2707: Astronomy Numbers

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Astronomy Numbers

Title text: I adopted a cat that weighs 12 solar masses. Laser pointers love chasing it.

Explanation

Space is big ^{[citation needed]}, to the point that it regularly defies our earthly notions of scale. As a result, most quantities in astronomy have huge scales beyond anything that humans regularly experience or measure. (In fact, the word "astronomical" is sometimes used colloquially to describe any extremely large quantity).

For example, Earth has a mass 10²³ times more than the average human, and the Sun is 10⁵ times more than that, which itself is 10¹² times less massive than the Milky Way. The same applies to speeds, distances, and time, which can often be measured in terms of light speed, light-years, and millions or billions of years. Because of this, it's a truly unusual occurrence for anything in space to end up in the fairly narrow range of scales of mass, size, speed, or time that humans can easily grasp.

Ponytail, a scientist researching something related to Earth's orbit, finds that on a particular date, Earth will be approaching the sun at a velocity of 65 miles per hour. To American ears, this is a very normal sounding value speed of a fast-moving vehicle, often used as a speed limit on highways in the US. As Ponytail is accustomed to astronomical values, she is thrown off by this and remarks that she finds it "suspicious" when reasonably human-scaled numbers come up in astronomy.

However, Ponytail seems to take this philosophy to an absurd degree by insisting that all scales should be as incomprehensible as astronomical ones, even those used for human-scale measurements, such as the weight of cats. In the third panel, the vet, Megan, is seemingly used to this problem (perhaps she gets a lot of astronomers, or Ponytail has a hypochondriac cat), so she restates the 12-lb weight of Ponytail's cat in solar masses. Since using this unit yields an incredibly small number, 3×10^-30 (a three preceded by a decimal point and 29 zeroes), it satisfies Ponytail's need for incomprehensibly scaled values. This weight is in fact about 13 lb 2 oz (about 5.5 kilograms), slightly heavier than the initial figure given for the cat, but within rounding error for the single digit of precision that Megan uses. According to 2205: Types of Approximation that rounding error is unusually small for an astronomer, though.

The Earth's orbital velocity around the Sun is far above any normal human scale (around 30 kilometres per second or 108,000 kilometres per hour). However, Earth has a fairly circular orbit around the Sun, so most of this speed ends up being tangential (sideways) rather than radial (towards or away from) the Sun, which is the value relevant for Ponytail's calculations. On January 1 (the date being discussed in the comic), Earth's radial velocity is close to its smallest value because we reach our closest point to the Sun in the first few days of January each year (in 2023, perihelion happens on January 4). Thus, by January 1, the Earth's velocity toward the Sun is nearly zero before it starts travelling away from the Sun again. This is how Ponytail ended up with the "suspiciously" small value of 65 miles per hour.

On the other hand, by April 3, 2023, Earth will be receding from the Sun by almost 500 meters per second or 1800 kilometres per hour, which is a less normal speed for the average person to encounter in everyday life^{[citation needed]}.

65 miles per hour is approximately equal to 105 kilometres per hour, although the even more typical scientific value (in SI derived units) would be 29 meters per second.

The title text makes a joke by reversing the typical cat behaviour of chasing laser pointer dots by envisioning a cat with a mass equivalent to 12 solar masses. The Schwarzschild radius for an object of that mass would be around 36 kilometres, so a cat-sized object of that mass would be a black hole, and would therefore bend all nearby light (including that from the laser) inwards towards its singularity. But then it should also draw in the physical laser pointer device itself if it is neither very far away nor in orbit.

An alternative explanation to the title text is that such a large cat would be incredibly alarming and would draw attention from law enforcement agencies, who would aim their guns (and consequently laser pointers) at the cat.

Transcript

[Ponytail is standing in front of a whiteboard writing on it with a pen, while Cueball looks over her shoulder from behind her. On the board is an almost circular ellipse with a cross that centers on a dot towards the left side of it. On the right side there is a small circle on the ellipse's line. There are several lines of wiggles representing unreadable text. To the left of the ellipse there are two lines near the top of and four near at the bottom of the ellipse. Ponytail is writing a fifth line below these almost under the ellipse. At the bottom to the left there is a rectangular frame with a line of text beneath it and at the bottom left corner there is a line forming a half closed rectangle around two dots.]

Ponytail: …And we need to correct for our elliptical orbit. On January 1^st, Earth will be approaching the sun at a rate of ...let's see...

Ponytail: 65 miles per hour.

Ponytail: Weird. Okay.

Cueball: Weird?

[Ponytail has turned towards Cueball, the pen is no longer in her hand and the white board is no longer shown.]

Ponytail: I get suspicious whenever I see a normal number in astronomy. We're not supposed to have those. Feels wrong.

Ponytail: Scales should all be incomprehensible.

