Main Page

Welcome to the explain xkcd wiki!
We have an explanation for all 3190 xkcd comics, and only 55 (2%) are incomplete. Help us finish them!

Latest comic

Go to this comic explanation

Jumping Frog Radius

|< < Prev #3181 (December 15, 2025)

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.

|< < Prev Random Explanation

Explanation

The Schwarzchild 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.

The comic suggests a more useful radius of large gravitational bodies. The "Jumping Frog radius" is the size of a planet so that its gravity keeps a champion jumping frog from being able to achieve escape velocity.

The title text points out that the r_jf of the Earth is about 1.5 light days, which is about 3 times the distance to Pluto. Since Earth's surface is much smaller than this^{[citation needed]}, no frogs will be able to escape, so they'll all collect here on Earth. As far as we know, all the frogs in the Solar System are on Earth, so the data apparently matches the theory.

The Schwartzchild radius is part of a solution to Einstein's field equations. It is usually calculated as the following:

r_{jf} = (2*G*M)/(c^2),

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

Instead of the 299,792,458 m/s speed of light, this comic uses a much smaller value of 4.5 m/s. 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. This much smaller denominator increases the calculated radius from the 9 mm Schwartzchild radius to almost 4*10^13 m, or just over 1.5 light-days. As Pluto is never more than about 0.3 light-days away from Earth, we can safely say that any frogs in the Solar System should be found on the surface of Earth, despite there likely not being a real frog prediction in general relativity.^{[citation needed]}

Transcript

[The panel shows a formula and a drawing to its right.]

r_jf = 2GM/(4.5 m/s)²

[A small planet with the radius marked as r_jf and a frog jumping on the surface. The frog jumps about as high as the planet's radius, saying "ribbit" in midair and "plop" as it lands.]

[Caption below the panel:]

More practically useful than the Schwartzchild 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.

Is this out of date? .

New here?

Last 7 days (Top 10)

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？ 2 113 102 130 DollarStoreBa'al 3 22 18 22 TheusafBOT 4 15 4 33 Firestar233 5 12 9 12 Headphones the stickman 6 11 8 11 R128 7 11 4 17 BunsenH 8 10 3 15 Sturmovik 9 9 9 9 Lp0 on fire 10 4 4 4 Victoria

Lots of people contribute to make this wiki a success. Many of the recent contributors, listed above, have just joined. You can do it too! Create your account here.

You can read a brief introduction about this wiki at explain xkcd. Feel free to sign up for an account and contribute to the wiki! We need explanations for comics, characters, themes and everything in between. If it is referenced in an xkcd web comic, it should be here.

• If you're new to wiki editing, see the explain xkcd:Editor FAQ for a specific guidance to this Wiki and the more general help on how to edit wiki pages. There's also a handy wikicode cheatsheet.

• Discussion about the wiki itself happens at the Community portal.

• You can browse the comics from List of all comics or by navigating the category tree at Category:Comics.

• There are incomplete explanations listed here. Feel free to help out by expanding them!

Rules

Don't be a jerk!

There are a lot of comics that don't have set-in-stone explanations; feel free to put multiple interpretations in the wiki page for each comic.

If you want to talk about a specific comic, use its discussion page.

Please only submit material directly related to (and helping everyone better understand) xkcd... and of course only submit material that can legally be posted (and freely edited). Off-topic or other inappropriate content is subject to removal or modification at admin discretion, and users who repeatedly post such content will be blocked.

If you need assistance from an admin, post a message to the Admin requests board.