The super weapon of GI Joe: Retaliation (spoilers)

Spoiler space for those who haven’t seen it
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In GIJ:R, Cobra was able to somehow place satellites in Earth’s orbit with a devastating new weapon. The satellites were equipped with giant tungsten rods that, in a demonstration on London, would be simply dropped using gravity and achieve an impact several times more than a nuclear weapon.

Owning to my 5th grade science class, I know that tungsten is one of the heaviest, if not the heaviest metal on the periodic table that can be handled safely. Cobra Commander probably was a good student in elementary school.

But I know nothing of the velocity of gravity and the mass of the rods or the height of the satellites. Would something dropped from orbit achieve such large impact as to be more than, let’s say a conventional nuke, or would the close distance from which it was dropped not allow it to achieve speeds that would be that powerful? Cobra Commander specifically said that the only propulsion was gravity. I have a sneaky suspicion that a giant metal rod wouldn’t be able to accelerate to such supersonic speeds

This is a real proposed weapon, but that’s not to say that the depiction of it was right. First of all, you do need some propulsion other than gravity, because you can’t just drop something from orbit onto the Earth. If the satellite opens its bomb bay doors, the rods inside aren’t going to just fall out-- They’re in orbit, too, so they’ll just stay in the bomb bay. Nudge them out gently, and they’ll drift back in. You’d need to give them a pretty hefty kick backwards to get them to hit the surface.

Second, as to the yield, they’d be far short of a nuke, as a moment’s thought would reveal. You can launch a great many such rods into orbit aboard a chemical-propulsion rocket, which has far less energy than a nuclear bomb, and most of that energy even is wasted (rockets are horribly inefficient). So each rod has much less energy than it took to put it in orbit, and the amount of energy it took to put each one in orbit is much less than a single rocket’s worth, and a single rocket is much less than a nuke.

What they’d really be useful for is finely-targeted strikes against relatively small targets. You won’t level a city with one, but you could certainly kill a tank.

Using this site, a rod dropped from the height of a geosynchronous satellite would be traveling about 2000mph when it hit the ground. (If you ignore the effects of atmospheric friction.) That’s pretty damn fast but not “nuclear bomb detonation” fast. And, of course, you can’t drop a bar from a satellite anyway as **Chronos **points out.

Now this doesn’t exactly answer your question but it is somewhat informative: NASA video of the Solid Rocket Booster ascent and descent. You can see that things in space slow down quite substantially with air resistance.
But as a thought experiment to think about the viability of Cobra’s weapon, the rods are going to convert potential energy into kinetic energy as they fall to Earth. Where did they get this potential energy? From rockets lifting the rods into space. So quite simply if the rockets were aimed right at the desired impact point, they could deliver the energy with similar efficiency.

Lastly, meteorites that hit Earth are traveling at much faster speeds than achievable by simple rocketry and since kinetic energy is related to the square of the velocity bring much more energy into any impact event.

But because you made me curious, so if we assume:

  1. No air resistance
  2. Acceleration due to gravity is 9.8m s-2 the whole time
  3. We’ll give a bonus 7.71 km/s speed. (This is the orbital velocity of the ISS and I’ll assume similar height for the drop of the “bomb”)
    a. Through movie making magic, all angular momentum and inertia is ignored and all of this energy is transferred into vertical impact speed
  4. drop altitude 400km
  5. 1000 kg “bomb” (Tungsten and/or density doesn’t matter except for air resistance and the resistance to disintegration at impact)

*Sorry ran out of time, I’ll try to finish up later. Unless someone wants to carry on.