explain xkcd - User contributions [en]

3181: Jumping Frog Radius

2026-05-11T23:29:06Z

Ozchess: removed sinkhole, grammar fix

{{comic
| number = 3181
| date = December 15, 2025
| title = Jumping Frog Radius
| image = jumping_frog_radius_2x.png
| imagesize = 339x243px
| noexpand = true
| titletext = Earth's r_jf is approximately 1.5 light-days, leading to general relativity's successful prediction that all the frogs in the Solar System should be found collected on the surface of the Earth.
}}

==Explanation==

The {{w|Schwarzschild radius}} is essentially the size of a {{w|black hole}} -- the maximum distance from the center where gravity is so strong that light can't escape. It is part of a solution to {{w|Einstein's field equations}}. It is usually calculated as
:''r''s = (2*''G*M'') / ''c''2
where ''G'' is the {{w|gravitational constant}}, ''M'' is the mass of the object, and ''c'' is the {{w|speed of light}}.
If ''M'' were the mass of the {{w|Earth}}, it would give the Schwarzschild radius for the Earth, which is about 9 mm. (If all of Earth's mass were compressed into a sphere of a bit less than 2 cm in diameter, it would become a black hole.)

The comic suggests a "more useful" radius: the ''Jumping Frog radius'' ''r''jf, which is the size of a "planet" such that its gravity keeps a champion {{w|Frog jumping contest|jumping frog}} from being able to achieve {{w|escape velocity}}. Thus [[Randall]] has instead of ''c'', the 299,792,458 m/s speed of light, used a much smaller value of 4.5 m/s, to represent the maximum speed of a jumping frog. It is possible that Randall got that value from [https://www.researchgate.net/publication/5661154_Explosive_Jumping_Extreme_Morphological_and_Physiological_Specializations_of_Australian_Rocket_Frogs_Litoria_nasuta this paper], which on page 179 puts an upper limit on the maximum velocity of adult Australian {{w|striped rocket frog}}s at 4.52 m/s. (The frog is shown making a "ribbit" sound, which is made by {{w|Pacific tree frog}}s and their relatives in North America and not by rocket frogs, but it's [https://www.imdb.com/list/ls052470723/ widely attributed to frogs all over the world].)

The drawing to the right of the formula shows a planet with exactly the radius ''r''jf. Thus the frog can jump really high compared to the planet's size (in this case about as high as the planet's radius), before it falls back down. This implies that the frog is jumping at somewhat less than the 4.5 m/s needed to escape.

The title text points out that the ''r''jf of the Earth is about 1.5 light days, which is about 7 times the distance to {{w|Pluto}} (compare to the 9 mm Schwarzschild radius). Since Earth's radius is much smaller than this, no frogs will be able to escape, so all frogs that stray into Earth's gravitational well would collect here on Earth. As far as we know, all the frogs in the Solar System are on Earth{{Citation needed}}, so the data apparently matches the theory. However, the reasoning is incorrect, as many other astronomical bodies in our solar system also have ''r''jf greater than their physical radius. If a frog were to be on any of those other bodies, they wouldn't be able to jump away to fall to Earth. Furthermore, five Solar System bodies (the Sun and the four giant planets) have gravity wells greater than Earth's, and therefore larger ''r''jf and greater ability to collect any frogs hopping around in interplanetary space. A flawed argument neither supports nor refutes the conclusion, although it is true as far as we know that all frogs in the solar system do live on Earth. Earth's ''r''jf exceeding its physical radius does accurately explain why, after evolving on Earth, no frogs have jumped to other celestial objects.

If you were to take a frog off the earth and put it in a tiny frog space suit, which somehow did not unduly inhibit its movement, it could jump off any number of the smaller bodies in the solar system. However, few of these bodies are small/low-mass enough for a frog to escape them, ''and'' large enough and close enough for us to observe them and accurately estimate their escape velocities. (The diameter of asteroid {{w|4942 Munroe}} is known to be about 3.45 km, but its shape and mass are unknown. Its surface has an [https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=2004942 exceptionally high albedo of 0.936], which suggests that the surface is mostly some kind of ice. If we assume that asteroid Munroe is spherical and entirely composed of water ice, with a density close to 1 g/cm3, its mass is 2.16 × 1010 kg, and its escape velocity is 0.041 m/s. If instead it's a solid sphere of meteoric iron/nickel with a density of about 8 g/cm3, its mass is 1.72 × 1011 kg, and its escape velocity is 0.115 m/s. In either case, Space Frog would have no trouble jumping away from Munroe.) Some examples:

