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Jumping Frog Radius

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Title text: 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.

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Explanation

This is incomplete: This page was created by an CHAMPION PLANET-JUMPING FROG. I have added a bit about the drawing. It is important I think that the planet with the frog has exactly the rjf radius. This means the frog cannot escape but just barely. Is there a physics relation behind the fact that the jumps height seems to be very close to the radius of the planet, i.e. rjf? Also Can someone calculate the size and mass of the largest object from which a champion frog can achieve escape velocity? Are there some named asteroids that are of sow low a mass that it would be possible for frog to jump of? (Of course there are some small enough... but do any of them have real names, like the one named after Randall)? Don't remove this notice too soon. If you can fix this issue, edit the page!

The Schwarzschild radius is essentially the size of a 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 Einstein's field equations. It is usually calculated as the following:

r = (2*G*M) / c²,

where G is the gravitational constant, M is the mass of the object, and c is the speed of light.

If M were the mass of the 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 jumping frog from being able to achieve 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 this paper, which on page 179 puts an upper limit on the maximum velocity of adult Australian rocket frogs at 4.52 m/s.

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 unavoidably falls back down, since the small planet is just massive enough to prevent the frog escaping.

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 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, it wouldn't be able to jump away to fall to Earth. 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.

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 = 2GM / (4.5 ^m/_s)²

[The drawing to the left 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.

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Discussion

Make changes, try things out, or just have fun with the wiki here! Just leave everything above the line alone, please.

---

This is a test. PoolloverNathan^{[stalk the blue seas]} 20:48, 16 March 2021 (UTC)

This is not. —While False (museum | talk | contributions | logs | rights | printable version | page information | what links there | related changes | Google search | current time: 20:29) 18:38, 17 November 2022 (UTC)

A foreign student asked me to help fight against his math teacher. That was unusual. He was in that class for just a couple of weeks. The teacher's phone number was sent to me. The student asked me to spam-call the teacher. 172.71.155.55 22:58, 18 September 2023 (UTC)

here i'm just messing around in html, ignore this

^furhhfghure _{guyrburgryhuyvfr} "rvhru"

interesting way of writing quotations xd

hmmm this one of putting "<p>" in a line break will come in handy for when i want it to start at the same place than the first line

Please beware that <p> on mediawiki also disables automatic paragraph breaks, so you need a closing </p> or you'll break automatic paragraph formatting for the rest of the page. Zmatt (talk) 22:06, 31 July 2024 (UTC)

edit: da hek did that "</div>" come from An user who has no account yet (talk) 14:14, 13 October 2023 (UTC)

hi uh its hard to get here. is this a reference to undocumented feature??? hmm... this is interesting.
108.162.241.216 02:05, 23 November 2023 (UTC)

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yum yum [citation needed]

Hiuiedeixgeyceiyedhcdiedcve {{trout}}

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<a href=" [AT THE JULY 28TH MEETING][tab] "Cancel the meeting! Our cover is blown.">
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  Add comment        Create topic (use sparingly)       Refresh 

Discussion

Make changes, try things out, or just have fun with the wiki here! Just leave everything above the line alone, please.

---

This is a test. PoolloverNathan^{[stalk the blue seas]} 20:48, 16 March 2021 (UTC)

This is not. —While False (museum | talk | contributions | logs | rights | printable version | page information | what links there | related changes | Google search | current time: 20:29) 18:38, 17 November 2022 (UTC)

A foreign student asked me to help fight against his math teacher. That was unusual. He was in that class for just a couple of weeks. The teacher's phone number was sent to me. The student asked me to spam-call the teacher. 172.71.155.55 22:58, 18 September 2023 (UTC)

here i'm just messing around in html, ignore this

^furhhfghure _{guyrburgryhuyvfr} "rvhru"

interesting way of writing quotations xd

hmmm this one of putting "<p>" in a line break will come in handy for when i want it to start at the same place than the first line

Please beware that <p> on mediawiki also disables automatic paragraph breaks, so you need a closing </p> or you'll break automatic paragraph formatting for the rest of the page. Zmatt (talk) 22:06, 31 July 2024 (UTC)

edit: da hek did that "</div>" come from An user who has no account yet (talk) 14:14, 13 October 2023 (UTC)

hi uh its hard to get here. is this a reference to undocumented feature??? hmm... this is interesting.
108.162.241.216 02:05, 23 November 2023 (UTC)

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

	Soup

yum yum [citation needed]

Hiuiedeixgeyceiyedhcdiedcve {{trout}}

This is the leaderboard:

Last 7 days (Top 50)

Rank Score Pages Changes Username 1 264 262 263 管委会篝火无法解放军“赐额“你去呢管理哦法？ 2 64 56 72 DollarStoreBa'al 3 22 18 22 TheusafBOT 4 15 4 33 Firestar233 5 12 9 12 Headphones the stickman 6 12 5 18 BunsenH 7 11 8 11 R128 8 11 4 16 Kynde 9 9 9 9 Lp0 on fire 10 9 4 10 Barry Margolin 11 6 3 5 DKMell 12 6 3 5 Sturmovik 13 5 1 6 Lordpishky 14 5 3 4 Potatocakethrow 15 5 2 4 David Garfield 16 4 2 3 CheshireCat 17 4 2 3 Trimutius 18 4 4 4 1234231587678 19 4 4 4 Victoria 20 4 1 3 Jeff 21 4 1 3 Treeplate 22 4 1 3 Cheesesentience 23 3 1 2 Kevin Stern 24 3 1 2 Magtei 25 3 1 2 Paul Nickerson 26 3 1 2 Ianrbibtitlht 27 3 1 2 Elektrizikekswerk 28 3 1 2 627235 29 3 1 2 SammyChips 30 3 1 2 boB 31 2 2 2 August Fuller 32 2 2 2 Steve Spivey 33 2 2 2 ExplainEuge.ca 34 2 2 2 Mathmaster 35 2 2 2 Bobthegoat123 36 1 1 1 Gopher 37 1 1 1 Joel Croteau 38 1 1 1 PDesbeginner 39 1 1 1 Dosbears 40 1 1 1 KelOfTheStars! 41 1 1 1 Take The A Train To Watertown 42 1 1 1 Heleatunda 43 1 1 1 NorthwardZoneHacker 44 1 1 1 Darth Vader 45 1 1 1 Qoiuoiuoiu 46 1 1 1 NotaBene 47 1 1 1 Fephisto 48 1 1 1 chris 49 1 1 1 Tooth 50 1 1 1 TheTrainsKid

<a href=" [AT THE JULY 28TH MEETING][tab] "Cancel the meeting! Our cover is blown.">
        Add comment