Built on Facts

Dropping Rocks: Los Angeles

So there’s this alien invasion flick called Battle: Los Angeles. It’s getting mixed reviews. Ebert hates it – “an insult to the words “science” and “fiction,” and the hyphen in between them.” With the caveats that his judgment is usually questionable, I haven’t seen the movie, and I don’t plan to see the movie, I’m thinking I’m relatively safe in trusting his opinion in this particular case.

Now it’s also true that judging this kind of movie by its physics is an exercise in foolishness, akin to complaining about the lack of 8 consecutive 24 episodes of Jack Bauer enjoying a good night’s sleep. Nonetheless, every physics blogger from time to time has to deploy the Canonical Planetary Warfare Complaint. Pour encourager les autres, or something like that.

It goes like this: consider a rock. A big one, the size of a car. What’s that, maybe 5 cubic meters? I have no idea, but we’re talking a nice big rock. The density of granite is something like 2.7 g/cm^3, so our rock has a mass of around 13,500 kilograms.

This rock is sitting in the cargo bay of the evil alien ship in low earth orbit. In such an orbit, the ship and thus the rock are traveling at some 8 km/s. The kinetic energy of that rock is

i-d4bb9fe09d6b78eb832985821d8a307f-1.png

Which works out to about 4.3 billion joules, which is conveniently just about the same amount of energy as a whopping 2000 pounds 100 tons of TNT (correction via Eric in comments – I misread the decimal point in the joules-per-ton conversion).

So any alien who wants to beat earthbound humanity into submission has a rather easy plan available: drop big rocks on power plants, railway hubs, highway chokepoints, and ports. Release a few dump trucks worth of gravel into low earth orbit to take out all the satellites just for kicks. Then pour a cup of tea and wait for a starving and suddenly stone-age humanity to wave the white flag. You’d need just a few thousand big rocks. Maybe a few hundred, judiciously applied.

The box office returns for my science fiction epic “Rocks Fall, Everyone Dies” are likely to be dismal*. But if you’re planning a planetary assault, you’d be hard-pressed to do better.

*Science fiction novelists are a hardier bunch, and use this trope all time time. Heinlein’s version is probably the most famous.

Comments

  1. #1 John Carney
    March 12, 2011

    I’m always amused by the notion that aliens might want to “invade [Earth] for it’s resources.” Anyone capable of crossing interstellar space doesn’t have a resource problem… At least not until they start sending expeditionary forces to distant solar systems.

  2. #2 Renolds
    March 12, 2011

    Egbert failed to grasp the concept of the movie. Its from the point of view of the soldier in that squad not the generals or world leader’s point of view.

    Frankly I found it refreshing that there wasnt a General McCow chewing some cud in one of these movies.

  3. #3 Tyler Breisacher
    March 12, 2011

    The seasons of 24 are not consecutive! There is always about a year or so in between seasons. Part of the fun of the first couple episodes of a season is finding out about what happened since the end of the previous season.

  4. #4 feralboy12
    March 12, 2011

    Also, in The Moon Is a Harsh Mistress, the moon rebels announce where those rocks are going to hit–and crowds gather on earth to watch.
    Now that’s realism.

  5. #5 Eric Lund
    March 12, 2011

    Which works out to about 4.3 billion joules, which is conveniently just about the same amount of energy as a whopping 2000 pounds of TNT.

    Check your decimal point–when I do the calculation I get 432 billion joules, which assuming your conversion to TNT equivalent is 0.1 kiloton. About the size of a small nuke.

    If an interstellar war ever did break out, a planet is the last place you’d want to be. That gravity well both hinders you and (as Heinlein showed) helps your opponent. Also, there is no strategic terrain to assist in your defense.

  6. #6 Joseph Hertzlinger
    March 13, 2011

    If the aliens want to take over Earth’s civilization (maybe they want samples of primitive technology for their museums), they’ll have to preserve it. That means they can’t use such crude means as mass-destructiom weapons.

  7. #7 Steve Killgore
    March 13, 2011

    The Moon Is A Harsh Mistress is a touchstone, and one of my favorite novels – it’s AI, social mores and memes, revolution, absolutely top shelf. David Gerrold’s War Against The Chtorr shows the alternative, not a beat-down but a real colonization, it would make an epic trilogy movie. (and speaking of David, I’m still disappointed in the silly changes made to the truth in The Martian Child, nothing about the truth needed to be changed)
    I enjoyed B:LA, like Flight of The Intruder it will suffer from a release that coincides with a week of real news. I believe that like 300 it is suffering from the disease of Hollywood (Liberals), since B:LA doesn’t portray American soldiers (and America) in a negative or at best morally-ambiguous light the film ‘isn’t worthy of praise’.
    As with Independence Day, yes, the ending is too neat – I would have counseled them to make two films, the first where we get smacked and the second as our survival and counterattack. Battlefield:Los Angeles could have and should have gone that route, creating a franchise – scenes from all around the world, some with characters with direct ties to the platoon in California (their Corpsman’s sister), fellow Marines in Okinawa, a relative in Jersey, etc.

  8. #8 Jamie
    March 13, 2011

    Nice post!

    But consider… a civilization that has the energy available to easily move such mass might actually find it more expedient to use death rays… or just drop fuel canisters. Or deploy a few solar mirrors that can be folded up and taken to the next planet once the job is done. I suppose it all depends on what they want from the planet and what their imagined resources are… I like the gravel idea, though. I’ll definitely remember that one next time I invade someone.

  9. #9 William
    March 13, 2011

    Why wouldn’t the rock’s potential energy due to gravity, be factored in to the total energy of the rock?

