William Herschel, who as an astronomer was a kind of natural philosopher, but his article gives no suggestion that he argued that his newly discovered Uranus absolutely had to be the final planet. Nyttend (talk) 07:06, 3 August 2025 (UTC)[reply]

This was probably about the seven classical planets or a variation of that list. For the longest time there was no reason to even speculate about there being more than these. Still, Johannes Kepler's Mysterium Cosmographicum has an argument of that sort: He equates the orbits of the planets to the Platonic solids. Since there are exactly five of the latter, that limits the number of planetary orbits. Kepler as a heliocentricist replaced the Sun by the Earth in his list of planets and dropped the Moon. There may have been earlier, maybe theological, arguments like that. Thomas Aquinas may have had a thing with the number seven. --Wrongfilter (talk) 07:14, 3 August 2025 (UTC)[reply]

It would not surprise me if Isaac Newton held such a view, but I haven't been able to find a mention of it by a cursory search, so it won't be something he strongly asserted; it's not mentioned in Isaac Newton's occult studies. {The poster formerly known as 87.81.230.195} 90.194.92.162 (talk) 13:37, 3 August 2025 (UTC)[reply]

Recently I was looking at the Burmese eight-day week, Burmese_zodiac#Weekdays, in which eight days are fitted into the space of seven by splitting Wednesday into two. These eight days are mapped to the eight cardinal compass directions, and to the planets, which are counted as eight by including the sun once and the moon twice.  Card Zero  (talk) 17:24, 3 August 2025 (UTC)[reply]

hm, Indian astronomers considered the lunar nodes (the two moving points where its orbit crosses the ecliptic) as two extra planets; perhaps in Burma they were seen as one. —Tamfang (talk) 19:54, 14 August 2025 (UTC)[reply]

See this note: "Hegel and the seven planets".  ​‑‑Lambiam 18:50, 3 August 2025 (UTC)[reply]

And of course we have an article: De Orbitis Planetarum. {The poster formerly known as 87.81.230.195} 90.194.92.162 (talk) 19:11, 3 August 2025 (UTC)[reply]

This story that Hegel's dissertation presented a proof, based on logic, of the absurdity of an eighth planet, is widespread. Having encountered it multiple times, I knew the "early-modern philosopher" of the OP's question was Hegel. A brief section in the article mentioning (and debunking) this myth may be in order.  ​‑‑Lambiam 07:31, 4 August 2025 (UTC)[reply]

Head-on crash tests

Imagine you want to study what happens in a head-on collision between identical vehicles at 100 km/hr. You have two pairs. One pair you accelerate to 50 km/hr, so the closing velocity is 100 km/hr. With the other pair, you accelerate one to 100 km/hr and leave the other sitting there, so the closing velocity is 100 km/hr. Your masses, speeds, and vectors are identical, so the two tests have identical momentums. But are the results likely to be identical or a good bit different? I just wonder if a moving vehicle is likely to behave differently from a stationary vehicle, due to effects from vibrations that will occur only at speed (e.g. oscillation), and the potential that parts might jiggle slightly loose (either when driving or at the start of the impact) and slightly shift positions from before they were first accelerated. Nyttend (talk) 07:03, 3 August 2025 (UTC)[reply]

The result won't be identical. With one car moving, friction with the ground is different, feeding extra energy into the system (in the centre-of-mass frame) after initial contact. There's twice the rotational energy in the wheels, now all concentrated in one car, the total angular momentum of the wheels is different and you get an asymmetry in the gyroscopic effects. For the final result, I expect the difference will be small, as the wheels only represent a small fraction of the car's mass, but I can't rule out this may be the difference between a car spinning away around its vertical axis and a car turning upside down. PiusImpavidus (talk) 08:37, 3 August 2025 (UTC)[reply]

In the first case the net momentum is 0. In the second case it is 100. In the first case the initial ke is 50*50*2, in the second 100*100. Therefore even assuming billiard ball physics the two collisions are not similar. Greglocock (talk) 09:09, 3 August 2025 (UTC)[reply]

Greglocock, I thought kinetic energy was mass times velocity. Now that I read the kinetic energy article, I see that I was wrong. If I'd realised that, I wouldn't have asked this question in the first place. Nyttend (talk) 03:52, 4 August 2025 (UTC)[reply]

Viewed from a reference frame moving with the velocity of the centre of mass of the system, the collisions between a pair of identical balls moving without friction would be indistinguishable.  ​‑‑Lambiam 18:46, 3 August 2025 (UTC)[reply]

Absolutely correct, the best sort of correct. Greglocock (talk) 22:36, 3 August 2025 (UTC)[reply]

This gets posited and debaed often enough we could probably have an article. Searching for car crashing 100 or two crashing at 50 brings up many hits. Here is Mythbusters's take on it. Matt Deres (talk) 01:38, 4 August 2025 (UTC)[reply]

So many of these results, including the Mythbusters, seem to assume car-versus-not-car when we talk about the 100-and-0 collision. Nyttend (talk) 03:52, 4 August 2025 (UTC)[reply]

In a world of spherical cows, that shouldn't be a surprise. Assuming the stationary object is practically immobile and inelastic, like a boulder or brick wall, removes a lot of confounding variables: is the stationary car parked? In gear? Against a curb? Matt Deres (talk) 13:43, 5 August 2025 (UTC)[reply]

A mistake in how our article stress energy tensor defines the first component of the tensor.

The mistake is described on the talk page of that article. Do you agree? HOTmag (talk) 12:46, 3 August 2025 (UTC)[reply]