- Beautiful isn't it?
The only home we've ever known.
But what if the only way to save the Earth
was to push it somewhere else?
Could we do that?
Let's get technical.
It is freezing out here.
(upbeat music)
Life, as we know it, depends
on two million septillion
kilograms of mostly hydrogen and helium
that forms an almost perfect sphere
that we humans call the sun.
And because we are so
dependent on the suns energy,
life on Earth has a time limit.
In a little over seven billion years,
the sun will have burned
through enough of its
hydrogen and helium fuel that it'll move
into another stage of its
life, the red giant stage,
and expand so much so that the Earth
and all the inner planets will be consumed
by just its radius.
And that, as they say, will be that.
How could we escape such a scorching fate?
Well that is the central
question in the novella
and recent Chinese blockbuster,
"The Wandering Earth".
And that story's solution is to construct
thousands of rockets
taller than Mount Everest
and just push Earth to
another solar system.
This would get us out of
the way of a red giant,
but is this even close to feasible?
What kind of engineering would this take?
Could we make a spaceship Earth?
Let's begin with the (humming),
let's begin with a simple case.
Using rockets to fling the
Earth out of the solar system.
The Earth goes around the sun more or less
in a circle because we are
gravitationally bound to it.
To change where or how the
Earth was orbiting then,
something would have to fight against
this constant gravitational force
and add energy to the entire system.
We are now describing
gravitational potential energy
and the more we wanted to
move something like a planet
through a gravitational field away from
a gravitational influence,
like giving it a larger orbit,
the more energy we would have to put in.
But just how much energy
would we have to put into
the Earth's orbit in order to fling it
out of the solar system?
Well, if we gave the Earth
enough kinetic energy
to equal or exceed the
gravitational influence
of what it's bound to
the sun, by say changing
its velocity, it's orbit
won't just increase
and get larger, it will
just fly off into the cosmos
never to return, always slowing down,
but never falling all the way back
into the suns gravity well.
So let's set gravitational
potential energy
and kinetic energy equal to
each other and do the math.
We know the mass of the
Earth, the mass of the sun,
how far the Earth and sun
are apart from each other,
and we know Newton's
gravitational constant.
So if we solve for V here, we
can get the escape velocity
from an Earth-like orbit.
Do this and you get an
escape velocity for Earth
from the sun of 42 kilometers per second,
an absolutely blistering
speed that could take you,
for example, from New York to Los Angeles
in just 95 seconds.
The good thing though,
is that we do not need
to get Earth moving at this ludacris speed
because we're already moving
at an absolutely crazy clip.
Do you feel like you're moving right now?
Well probably not, but
you've always been moving.
Since you were born every
single molecule of you
has been absolutely racing around the sun.
And because of this, you've never felt it.
Earth's orbital velocity
is already a substantial
30 kilometers per second around the sun.
And so if we wanted to push
Earth out of the solar system
all at once, we wouldn't
have to add 42 kilometers
per second, we'd only have
to add the difference,
around 12, and then Earth would be
on its way to Alpha Centauri.
However, because the plan
in "The Wandering Earth"
specifically, an understandable plan,
is to slowly push the Earth
out of the solar system
over the course of
decades, we need to change
the Earth's velocity by a lot more
than 12 kilometers per second.
In a slow, constant
spiraling outwards burn
for example, where the sun
is always pulling on you
the entire time, you
need to instead exchange
all of this orbital
velocity and kinetic energy
for potential energy.
You are spiraling outwards
getting further and further
away from the sun, slowing
down, down, down, down
until you escape the
suns influence with zero,
or there about zero, kilometers per second
and you have no orbital velocity
because you are no longer orbiting.
However we actually accomplish
this, this all means
that we would need to cancel
out a full 30 kilometers
per second of ancient orbital velocity
to escape the suns influence.
Kind of like slowly getting
off a cosmic merry go round
when it's slow enough
and safe enough to do so.
And doing all of this
would be the greatest feat
of engineering ever attempted.
