What if Earth grew 1cm every second?

How long would it take for people to notice their weight gain if the mean radius of the world increased by 1 cm every second? (Assuming the average composition of rock were maintained)

IMPORTANT NOTE
*******************
We would like to apologize for making two mistakes in this video - thanks to viewers for pointing them out!
1) Silly error: after the Chandrasekhar limit, the Earth would first become a neutron star. Only after it gained even more mass would it pass the Tolman–Oppenheimer–Volkoff limit and finally become a black hole
2) Subtle error: if the earth kept expanding with a constant density, eventually it *would* become a black hole because the Schwarzschild radius of a black hole is proportional to its mass M, while the radius of a sphere of constant density is proportional to M^(1/3), and eventually M gets bigger than M^(1/3)

Credits
*******
Randall Munroe | Narrator
Henry Reich | Writer & Director
Lizah van der Aart | Illustration and Video Editing
Ever Salazar | Chief Chaos Controller
Know Art Studios | Music & Sound Effects

What If? The Video Series is the official adaptation of the What If? books by Randall Munroe and is produced by Neptune Studios LLC.

Henry Reich is the creator of MinutePhysics and executive producer of MinuteEarth and MinuteFood and founder of Neptune Studios LLC (the parent company for all three youtube channels).

©2024 xkcd, inc.

[xkcd_whatif]

We would like to apologize for making two mistakes in this video - thanks to viewers for pointing them out!
1) Silly error: after the Chandrasekhar limit, the Earth would first become a neutron star. Only after it gained even more mass would it pass the Tolman–Oppenheimer–Volkoff limit and finally become a black hole
2) Subtle error: if the earth kept expanding with a constant density, eventually it *would* become a black hole because the Schwarzschild radius of a black hole is proportional to its mass M, while the radius of a sphere of constant density is proportional to M^(1/3), and eventually M gets bigger than M^(1/3)

[unconcernedsalad]

as a longtime xkcd fan it’s fascinating to see how well the what if series translates to video format. i know there’s alot of work needed to translate the blog into something more appropriate for video, but the transition does feel seamless. almost like it was in video format this whole time. anyways, amazing work, keep it up !!

[MichalBrat]

According to my scale this process has already started like 25 years ago

[Baiko]

TIL, I'm not overweight, I'm just in Helsinki.

[PaddyQuiggin]

"under realistic physics" at 4:14 is very funny in the context

[asterozoan]

A small correction: you mention the White Dwarf Earth reaching the Chandrasekhar limit (1.4 solar masses) and becoming a black hole, but in fact above that limit it would become a neutron star (and release a vast amount of energy in a type 1a supernova).
The neutron star would then continue to expand until it reached the catchily named Tolman–Oppenheimer–Volkoff limit, around 2.1 solar masses. Only at that point would we get a black hole.

[The-EJ-Factor]

This would be such a scarily dreadful apocalypse. Just because of how slow it is. It’s similar to having a disease that is hard to notice because the symptoms are small, and figuring out that it is terminal and that there is nothing you can do and it only gets worse from here. Like that thing that slowly turns your body into bone, and you eventually have to decide that you will be sitting or laying down the rest of your life.

[seagie]

That's a kerbal challenge. You need to evacuate earth, and the longer you wait the more delta it costs...

[michaelhoffmann]

Minor correction: the Chandrasekhar Limit is where a dwarf start become a neutron star, not (yet) a black hole. Around 1.4 Msol, IIRC <checks Wiki> yep! 1.4. And 2.3-ish for neutron stars to collapse to black holes.

[YonatanZunger]

4:30 Technical note: it would collapse into a neutron star at this point. Black hole formation would take another few millennia, not least since each collapse stage will create a shock wave that blows out a good third to half of the Earth's newly-acquired mass. We'd get to be a Type I supernova!

[davecorry]

I love the subtle sadness of the quiet music to the end-credits. It plays throughout the video, but at the end, it's alone. All alone.

[Justcallmekai]

The earth grew 400 cm between the time this video posted and I clicked on it

[bucketeer]

the music is WAY too happy for this type of video 😭

[smizmar]

11 months ago, xkcd made a great decision, at least according to what I see as the oldest video on your channel, have literally just stumbled upon this now. So good!! It reminds me of the good old days of youtube. Where we take real physical principles and apply them to ridiculous situations. I love the genie 3 wishesesque way you answer the questions, answering exactly what the question asked, but just not in the way the person may have initially predicted :P

[barnabasjthomas]

xkcd has been one of the founding pillars of my childhood. Love ya, Randall!

[sykes]

Even if the density of the Earth were somehow kept constant, it would still eventually become a black hole. The density of a Schwarzschild black hole (the mass divided by the volume enclosed by the event horizon) can be found by combining the formula for the Schwarzschild radius and the volume of a sphere and is equal to: (3*c^2)/(8*pi*G*r^2). If we then set this equation equal to the density of Earth (5500kg/m^3), we can find a radius of 1.7095×10^11 meters. So, even if it was held up under its own gravity somehow so as to keep the density constant, the earth would still turn into a black hole when its radius reached about 1.14 AU. Which would take ~542, 100 years.

[opiniononion]

And then there would be people denying the growth and as proof they would hammer two nails into the ground in the floor of their house.
After a week they say "see? Still the same distance apart!"

[Noah-fxcm]

A genius is not someone who can anwser any question, but someone who asks a question no one asked before

[kanizh]

So, if Earth grew 1cm every second, I'll die in 100 years... Hm, ok.

[Platitudinous]

Glad that I finally know how "Roche limit" is pronounced! Now I can say the title of the coolest Kirby soundtrack correctly.