g'day my smart mates my name is dylan dance i'm a physicist from the land down under
grab a coffee grab a chair grab a vegemite sandwich grab whatever you want to grab let's talk
some natural philosophy so today we're going to be watching some more dragon ball super dragon ball
z whatever and we're gonna do some calculations i am gonna try and calculate how powerful goku
spirit bomb is we've also got a white board now so it should be a bit easier for you guys to see my
beautiful calculations um i might actually hang it up here something like that so anyway
let's watch some dragon ball z let's watch my boy goku kick some butt
vegeta what did you say his power level is it's over 9 000. the ultimate meme
in physic when you study a math or a physics degree that meme pops into your head so much but
have you ever thought about what the hell are the units here this power level nine thousand
what units what does that even mean nine thousand what nine thousand likes on a youtube video
on that note let's try and get over 9000 likes on this video that would be epic
now all right time to do some calculations so here's what we're going to do we're going to
first work out how much energy approximately went into that spirit bomb that we first saw
and then we'll work out how many humans would it take to produce the energy to form that spirit
bomb and then to take it one step further we're going to see how many humans it would take to
produce a spirit bomb the size of the sun and we can work out how long that would take so in
dragon ball these spirit bombs are thought to be fueled by pure energy which is known as ki
in the show now you can't actually have pure energy in our universe as far as we can tell
there's a lot that we don't know all right you might have heard of dark energy dark matter
these things who knows could be pure energy and then the other weird thing about this
key in the show is that it stems from any form of life so here's what we're going to do we're
going to model these spirit bombs as photon gas spheres to approximate the physical parameters
as dictated by this universe so we're going to imagine these spherical distributions as
pure photons by doing this we can work out approximately how much energy is required
we're going to assume only humans only humans allowed for this spirit ball let's calculate
i don't think you can see the blue marker so let's use some chore
calculations are in and the verdict is doesn't work surprise surprise it's an anime
but let's talk about it let's break some of this down before i share the final result and what that
means let's just go over it a tiny bit really not going to talk much about it because it will bore
a lot of you i had to get pretty nerdy to work this one out but uh you can see here i've used
the wavelength which is what this little thing represents as because it's roughly blue and then
you can use this little equation here to get the total energy of the spirit bomb and then you can
use this equation here to get you rearrange for this thing down here which is meant to be a t
and you can get the time it takes for the spirit bomb to form um and this one up here is total
number of particles in these photon spheres and this is temperature we ended up using that as
a constant um so the results what did we get so for that first spirit bomb that we saw i've just
called it here as large i worked out how much energy it would take and it works out to be about
3.18 times 10 to the 51 joules i also had to work out how much the average human would supply so i
made a bunch of assumptions there but i did that somewhere about 5.8 times 10 to the four joules
per person and you get the amount of humans it would take for goku's first spirit bomb and that
works out to be about where is it here 5.51 times 10 to the 46 humans there's about 7 billion people
on earth so that's about a billion billion billion billion billion times the amount of people on
earth required so you'd need about five earths just to fuel that first spirit bomb of goku's
we also then went on to calculate how long it would take for a spirit bomb the size of the sun
and that works out to be 1.4 times 10 to the 26 seconds you convert that into years and that gives
you four quintillion years which is about twice the age of the universe daddy goku is a daddy
wait a second there king kai must live on that tiny little planet check that out
man i'm getting squashed down here how could anyone live in a place with this much gravity this
is so great because this teaches you so much about gravity i remember when i was a young boy because
i was such a little nerd i calculated how dense this little planet was whatever it is and it turns
out that this little thing has so much density it couldn't exist in our real universe because
it would be so dense this thing it would turn into a neutron star where the density is so strong that
the atoms kind of merged together and all you have is a bunch of neutrons literally almost touching
these neutron stars are some of the densest things in the universe they have so much mass
crammed into a small volume which means they have a high density that also means there's a lot of
energy because mass and energy are equivalent thanks to einstein but this also means there's
a huge amount of gravity it's so dense that if you've got a tablespoon of neutron star mata it
would weigh as much as mount everest and if you squeeze something even closer together you will
actually form a black hole it's when you overcome the neutron degeneracy pressure and the neutrons
collapse in the hole in this fabric of space-time and we have no idea what's really going on down
there but anyway my point is that they've given you a really great representation of what gravity
is like did you notice how in the distance that there was no gravity and it wasn't until he got
close to king kai's little planet that the gravity increased enormously this is what real gravity is
like it falls off with one over the square so an inverse square law so gravity in real life as you
get closer to say a black hole it exponentially increases if you replace the sun with a black hole
the earth would actually continue to orbit it the exact same way it would get a little bit cold i
think that's enough nerdiness for one video so please like and subscribe takes a lot more effort
to make these videos than it looks and it would be greatly appreciated if you take two seconds
to do that and i'll catch you guys next time for some more silly nerdy calculations about anime
movies whatever it is we're doing uh so yeah have a great day guys i'll see you next time