In 2006 we launched the
New Horizon's space probe
with a velocity that would take
it out of the solar system,
so we have done this kind of thing before.
The problem with doing it with Earth is
Earth is so dang heavy.
The Earth is obviously
huge relative to us,
but just think about for
a second how much of Earth
do we actually interact with?
All of the forests, all of the oceans,
every living thing you've ever seen,
all of human civilization,
all of the human experience
has existed in a volume
of Earth that is less
than 1% of the whole.
If we had to move the Earth
to another solar system
and we wanted to maintain some semblance
of life as we know it,
we couldn't just move
1% that is the biofilm that we call life.
We would have to move 100% of Earth
to maintain the biosphere, the geology,
the magnetosphere, our
gravity, everything.
100% of Earth is six
trillion trillion kilograms,
six with 24 dang zeroes after it.
And if wanted to move all
of this with some relative
speed in some time frame,
we would have to provide
a lot of thrust, which would
have to come from our rockets.
Back in the envelope
though, using a simple
force equals mass times
acceleration equation,
the mass of Earth and the
orbital velocity we have
to cancel out, along with the time frame,
let's say something like 15
years like "The Wandering Earth"
uses, we get a thrust value that has
20 zeroes after it, that's a lot.
So now we have to look up
how our rockets stack up.
Slow burn baby, slow.
Now, the simplest way
to, ope, still thrusting.
There we go, the simplest,
most straight forward
approach to turn Earth into a spaceship
would be to first stop the
rotation of the planet,
which would cause a
natural disaster unlike
we've ever seen before, but
let's ignore that for a second,
pick one hemisphere of
earth because we want
the thrust point in one direction
for pretty much the entire time,
and then dot as much of that hemisphere
as we can with rockets.
These rockets would have
to be engineering marvels
like the world has never seen.
And to get an idea of just how much thrust
each one would produce, let's look to
"The Wandering Earth" again
and say we use 10,000 rockets.
If all of our Earth
engines needed to add up
to our total estimated
thrust, then every single
one of them would have to produce 37,
wait, wait, wait a second.
Thousand trillion
newtons of thrust, crazy.
And if we choose a pretty
beefy boy in terms of thrust
like the Raptor engine from SpaceX,
you can see that even though it produces
a lot of thrust, it
would still take billions
of Raptor engines just to equal one
of our Earth moving engines.
And all of these engines
would take up a lot of space.
(dramatic music)
Let's assume that because our scenario
is a literal doomsday
scenario, we as humans
are willing to put as many
rockets as we can possibly fit
on one half, or one hemisphere of Earth.
How much construction,
looking at this map,
do you think we'd need to do?
I have indicated here with a single dot
a surface area required for a number
of SpaceX Raptor engines.
Not any of the infrastructure
we would probably
have to build around them,
just the thrusty bits.
Looking at this dot, how many other dots
do you think we would
have to draw on this map?
Take a second to guess, I will wait.
I will give you a hint,
it's not this many dots.
It's this many.
Using current technology,
the number of rockets
that we would need to slowly
push out of the solar system
would literally cover every square inch
of one half of Earth.
Every square centimeter of ocean,
every square meter of land, everything.
Our wandering Earth
then would have to look
something like this, which
is objectively super awesome,
but shall we say totally
and completely implausible.
I think we need to go sci-fi.
We would have to cover literally
half the planet in rockets.
So I don't think chemical
propulsion is the way to go.
So what about nuclear fusion?
Oh, that's where that was.
To it's credit, "The Wandering
Earth" doesn't suggest
that regular old chemical
rockets are the solution
to the Earth moving
problem, instead saying
that they use giant
nuclear fusion engines,
taller than Mount Everest
as their Earth pushers.
And this makes everything
a bit more believable
because one of the
advantages of a theoretical
nuclear fusion rocket is the speed
at which they can throw
fuel into the void.
However, even if fusion engines
could turn Earth's crust
directly into fuel through
the fusion process,
even if all of these
fusion engines could fit
on one half of Earth, and
even if they could provide
the required thrust in total,
fuel would still be a big problem.