{| class="wikitable"
!Celestial Body!!Escape Velocity (m/s)!!Frog Escape?!!Notes
|-
|Deimos||5.6||X||The smaller of Mars's two moons
|-
|Ersa||ca. 1||✓||Minor moon of Jupiter
|-
|Halley's Comet||ca. 2||✓||Notable comet, orbiting the sun every 76 years
|}

==Transcript==
:[The panel shows a large formula to the left and a small drawing to the right. The formula's right side is drawn above and below the division line:]
:''r''jf = 2''GM'' / (4.5 m/s)2

:[The drawing to the right shows a very small planet with the radius indicated with a labeled dotted arrow pointing from the center straight up to the edge of the planet. A frog is shown jumping on the surface. This is indicated with a parabolic dotted line going from a frog sitting on the surface near the top of the planet, up to the frog shown soaring through the air with its limbs stretched out about as high above the surface as the planet's radius. At this point the frog is making a sound. Then the dotted line goes down to about a quarter of the way around the planet where the frog lands making a noise, with lines around the frog representing the impact.]
:Arrow label: ''r''jf
:Frog: Ribbit
:Landing: Plop

:[Caption below the panel:]
:More practically useful than the Schwarzschild radius, the '''''Jumping Frog Radius''''' is the radius at which an object's gravitational pull is so strong that even a champion jumping frog can't escape.

{{comic discussion}}<noinclude>
[[Category:Physics]]
[[Category:Astronomy]]
[[Category:Animals]]
[[Category:Geometry]]
[[Category:Math]]
[[Category:Pages with broken file links]]

1919: Interstellar Asteroid

2026-05-11T03:28:23Z

Ozchess:

{{comic
| number = 1919
| date = November 22, 2017
| title = Interstellar Asteroid
| image = interstellar_asteroid.png
| titletext = Every time we detect an asteroid from outside the Solar System, we should immediately launch a mission to fling one of our asteroids back in the direction it came from.
}}

==Explanation==
{{w|ʻOumuamua}} is the first detection of an [https://www.nasa.gov/planetarydefense/faq/interstellar interstellar asteroid] passing through the Solar System originating from another solar system.

[[Megan]]'s list of objects with a similar shape ratio:
* The 1:4:9 {{w|Monolith (Space Odyssey)|monolith}} from the sci-fi movie ''{{w|2001:_A_Space_Odyssey_(film)|2001: A Space Odyssey}}''.
* A {{w|Star Destroyer}}, a spaceship in the ''{{w|Star Wars}}'' universe. This one seems particularly unlikely, as the Star Wars mythos is set a long time ago in a galaxy far, far away, and rarely (if ever, depending on the continuity) strays outside of said galaxy.
* Huge eggplant emoji (🍆, U+1F346 Aubergine, commonly used to represent a penis).
* Statue of {{w|"Weird Al" Yankovic}}, an American singer and parodist.
* iPhone XXXXX, likely making fun of Apple's {{w|iPhone X}} and larger in size. Multiple X's generally have a sexual connotation (see [[1571: Car Model Names]]). It could also refer to adding Xs to an acronym like XXL (extra-extra large).
* [http://voltron.wikia.com/wiki/Voltron_(Voltron_Force) Voltron], a giant robot from the animated series ''{{w|Voltron|Voltron: Defender of the Universe}}''.
* A giant {{tvtropes|BurialInSpace|space coffin}} with someone inside.

As soon as Megan lists off the last item, she is about to start speculating within her own speculative scenario about who or what might be in the coffin before Cueball interrupts her. Cueball attempts to bring Megan back down to earth by reminding her that she has too little data to work with (one data point), but Megan is far too excitable to listen to reason. A good example of the dangers of speculating irresponsibly, it would seem.

It could also be argued that Megan with this makes fun of many news outlets whose first reaction to a new space body often seems to be to search for something to compare its shape to, such as with the [https://en.wikipedia.org/wiki/67P/Churyumov–Gerasimenko#Shape 'rubber duck' comet]. Making fun of media covering science news is a recurring theme on xkcd.

The title text suggests taking reciprocal action by sending asteroids away when the solar system receives them. This would, of course, be difficult, given the amount of energy needed to shift asteroids outside of the Sun's gravity hold. On top of that, it appears to imply that some non-human entity is sending these rocks, which is an inane idea. This could be a reference to the movie {{w|Starship Troopers (film)|Starship Troopers}}, where a race of aliens mankind is at war with supposedly hit Earth with asteroids. Given that a typical interstellar traveler -- like the one spotted now in real life -- spends millions of years getting from one star system to another, the movie's idea is plain stupid; in fact, the movie gives no proof the aliens were actually responsible, leading to a common fan theory that the asteroid was indeed random space junk and the aliens are being framed by the human government as pretense for war.

