[ Article crossposted from alt.destroy.the.earth ]
[ Author was Ryan/Todd ]
[ Posted on Fri, 17 Feb 1995 02:06:34 GMT ]
This is the end product of the minds of Ryan Kolter and Ronald
T. Fox. (I get my name first because I'm typing the darned paper).
The project took nearly a month from start to finish to hammer out.
Our goal: to determine if it's mathematically possible to knock
the Earth into the sun, using a variety of techniques. We have
presumed nuclear explosions as our primary method of force,
calculating their explosive force based on the explosive capacity
of TNT (a one megaton nuke makes an explosion as big as one (in mass)
megaton of TNT slurry). We have not considered such futuristic
things as salted cobolt (which has never been made for explosive effect),
pure fusion, or matter/antimatter reactions. In short, using
existing or soon to be existing technology, is it possible?
Though some results would blow the earth into bite size pieces,
melt the crust like butter (making all the suddenly deceased
pavers very happy, I suppose), or at the very lease eradicate all
life on the planet, a VALID option is one that actually moves the
Earth into a terminal orbit (an orbit which intersects the sun).
I (Ryan) came up with a lot of interesting possibilities, and Todd
(who says he "likes orbital mathematics and is seeking professional
help") did the calculations.
Below are a lot of the numbers we used. Other numbers are
given in the proofs we used below.
Mass of Earth: 5.976x10E24 kg
Mass of Moon: 7.35x10E22 kg
Mass of Io: 8.89x10E23 kg
Mass of Titan: 1.35x10E23 kg
Mass of Ganymede: 1.48x10E23 kg
Mass of Phocaea (an asteroid): 1.07x10E18
Mass of Ceres: 2.87x10E21 kg
Magic Number: 1.61x10E29 km.kg/s (amount of momentum you must remove from
the Earth in order for it to adopt a terminal orbit. Divide this
by the mass of the object(s) you hurtle at it, and you get the
objects required speed).
Second Magic Number: in order to cause the Moon to slow down enough
to hit us, 1.575x10E27 joules of energy must be released, which would
slow the moon from 1.018km/s to .207 km/s.
TNT (slurry): 800cal/g or 3.0379x10E15 J/megaton
Orbital radius of Earth: 149.5x10E6 km
Orbital radius of Moon: 384400 km
Orbital radius of Ceres: 413.7x10E6 km
We look at a series of possibilities:
1) Moving the earth with a single nuclear blast.
2) Moving the earth by making the moon hit us.
3) Move the earth by causing a large moon of another planet
or large asteroid hit us.
5) Massive bombardment by asteroids.
6) accelerating a single object at massive velocity.
7) Multiple object impact.
--ONE-- (Explosions on Earth)
To sufficiently slow the earth with man-made explosions alone (presuming
100% yield), we would need to create 2.17x10E33 joules of energy, or
in other words detonate 7.13x10E17 megatons of TNT (or nuclear
Conclusion: It's physically impossible to move the Earth via
manmade explosions alone.
--TWO-- (Explosions on Moon. Moon hits us)
The moon moves at 1.018km/s, and must be decelerated (err...
negatively accelerated) to .207 km/s in order for it to hit the
This would require 1.575x10E27 joules of energy, or 5.12x10E11 megatons
of TNT or it's equivilent in nukes (anyone have a 512,000,000,000 megaton
nuke out there?)
Even if it could be done, the mass of the moon (7.35x10E22) moving
at .207 km/s would not produce enough energy to move the earth into
a terminal orbit. By causing the moon to hit the Earth, you are
simply changing it's orbital velocity relative to the sun, so slowing
the moon down and causing it to hit the earth will not be enough to
knock the system (earth and moon) into the sun.
Conclusion: It's physically impossible to move the Moon via
explosions alone, nor would the moon be moving at suficient
velocity to shift the Earth to a terminal orbit.
--THREE-- (Shift a moon or large asteroid to hit us)
In order to shift IO out of orbit and cause it to plummet towards
the Earth, we would need an explosion of 1.4x10E35 joules of
energy (4.7x10E19 megatons of TNT). This isn't feasable... even
if it were, and taking into account the pull of the sun and the
slingshot effect around Jupiter, Io would only be going 45km/s,
which would do little more than utterly obliterate life on
earth and melt the planet's surface into a gooey (and rather warm)
consistancy. Io would have to be moving at a speed of 5609.1 km/s to have
enough momentum to slow the earth to a terminal orbit. To give you some idea
of the magnitude of this velocity, the Earth's present orbital velocity is
only 29.79 km/s.
Indeed, based on this, it's obvious that we cannot move Titan (which
weighs in at 1.35x10E23 km) or Ganymede (1.48x10E23).
We can take this further to show that you simply cannot shift any
one body at sufficient velocity via explosions alone (presuming you
can get it out of it's original orbit at all), such that it hits
the earth and knocks us into a terminal orbit.
Conclusion: Explosions alone won't destroy the Earth, even
if used to shift mass to hit the Earth.