[Across the top of the next panel there is a label:]

Earlier, at the vet:

[Megan in a lab-coat raises her hand palm up towards an animal carrier cage standing on her desk. The cage has a handle and five air holes are at the top. Behind two of them something black inside the cage can be seen. Ponytail is standing on the other side of the desk looking at Megan.]

Megan: Your cat weighs 12 lbs.

Ponytail: Ridiculous, nothing weighs "12". You must mean 10^-20? Or 10⁴⁰?

Megan: Fine. Your cat weighs 3x10^-30 solar masses.

Ponytail: Okay. Better.

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Discussion

First time I've ever seen a completely blank page. IJustWantToEditStuff (talk) 20:27, 5 December 2022 (UTC)

Everyone's enthralled by ChatGPT. 172.69.22.35 04:01, 6 December 2022 (UTC)

It's also notable that something weighting 12 solar masses will collapse into black hole on it's own, unless it resist collapse through thermal pressure like stars. -- Hkmaly (talk) 21:26, 5 December 2022 (UTC)

But not cats, because cats have hair, and black holes have no hair. 172.71.186.94 18:06, 6 December 2022 (UTC)

The Earth moves relative to the sun at 66,000 MPH. In what frame of reference is it 65 MPH? It isn't like Randall to get a number wrong. Maybe the magnitude of the distance from Earth to Sun changes at a closer rate, but even this is nearly 180 MPH if I'm calculating correctly. Mannerisky (talk) 21:37, 5 December 2022 (UTC)

You're thinking orbital speed, she's talking orbital oscillation. That is, the speed at which the distance between earth and sun changes. 198.41.242.240 21:51, 5 December 2022 (UTC) ADDITION: Orbital oscillation has both a mean/average factor and a current factor (which is at it slowest while at the apsides, and given the context the one being calculated) 198.41.242.85 22:46, 5 December 2022 (UTC)

I get the sense that the thing that they're planning for January 1st is a precisely-timed new year's party and nothing to do with space exploration. -- 172.71.242.156 (talk) (please sign your comments with ~~~~)

Obligatory ChatGPT explanation

Me: The following is a transcript from the latest xkcd comic. Please write an explanation of the comic: [transcript copied verbatim from its current state omitted]

ChatGPT: In the xkcd comic, Ponytail and Cueball are discussing Earth's orbit around the sun. Ponytail notes that Earth will be approaching the sun at a rate of 65 miles per hour on January 1st. Cueball responds, "Weird?" Ponytail explains that they usually see only complex and incomprehensible numbers in astronomy, and seeing a "normal" number like 65 miles per hour feels wrong to them. This reflects the common perception that numbers in the sciences, especially astronomy, are often complex and difficult to understand. Earlier in the comic, Ponytail also expresses skepticism at a "normal" number when Megan in coat tells them that their cat weighs 12 lbs. Ponytail suggests that it must actually weigh either 10-20 or 1040 instead. Megan responds by saying that the cat's weight is actually 3x10-30 solar masses, which Ponytail finds more acceptable.

I wish superscipts would survive copy-paste, but I have to admit it's better than the esoterica-laden verbosity that's up now.

Superscripts? You could have easily added the ^{^whatever} to your copypasta. Not much work (much less work than my having to <nowiki> this explanation for you), especially given how much other typing you seem to have done... 172.70.91.58 10:56, 6 December 2022 (UTC)

I'm not sure you understand. I only typed the 14-20 word prompt prefix. The explanations above and below were generated by ChatGPT. 172.71.154.158 18:15, 6 December 2022 (UTC)

Okay, WTAF is "ChatGPT" and why would there be anything obligatory about it, and why did someone above think that people were busy with him/her/it? This seems very out of the blue, first time seeing that username, never mind mentioned... NiceGuy1 (talk) 04:55, 10 December 2022 (UTC)

[Take two, using the prompt prefix, "The following is the wikitext transcript from the latest xkcd comic. Please write an explanation of the comic in wikitext. The title text should be explained in a seperate paragraph at the end:"

ChatGPT: In the latest xkcd comic, two characters are discussing an elliptical orbit and the rate at which Earth is approaching the sun. One character, Ponytail, is suspicious when she sees a normal number (65 miles per hour) in their calculations and suggests that scales in astronomy should all be incomprehensible. This is a reference to the fact that astronomical numbers are often very large or very small, and can be difficult for non-astronomers to comprehend.

Earlier in the comic, Ponytail is at the vet with her cat, and the vet tells her that the cat weighs 12 lbs. Ponytail finds this ridiculous, as nothing weighs 12. She suggests that the cat must weigh 10^-20 or 10⁴⁰ instead. The vet then tells her that the cat weighs 3x10^-30 solar masses, which Ponytail finds more acceptable.