==Transcript==
:[Megan walks towards Cueball while looking at her phone. Cueball sits in front of his laptop.]
:Megan: Hey, you know that asteroid that tumbled past from another star system? It's apparently really long and skinny.
:Megan: Like a ratio of 6:1 or 10:1.
:Cueball: Weird. Wonder what it's shaped like.

:[Megan lowers her phone and looks up. Cueball looks backward.]
:Megan: Without more data, it would be irresponsible to speculate further.
:Cueball: So...you're going to?
:Megan: ''Absolutely.''

:[Frameless panel focusing on Megan.]
:Megan: Here are some objects with a similar shape ratio:
:Megan: The 1:4:9 monolith from ''2001: A Space Odyssey''.
:Megan: A star destroyer.
:Megan: A huge eggplant emoji.

:[Same setting with Megan and Cueball.]
:Megan: A statue of Weird Al. An iPhone XXXXX. Voltron.
:Megan: A giant space coffin. But who could be inside? We can only guess. I'll start:
:Cueball: This is all based on ''how'' many data points, again?
:Megan: One. But it's a ''perfect'' fit!

{{comic discussion}}

[[Category: Comics featuring Megan]]
[[Category: Comics featuring Cueball]]
[[Category:Star Wars]]
[[Category:Astronomy]]
[[Category:Emoji]]

3192: Planetary Alignment

2026-05-09T18:30:45Z

Ozchess: /* Explanation */

{{comic
| number = 3192
| date = January 9, 2026
| title = Planetary Alignment
| image = planetary_alignment_2x.png
| imagesize = 740x327px
| noexpand = true
| titletext = We're going to need to modify the surface to mount it on the test stand. Which ocean basin do you like the least?
}}

==Explanation==
This is the third in a [[:Category:Home Inspections|series of comics]] about [[Ponytail]] inspecting Earth as if it were the client [[Cueball]]'s house.

[[Ponytail]] (presumably a planetary mechanic, which is not a real thing{{citation needed}}) appears to have been inspecting a planet, which seems to be the Earth, as if it were a vehicle. She is informing [[Cueball]] of the results, as if he were the owner of the planet.

According to her, the planet needs to be re-aligned, as the {{w|Earth's magnetic field|magnetic}} and {{w|Earth's rotation|rotational}} axes of the planet are 400 miles (640 km) offset from each other. She claims that this could create a number of problems with the planet, such as unbalanced magnetic fields. This is presented in the same casual manner as a car mechanic might regarding {{w|wheel alignment}}, or perhaps even the {{w|tire balance}}. Earth's magnetic alignment does change (both {{w|Geomagnetic pole#Movement|gradually drifting}} and {{w|Geomagnetic reversal|relatively sudden reversals}}), but not for any reasons that can be compared to typical vehicle maintenance issues.

Ponytail mentions radiation anomalies over the South Atlantic ocean. This is a real phenomenon, known as the {{w|South Atlantic Anomaly}}, where satellites experience increased malfunctions because solar radiation is higher than average, due to the alignment of the magnetic field, as well as {{w|Large low-shear-velocity provinces|a massive rock structure underneath Africa}}.

In the final panel, Ponytail says that they will provide a loaner planet while Earth is in the shop. This is typically done with vehicles, not planets,{{Citation needed}} but perhaps this particular shop has a [https://www.clivebanks.co.uk/THHGTTG/THHGTTGradio3.htm very large back room]. Ponytail then asks if a gas giant is okay, as they are out of solid surface planets. This is likely alluding to the practice of car dealerships offering replacements or loaner vehicles that are very different from those brought in for service, which can greatly frustrate and inconvenience the customer.

The title text continues the mechanic metaphor, stating that they (the shop) will have to modify Earth to fit it on the test stand, asking Cueball which ocean basin he likes the least, implying that they intend to remove or alter one of the Earth's oceans to mount it for adjustment and retesting.

This is the second comic in recent history with the word "Alignment" in the title, with [[3177: Chessboard Alignment]] being the first.

==Transcript==
:[Ponytail is approaching from off-screen, holding a clipboard and some sort of handheld apparatus. She is talking to Cueball, standing to the right.]
:Ponytail: The inspection revealed a few problems.
:Ponytail: Looks like your planet needs an alignment.
:Cueball: Oh?

:[Close up of Ponytail.]
:Ponytail: Yeah, your magnetic axis is 400 miles off-center from your rotational one.
:Cueball (off-panel): Is that bad?