--FOUR-- (Titan hits Moon... knocks both into retrograde orbit
matching Earth... six months later, KABOOM)
It's already been shown that we could not move Titan via explosions
alone... However if we could (in the future), we tried a different
approach. Could we make Titan hit the moon, send them both into
a retrograde orbit, and have the Titan/Moon object hit us six
months later? (A retrograde orbit is one that moves against the
direction of all the planets... in other words in this case, coming
at us in our own orbit).
Though we could knock the moon into a retrograde orbit, even then,
the final collision wouldn't slow us down enough (but would be
an incredible light display!). It would be very tricky to get Titan to hit
the moon just right so it would adopt the right orbit, but then it's momentum
would only be a measly 1.23e25 kg-km/s, less than .007% of what we need.
Conclusion: Wouldn't work, but would certainly leave nobody left
--FIVE-- (Massive bombardment by asteroids)
Though we could very easily move a moderate sized asteroid (100m diameter)
into whatever position we wanted, it would take many hundred thousand
of them to decelerate the earth enough. Nudging an asteroid from the
asteroid belt & getting it to strike the earth is feasible - 100 megatons of
energy could cause a 305m diameter asteroid to tag us. However, this asteroid
would have a mass of only 8.07e10kg (which would be enough to ruin your day,
but we're talking about the whole Earth here) and a velocity of 38.85 km/s.
Even if we assume that this asteroid is moving in a retrograde direct8ion
around the sun, the resulting inpact would give you a momentum of 5.54e12 kg-
km/s. With that pathetic impact, you'd need thirty thousand trillion of these
collisions (2.91e13 for those of you adverse to Sagannumbers).
Conclusion: Just not feasable. With so many objects required,
we don't have the explosive capability, and even if we did, we
couldn't guarentee that enough WOULD hit us.
--SIX-- (Accelerate a single object at VERY fast velocity)
From the previous points, it is clear that an asteroid like the one we were
just discussing would have to be travelling well in excess of the speed of
light to slow the earth sufficiently. Also, since we are assuming that the
energy of this explosion is imparted as kinetic energy through some
miraculous device, and since kinetic energy increases with the square of
velocity (but momentum, which is transferred in the impact of the asteroid
and earth, increases linearly with velocity), it is an unfavorable tradeoff
to simply accelerate an object using nukes. If you use nukes to change an
object's orbital parameters, you can take advantage of some stored
gravitational potential energy. Whew!
Conclusion: What a horrible mess. Big crater. Wobbly planet, but
we'd still have (at least most of) the earth here.
--SEVEN-- (Multiple object collision)
1) Divide the earth's nuclear stockpile into two groups.
2) Take group 1 (all but 10,000 warheads) & use the different nukes to nudge
RETROGRADE asteroids into two seperate masses. Mass #1 (called L'il Rok)
has a mass of 1.04e20 kg and an orbital radius of 414.5e6 km.
Mass #2 (Big Rok) has a mass of 3.35E22 kg and an orbital radius of 315e6 km.
Using the same method as in Part Five, we can show that a
nuclear stockpile of 10,000 50- megaton warheads can cause an asteroid with a
mass of 4.05e14 kg to hit the earth; we are just trying to get them to move a
few million kilometers, a mere 10% of that distance.
3) Take group 2 (10,000 warheads worth) & hit L'il Rok. This will drop it's
orbit down to 413.7e6 km, which just happens to be the orbit of Ceres....
then, just watch the fun!
4) The collision will cause Ceres to drop down to an orbit of 315e6 km, which
will cause it to smack into Big Rok
5) This collision will cause the L'il Rok/Ceres/Big Rok clod (which you can
name after your mother, if you like) (which is also orbiting the sun in a
retrograde direction, remember....) to strike the unsuspecting Mars, which
has thus far avoided serious adte scrutiny. The ensuing impact, while not
only being fun to watch, drops the Martian orbit down to a perihelion of
149.5e6 km, which all good orbital dynamics weenies recognize as the orbital
distance of ..... The Earth! Mars smacks into the earth with a relative
velocity of over a thousand km per hour. The net effect? What used to be the
earth has a year of 375 days now, a more irregular orbit, and is shaped like
a diseased potato.
Conclusion: Probably never happen... though it could be done in stages
(moving asteroids into retrograde orbits, then so on...). Still wouldn't
knock the earth into the sun.
Via the laws of Physics and mathematics, it has been shown that
it is just not feasable to move stellar bodies around. Though we
could crack the crust, obliterate all life on earth (many times over),
blow it into small fragments that would orbit the sun like
the asteroid belt, prevent life from EVER FORMING AGAIN on the
planet, melt it's surface into a puddle (pleasing pavers everywhere...
hmm... we'd have to toss another asteroid in just to give them
road bumps), and even change Earth's orbit and/or change it's shape,
we haven't found a mathematically viable way of hitting the earth with
enough force to knock the planet into the sun.
The possibility of pushing the Earth into the sun is, by our current
technology, simply not possible.
Ryan Kolter (email@example.com)
Chaos is. Unless it isn't at the moment.
R. Todd Fox (firstname.lastname@example.org)
We were once so close to Heaven
Peter came out & gave us medals
Declaring us the nicest of the damned - TMBG
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