  10. #10 Kris Rhodes
    March 13, 2011

    Moon is a Harsh Mistress is probably my favorite book ever. Everyone should read it. Also, would be a great movie.

  11. #11 Roger Sweeny
    March 13, 2011

    William,

    It would have to be added. The lowest LEO is about 320,000 meters. Multiplying by a mass of 13,500 kg and a g of 9.81 m/s*2 gives about 42.4 billion joules, almost ten times as much as the initial kinetic energy.

  12. #12 Michael Churvis
    March 14, 2011

    It seems to me that the best way to subjugate humanity and it’s infrastructure would simply be to shut it down. For instance, all modern/rapid communication, mass transit systems, and inorganic transportation could be shut down with a high altitude directed EMP generator(s). Keep this device(s) running for, say, 3 years. Then at the peak of humanity’s fragmentation, send down some impressive air units bristling with loud guns to drop the human’s morale further. Once the humans have been subjugated, flip the switch on the EMPs and resume the industry.
    Power expense: 6/10
    Material expense: 1/10
    Invader life expense: 0/10
    Human life expense: 1-3/10

  13. #13 Paul Murray
    March 14, 2011

    So, instead of “Rods from God”, we have “Rocks from Spock”.

  14. #14 John Haigh
    March 14, 2011

    A film of Moon is a Harsh Mistress? I hope not, look what holywood did to Starship Troopers.

  15. #15 Ned Wright
    March 14, 2011

    I use the following way to remember the conversion of kinetic energy into kilotons: A ton of mass at 2.8 [or 2.9] km/sec has an energy equal to the energy of a ton of TNT. This makes total sense because 3 km/sec is a typical rocket exhaust velocity. So 13.5 tons at 8 km/sec is 13.5*[8/2.8]^2 = 10^2 tons of TNT.

    Potential energy from low Earth orbit is only about 10% of the kinetic energy. But for an asteroid approaching the Earth with relative velocity v is speed at impact is sqrt[v^2+(11 km/sec)^2]. The 11 km/sec is the escape velocity from Earth and represents the potential energy.

    I haven’t seen B:LA but I liked the book “The Moon is a Harsh Mistress” and I also liked “Footfall”.

  16. #16 Russ Willis
    March 14, 2011

    As a geologist I’d venture to say that it would be unlikely aliens would use granite boulders for their assault on Earth. They could have access to granite if they lived on an tectonically active planet, but it would be a hassle to transport such a payload across the universe. It may be easier for them to scavenge meteoroid material, which is most commonly ordinary chondrite, with a density of about 3.5 g/cc or more. So, they could inflict even more damage!

    Nice blog… subscribed.

  17. #17 Ken
    March 14, 2011

    The Moon is a Harsh Mistress is a good read, and one of my favorites. However it would make a crappy movie because much of the book is dialouge between characters talking about politics. A movie version would be terribly slow.

  18. #18 Win on Numbers
    March 14, 2011

    I try not to take things too seriously. That is where the ficton part of science-fiction comes in.

  19. #19 rob
    March 14, 2011

    i like the end of Ebert’s review:

    “Young men: If you attend this crap with friends who admire it, tactfully inform them they are idiots. Young women: If your date likes this movie, tell him you’ve been thinking it over, and you think you should consider spending some time apart.”

    i absolutely loathe Starship Troopers: Teh Movie. the book is great though. Footfall was a fun book. Moon is a Harsh Mistress is good. (Really? a movie? prediction: it will suck with loads of suckitude) Forge of God was good too. Neutronium/anti-neutronium collision! at the center of the Earth! boom.

  20. #20 Peter
    March 18, 2011

    Why transport tons of rock? Simply tweak the orbital parameters of a asteroid to impact the moon. Earth is then bombarded by all the bits of moon debris. Smaller asteroids would provide enough proof of concept that total surrender of the planet would follow with minimal damage and minimal energy cost.

  21. #21 Sohbet Arkadaslik
    March 20, 2011

    Düşük Dünya yörüngesinden Potansiyel enerji kinetik enerjinin sadece% 10′dur. Ama göreceli hız v ile Dünya yaklaşan bir asteroid için darbe de hız sqrt [v ^ 2 + (11 km / sn) ^ 2] dir. 11 km / sn Dünya’dan kaçış hızı ve potansiyel enerjisini temsil eder.

  22. #22 Tercel
    April 10, 2011

    If you are capable of interstellar travel, then I assume you are capable of travel near light speed. That same boulder impacting at 0.9c would be an absolute cataclysm.

  23. #23 Sohbet Arkadaslik
    April 14, 2011

    Film: i kesinlikle Starship Troopers tiksinmek. kitap rağmen harika. Ayak sesi eğlenceli bir kitap oldu. Ay bir Harsh Mistress iyi olmasıdır. (Gerçekten tahmini bir film:? O suckitude yükleri ile emeceksin) Allah’ın Forge çok iyi oldu. / Anti-neutronium çarpışma Neutronium! Dünya’nın merkezinde! bom.

  24. #24 Michael Varney
    May 8, 2011

    Hummm, I wonder how much of the mass of the rock would ablate during atmospheric transit?
    How much energy is lost to friction?
    Would a car sized granite rock make it to the surface in one piece?
    Angle of incidence?
    Tensile strength constant throughout body?

    Hot potato!

    http://www.ask.com/wiki/Bart%27s_Comet

    Oh wait… I read a paper about this somewhere. ;)

    http://impact.ese.ic.ac.uk/ImpactEffects/

The site is currently under maintenance and will be back shortly. New comments have been disabled during this time, please check back soon.