:[The view zooms back out, showing Ponytail holding her equipment, with Cueball holding a hand to his face, as if thinking.]
:Ponytail: The unbalanced magnetic field could cause radiation anomalies over the South Atlantic. Have you noticed any spacecraft equipment failures in that area?
:Cueball: There '''''have''''' been a few, actually.

:[The final panel shows the same as the third, apart from Cueball's gestures.]
:Ponytail: We can give you a loaner while yours is in the shop. Is a gas giant OK?
:Cueball: I'd '''''really''''' prefer a solid surface.
:Ponytail: Sorry, it's all we have. But it'll just be for a few days.

{{comic discussion}}
<noinclude>

[[Category:Comics featuring Ponytail]]
[[Category:Comics featuring Cueball]]
[[Category:Geology]]
[[Category:Physics]]
[[Category:Astronomy]]
[[Category:Space]]
[[Category:Home Inspections]]

3242: Aperiodic Table

2026-05-07T15:01:18Z

Ozchess: /* Explanation */ We don't need this line; there's a category for it

{{comic
| number = 3242
| date = May 6, 2026
| title = Aperiodic Table
| image = aperiodic_table_2x.png
| imagesize = 740x464px
| noexpand = true
| titletext = Scientists occasionally invent alternative periodic table layouts, which is usually a sign that they don't have enough enrichment in their enclosures.
}}

==Explanation==
{{incomplete|This page was created APERIODICALLY. Don't remove this notice too soon.}}
The {{w|periodic table of the elements}} is a diagram often used to show the properties of the {{w|chemical elements}} that make up the world. Its structure represents several properties of the elements. For example: all elements in a single column will have similar chemical properties; their atoms increase in size going top to bottom; atoms of elements in a given row decrease in size going left to right, with only a few exceptions; there are similar trends in their tendency to gain or lose electrons, and other properties. Elements in a given row increase in the charge of their nuclei going left to right, but that's essentially by definition: they're ordered by atomic number, which is the same as their nuclear charge.

[[Randall]] spoofs this concept by creating a similar view that is much less useful. The original table is "periodic" because it has consistent, repeating patterns that are represented by the horizontal position of the elements. Randall's 'table' is "aperiodic", meaning it has no consistent, repeating patterns. Instead, it is just a meandering line ordered by {{w|atomic number}}. To fit into a compact space, the sequence snakes back and forth and (roughly) down the page. This presentation is not actually helpful{{cn}}, since it contains little information other than the atomic number of each element. Faint colouring on each box does show its category, but due to the dull colours that is also quite inconvenient to use, and depicts this information in an unnecessarily unhelpful and hard-to-read format.

The title text makes fun of scientists being cooped up in their labs by comparing them to animals kept in enclosures, suggesting that their creation of {{w|Types of periodic tables|alternative periodic table layouts}} is a result of a lack of enrichment activities to keep them occupied and satisfied in their lab. Researcher enclosure enrichment was previously mentioned in [[3052: Archive Request]]. The way the way the question is worded interestingly enough starts by seeming to imply the common thought that people aren't working enough, then revealing the 'human zoo' explanation.

==Transcript==
{{incomplete transcript|Don't remove this notice too soon. All 118 elemenmts and their number should be included in a full transcript.}}

:The Aperiodic Table of the Elements
:[Rectangles showing the atomic symbols and atomic numbers from H (1) through Og (118) are arranged in a serpentine chain. Each rectangle has the atomic number in small numerals at the upper left and the atomic symbol in large letters. The color of each rectangle matches the the pattern of a standard periodic table. For example, the noble elements all have a red background.]

{{comic discussion}}<noinclude>

[[Category:Comics with color]]
[[Category:Periodic table]]
[[Category:Chemistry]]

3242: Aperiodic Table

2026-05-07T04:18:49Z

Ozchess:

{{comic
| number = 3242
| date = May 6, 2026
| title = Aperiodic Table
| image = aperiodic_table_2x.png
| imagesize = 740x464px
| noexpand = true
| titletext = Scientists occasionally invent alternative periodic table layouts, which is usually a sign that they don't have enough enrichment in their enclosures.
}}

==Explanation==
{{incomplete|This page was created APERIODICALLY. Don't remove this notice too soon.}}
The {{w|Periodic Table of the Elements}} is a diagram often used to show the properties of the elements that make up the world. Its structure represents several properties of the elements- for example, all elements in a single column will have similar chemical properties, and their atoms increase in size going top to bottom. Atoms of elements in a given row decrease in size going left to right, with only a few exceptions, and there are similar trends in their tendency to gain or lose electrons, and other properties. Elements in a given row increase in the charge of their nuclei going left to right, but that's essentially by definition: they're ordered by atomic number, which is the same as their nuclear charge.

