Talk:3181: Jumping Frog Radius

first Qwertyuiopfromdefly (talk) 05:17, 16 December 2025 (UTC)

Question: Would a correct interpretation be "if a champion jumping frog were to be located just under 1.5 light-days from earth, and if there we're no other gravitational bodies nearby, and if said frog then performed its mightiest jump directly away from earth, then the frog would eventually be overcome by Earth's gravitational field and would eventually land on Earth's surface"? Pgn674 (talk) 06:26, 16 December 2025 (UTC)

I guess that is exactly how it should be interpreted. Or more interesting if it was just outside this radius and somehow could gain exactly 4,5 m/s extra speed then it would escape Earth (if there was anything to push of against that was heavy enough to move basically only the frog forward, then that would change the mass behind the frog so... That was why I wrote gain exactly rather than jump). --Kynde (talk) 07:36, 16 December 2025 (UTC)

or its mightiest jump in any direction (that doesn't cause it to crash through the Earth) since the escape speed is the same in all directions (relevant xkcd:https://what-if.xkcd.com/68/ ) --178.197.223.163 09:21, 16 December 2025 (UTC)

The only two variables are rjf and M, so plotting a 2 axis graph plotting the relationship between M and rjf should be possible. Zabadoh (talk) 08:20, 16 December 2025 (UTC) ^{[You sign after your contribution]}

As frogs usually collect on the surface of worlds ^{[citation needed]}, the *surface* escape velocity is most important. The crossover point for a planet with earth-like density (5515 kg/m³) is 2.6km, above that, the rjf falls below the surface, and the planet can accumulate frogs. Smaller bodies are, however, usually less dense; an interesting borderline candidate is Chicxulub, which had an rjf of 3-4km, and a radius of 5-6km so could have just about held onto its frogs, for a while at least. JeffUK (talk) 10:04, 16 December 2025 (UTC)

It would be interesting to look at the R_jf values of a frog, to consider where new limits are put upon the frog for M-masses that aren't totally dominating the scenario of "frog leaves mass"... 82.132.237.93 11:03, 16 December 2025 (UTC)

I interpreted it as a reference to the Mark Twain short story The Celebrated Jumping Frog of Calaveras County. Gustaveeiffel314 (talk) 12:25, 16 December

I also suspected an allusion to Twain's short story, but then I read it at archive.org/details/celebratedjumpin00twai and found no parallels. The earth's radius wasn't the problem, it was 5 pounds of quail shot. That frog didn't land with a "plop" but "as solid as a gob of mud." There is no mention of "champion" in the story. The 1865 population of Calaveras County (post Gold Rush) was down below 15,000. That is, the frog shown in #3181 probably came from somewhere else that really knows how to breed frogs with muscular legs, maybe France. Before I risk overthinking this, I'm going to conclude that #3181 is not a Twain reference. Bismuthfoot (talk) 14:37, 16 December 2025 (UTC)

What's with all that text in the incomplete explanation warning box? It seems like it belongs in the discussion. Barmar (talk) 15:05, 16 December 2025 (UTC)

Erm, the current text has a statement that rjf < 4.5m/s for other planetary bodies. Seems like it is mixing measurements, a radius would be a distance, not a velocity. It might be trying to say that other planetary bodies have an ESCAPE VELOCITY of more than 4.5 m/s, so jumping frogs on the surface of those planetary bodies couldn't get out of that planet's gravity well. ~~ 57.140.32.36 (talk) 15:53, 16 December 2025 (please sign your comments with ~~~~)

Don't recognise your statement (until I check the current state of the main explanation), but a radius can be defined as a vector, as can a velocity. Pretty sure that's not what it says (or should be saying), but there is a possible interchangability if analysed in the 'right' way. 82.132.237.93 17:00, 16 December 2025 (UTC)

(ETA: Nope, can't see where "the current text has a statement that rjf < 4.5m/s for other planetary bodies" - Unless I'm missing some obscure reference to it that you're not!) 82.132.237.93 17:04, 16 December 2025 (UTC)

It might be worth pointing out that frogs found on the surfaces of other planets in our solar system will have other reasons for not being able to jump to escape velocity (eg., they are no longer alive) 2A09:BAC2:6188:123C:0:0:1D1:CF 01:20, 17 December 2025 (UTC)

A frog does not have to be alive to jump, it could be a mechanical one. SDSpivey (talk) 02:44, 17 December 2025 (UTC)

A mechanical frog couldn't be a champion jumping frog though, because only biological frogs are allowed to compete. 76.22.93.146 03:38, 17 December 2025 (UTC)

I disagree with the point about the flawed argument of frogs all being on earth. With a simple assumption that no aliens have transported a frog off world, basic taxonomy says that anything resembling a frog on another planet would infact not be a frog and would be a result of convergent evolution. I also think that aliens moving stuff around is not a common inclusion in physics formulas. So perhaps still falwed but not as strongly flawed as implied in the main text. 2001:14BA:A086:FF00:39D0:B88:A6EF:5F9C 08:28, 17 December 2025 (UTC)

That doesn't negate the point that if a frog was loose in space, it could be trapped in the gravity well of another planet and end up there rather than Earth. The 'theory', in the way it is expressed, contains the hidden implication that frogs start off floating around freely - not on any planet. 82.13.184.33 09:34, 17 December 2025 (UTC)

There's always the theory of Panfrogspawnia... ;) 82.132.238.175 11:59, 17 December 2025 (UTC)

Hmm.. How about frogs taken to the ISS for experimental purposes? Surely there's one or two if those? 2A00:23C8:253C:101:5BC5:789F:56FB:A042 08:42, 17 December 2025 (UTC)

From a general relativity point of view the ISS is not really different from the surface of Earth. In fact if you factor in the Jumping Frog Radius you can redefine the surface of Earth as englobing the orbit of the ISS, as, basically, the "surface of the Earth" is just some stuff jumbled together by gravity, so this technically applies to the ISS as well. 78.241.48.142 11:06, 17 December 2025 (UTC)

The ISS isn't in a constant frame of reference to the Earth's surface. If you want to redefine the surface of the Earth as being the "spherical ISS-like sphere" then that's a different body (loosely akin to the differences between analysing static and rotating black holes, for schwarzschild radius purposes).

In fact, you have to do most of the work to get to ISS's orbit (far more than 'merely' getting to its altitude), 9.4km/s (ish). You only need about ~1.7km/s more to escape Earth entirely.

Not quite within Champion Frog reach, of course. Or not a single CJF, but by using a lot of them, and by careful configuration of a stack of those frogs using the RocketFrog Equation, you could probably get at least one small frog to entirely leave Earth's gravitational influence. As you might from Earth, but you'd need a lot more frogs. 82.132.238.175 11:59, 17 December 2025 (UTC)