The title text jokes about adopting a cat that weighs 12 solar masses, which would be extremely large. Laser pointers would love chasing it, as it would be an impressive target.

Meh.]

I propose we create a bot to summarize the transcript with the text-davinci-003 API and paste it into the top of discussion whenever the Transcript is expanded more than 10%. Yays and nays? 172.71.154.39 03:55, 6 December 2022 (UTC)

Yea. Both have a few serious but easily noticed and easily correctable flaws, but both are far better than the borderline-trolling six paragraph wall of text for the simple, silly joke we have at the moment. 172.69.33.245 06:09, 6 December 2022 (UTC)

I'd like to see it with the past dozen recent transcripts before deciding, and would do it myself if work wasn't busting my butt this afternoon. Someone please go for it. 172.70.214.151 20:01, 6 December 2022 (UTC)

I tried just now, but it's hammered to the point of completely unusable, timing out and reporting errors, and then an alert message saying to be patient while they try to scale. I like the idea but I'm skeptical of how it will do on the immediately previous 2706: Bendy and similar very visual gags. 172.69.22.16 17:26, 7 December 2022 (UTC)

...my conclusion after doing a couple is that we're not going to be satisfied automating (at least with the prompt I was using from here) but it's a useful tool for producing simple explanations if operated manually. 172.71.158.217 17:54, 7 December 2022 (UTC)

Why is it as big as 65 mph? Where did the 65 mph figure have come from? A formula? Taking a linear change from minimum velocity (-500 m/s 12 weeks earlier), 4 days before the perihelion gives 86 km/h (53 mph), three days gives just 64 km/h (40 mph). But those are surely too big, since the rate of change of radial velocity would be slowest around perihelion and aphelion. I wouldn't expect the above-calculated rate of change until weeks out from perihelion. 172.68.210.5 08:23, 6 December 2022 (UTC)

Using an ephemeris service, I get 27.6 m/s or 61.8 mph- a bit lower than Randall's record but still in the ballpark. The reason is probably because of the effect of the Moon's orbit on Earth. Of course it's not a huge effect, but when we're working in just a few miles per hour, it definitely has a monthly effect.

I did a rough calculation using the position of the Earth-Moon barycentre, and came up with an average Sun-relative radial speed (unsigned velocity) for the Moon of 26 km/h (16 mph). So yes, that could explain some of it, but I still think the contribution of Earth's orbit would be very small around the perihelion (and aphelion). 172.68.66.114 21:17, 7 December 2022 (UTC)

Surely the really weird thing is an astronomer using non-SI units? 172.70.86.12 09:40, 6 December 2022 (UTC)

Just changed the "weight" of the Earth to the "mass", in the explanation. Apart from anything else, the weight of the Earth standing on a typical human('s feet?) is exactly equal to the weight of a typical human standing on the Earth. And things would be screwy, if not. And don't try to 'weigh' the Earth upon the surface of a duplicate Earth, that invokes a number of Health And Safety violations, at minimum, and the results would be questionable. 172.70.91.58 11:13, 6 December 2022 (UTC)

It would probably invoke a What If? as well.172.70.91.75 09:44, 7 December 2022 (UTC)

I interpreted the title text not as the 12-solar-mass star bending the light from laser pointers, but the laser pointers *themselves* "following" the star because they're close enough to it to orbit said star (or at least, on hyperbolic trajectories influenced by the star). Trimeta (talk) 16:46, 6 December 2022 (UTC)

This reminds me of how in the Planck system of units the derived unit of momentum has a value of approximately 6.5 kg m/s which is a strangely normal unit. 172.70.206.204 22:35, 6 December 2022 (UTC)

It's derived from the Planck mass, which is an annoyingly large 22 micrograms. I was coming here to point that out. 162.158.79.189 17:06, 7 December 2022 (UTC)

I so expected to see more references to the Hitchhikers Guide to the Galaxy references since the description starts out like a quote from the Guide MK I. WJBodin3 (talk) 01:05, 7 December 2022 (UTC)

I take that as a bonus ref. There really aint any H2G2 links in the comic (aside from the assertion that Space Is Big, which isn't exactly its unique observation). Putting more in would be distracting. (Already, I think it's overguilded, lillywise, but not so much that I'd remove an excess link.) 172.71.178.207 06:44, 7 December 2022 (UTC)

Yeah - you always get problems once the guilds start getting involved. Mind you, Hitchhiker's has been guilded itself.172.70.91.75 09:43, 7 December 2022 (UTC)

(Well, that was an honest typo. I know enough not to type the "u" in "gild", but my fingers clearly did not, or it was a Qwerty-crosskey. Still, it provoked a funny and intelligent response.) 172.71.178.207 15:28, 7 December 2022 (UTC)

Ponytail gets religion

Clearly, Ponytail is a Saganist. 172.70.163.47 11:12, 2 November 2024 (UTC)