Randall spoofs this concept by creating a similar diagram that is much less useful. The original table is "periodic" because it has consistent, repeating patterns that are represented by the horizontal position of the elements. Randall's table is "aperiodic", meaning it has no consistent, repeating patterns. Instead, it is just a line in order by {{w|atomic number}}. To fit in the same space as a normal periodic table, the sequence snakes back and forth and down the page in a space-filling manner. The diagram is not actually helpful, since it contains next-to-no information other than the atomic number of each element, plus faint colouring on each box to show its category, though due to the dull colours that is also quite inconvenient to use, and it depicts this information in an unnecessarily unhelpful and hard-to-read format.

Chemistry and the periodic table is a periodic theme on xkcd, with there being many comics featuring humorous variations and "fixes" of it, such as [[2639: Periodic Table Changes]] and [[2975: Classical Periodic Table]].

The title text refers to {{w|Types of periodic tables|alternative periodic table layouts}}. Enclosure enrichment was previously mentioned in [[3052: Archive Request]].

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}

:The Aperiodic Table of the Elements
:[Rectangles showing the atomic symbols and atomic numbers from H (1) through Og (118) are arranged in a serpentine chain. Each rectangle has the atomic number in small numerals at the upper left and the atomic symbol in large letters. The color of each rectangle matches the the pattern of a standard periodic table. For example, the noble elements all have a red background.]

{{comic discussion}}<noinclude>

[[Category:Chemistry]]
[[Category:Periodic table]]
[[Category:Comics with color]]

3176: Inverted Catenaries

2026-05-06T15:04:47Z

Ozchess: /* Transcript */ it's an analog to snow; where do trees come in?

{{comic
| number = 3176
| date = December 3, 2025
| title = Inverted Catenaries
| image = inverted_catenaries_2x.png
| imagesize = 317x317px
| noexpand = true
| titletext = Some tires are marketed as 'all-shape tires,' but if driven in a climate with both inverted catenary falls and triangle falls, they wear out really fast.
}}

==Explanation==
During the winter, in snowy / icy areas, people may replace their car's summer or all-season tires with {{w|Snow tires}} made specifically for the cold environment. In this comic, instead of snow, rounded shapes called inverted {{w|Catenary|catenary curves}} fall from the skies. On a plane covered in inverted catenaries all the same size, square wheels whose side length matches the arc length of the catenary [https://mathtourist.blogspot.com/2011/05/riding-on-square-wheels.html are capable of rolling smoothly], contrary to how they would act on a normal road. People have made real tracks demonstrating this. Regular wheels would cause a significantly bumpier ride on this terrain, so Cueball plans to swap them out with {{w|square wheel}}s to better suit the season.

Note, however, that this assumes the catenaries are arranged periodically with no spacing between them, fully cover the surface, and are consistent in shape and orientation. The orientation would also restrict the direction of travel, effectively meaning your vehicle would be traveling on rails. Changes in direction could be managed using catenaries whose arc length was consistent but whose segment length varied, with the variations in vertical size being accommodated by vehicles' suspension systems. Letting the direction changes be controlled by drivers (e.g. branching roads) would require complex 3D road surface shapes.

The title text mentions all-shape tires (as a play on all-season tires), which are advertised to supposedly fit any shape road. However, different shapes would require very different wheels; for example, falling triangles would form a sawtooth road, for which one would optimally use wheels pasted together from pieces of an equiangular spiral. The all-shape tire is said to wear out very quickly like low quality all-season tires used to. (The best modern all-season tires perform better than the average winter tire and have a 62k mile warranty.)

The comic might be a comment on the aforementioned experiments. While mathematically interesting and a good example of experimental mathematics (see [[3180]]) the "real life" applications of this are rather... limited. At least in this literal form.

==Transcript==
{{incomplete transcript|Don't remove this notice too soon.}}
:[Megan and Cueball are walking together as inverted catenary curves fall from the sky. A few have landed in a regular formation, all flat-side down and evenly spaced, with some touching each other.]
:Cueball: Oh wow, the first inverted catenary fall of the year!
:Cueball: Time to swap out my all-season tires for square ones.

{{comic discussion}}<noinclude>
[[Category:Weather]]
[[Category:Geometry]]
[[Category:Comics featuring Cueball]]
[[Category:Comics featuring Megan]]