This may be the most famous equation
in all of rocket science.
The very cleverly named Rocket Equation.
It is able to take what we want to change,
in terms of velocity for our space craft
and relate that to the
exhaust velocity coming out
of that spacecraft and how much mass
we started off with and how
much mass we finally end with.
This change in mass is
how much fuel we need.
If we now give our nuclear fusion rockets
an absolutely ridiculous exhaust velocity
thanks to the millions
of degrees plasma created
in these fusion reactions, then we can use
our change velocity we wanna give to Earth
to solve for what percentage of Earth
we want to use as fuel.
To move our spacecraft
out of the solar system
under all of our assumptions,
we would only need to use
.3% of its total mass in terms of fuel,
but remember that our spacecraft is Earth.
Let's remember that
everything you know and love
accounts for less than
1% of Earth's total mass.
So in that context, this
.3% number is more like
30% of everything you've ever seen.
To power these futuristic
nuclear fusion reactors,
yes we would only need to use
.3% of Earth's total mass,
but not all of Earth's total mass
is readily available to us.
So we would need to throw
into these fusion reactors
the equivalent of 13 times the mass
of all the world's oceans combined.
Even if we could make reactors like this
and move Earth with them,
we might not have the fuel
to supply them or the ability to.
And we don't even have
fusion engines right now
nor do they seem to be on
the technological horizon.
Using current technology
like SpaceX Raptor engines
and the rocket equation, we
could calculate that we would
eventually have to throw the
equivalent mass into space
from our spaceship, which
is Earth, of 98.98%,
and if we had to do
that, just to push Earth
out of the solar system,
just .02% would remain,
meaning that everything, eventually,
all the animals, all of
humanity, civilization,
plants, geology, everything,
would have to fit
on a spaceship Earth the
size of a large asteroid.
Because we'd have to use
the majority of Earth's mass
as fuel, just a few years after launching
spaceship Earth towards Alpha Centauri,
we would run out of space
for pretty much everything.
The rockets, the animals,
the plants, the food, us,
I don't know if we wanna
make a spaceship Earth.
So could we turn the
Earth into a spaceship
to escape a dying sun?
Well, using today's technology,
we would have to make
trillions of our best rockets
and then move everything
on one hemisphere of Earth
in terms of resources
to one side, and then dot
that entire other side
with rockets, literally
every square centimeter,
and then use so much of Earth as fuel
that by the time we got
to where we were going,
we would be reduced to the
size of not a planet anymore.
Obviously all of this
is totally improbable,
if not completely impossible.
Using fusion engines would
make everything easier,
but space and fuel would
still be a problem.
For now, the only trip that
the Earth will be taking
around a star is another one
around the sun, because science.
I'm taking this.
(upbeat music)
And I should say there's
a lot of other ways
that you can approach
this kind of calculation.
You can change the trajectory,
you can change the engines
or orientation, the power requirements,
but what I will say is that basically
any combination of
variables that you pick,
it still is completely implausible to do.
Either it would take you,
with current day technology
like millions or billions
of years to leave
the solar system and then
it's gonna be too late
and you're gonna be engulfed by the sun,
or the power requirement
is so crazy for you
to launch yourself out of the solar system
like New Horizons that it's just something
we probably won't ever create
in terms of engineering.
So that's, that doesn't work so much.
But "The Wandering Earth"
does get a lot right
from having to slow down
and stop the rotation
of the Earth, and population
die-offs and all that stuff.
It's pretty fun and I
appreciate the science in it.
Thank you so much for watching today
and a huge thank you Doctor Ethan Segall
and Matter Bean for their
help on this episode.
If you enjoyed this episode
of "Because Science"
about spacey stuff, you
can check out some of
the other videos that we've done like
what would happen if you
actually pulled the moon to Earth
like in Majoras Mask,
and why you definitely
why you do not want Superman
to reverse the Earth's rotation.
You can follow us @BecauseScience here
on these social media platforms
where I take suggestions
for future episodes, and hey, thanks.
(upbeat music)
