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Comment by jl6 | Hacker News Reader

Assuming it’s at the upper range of the size estimate above, and of average rocky density, the kinetic energy of the impact would be something like a 10 billion megaton nuke.

If we could steer it to hit one of Mars’s poles, it might do a bit of terraforming for us!

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Where did my math go wrong? I got about 50,000 megatons. Assuming the high-end of 22km and a rocky/metallic density of 5000 kg/cubic meter (and assuming it's a cube):

  kinetic energy = 1/2 m v**2 = 1/2 * size * density * v**2
  = 1/2 *(22000 m)**3 * (5000 kg/m**3) * (90 m/s)**2 / (4.184E15 J/megaton)
  = 52,000 megaton

If it's an icy comet then the density is more like 500 kg/cubic meter, or 1/10th that number.

1040 x more energy that the Tsar Bomba.

Or 5-ish Tsar Bomba per country on Earth.

Or 3466 Hiroshima nukes.

Or 17 Hiroshima nukes per country.

In light of the error in the parent comments math, I retract my previous comment and substitute the following bit of awkward silence:

…

We all make mistakes, as the Dalek said climbing off the dustbin.

FWiW .. here's mine (or is it?)

One Tsar Bomba ~ 50 megatonne. One Hiroshima bomb ~ 15 kilotonne.

One Tsar Bomba ~ 50,000 / 15 ~ 3,333 Hiroshima bombs.

1,040 x Tsar Bomba ~ 3,466,667 Hiroshima bombs.

Oops.

Every time I see your username I can’t help but say it in my mind as Defrost Kelly, some kind of frozen Dr. Leonard "Bones" McCoy

Imagine how I feel every time I see "Dalek" instead of my surname.

90 m/s?

Way too slow, it's more like 70km/s (or 90) - seems you left out a k.

Yes, that was my error - thanks!

I can not confirm this; the parent calculation is the correct one. I can't immediately find what your error was. (edit: It's your [km/s]—you wrote [m/s] by mistake).

    (let* ((ρ ([g (cm -3)] 5))
           (d ([km] 22))
           (m (* ρ (expt d 3)))
           (v ([km (s -1)] 90))
           (ke (* 1/2 m (expt v 2)))
           (kg-tnt ([J (kg -1)] 4.2e6)))
      (values (/ ke kg-tnt)
       (as [megaton] (/ ke kg-tnt))))
    
    5.133857142857142e19 [KG]
    5.133857142857143e10 [MEGATON]

My mistaken use of m/s instead of km/s, in a squared term, indeed gives a HUGE difference.

Thanks!

Based on the corrected 90 km/s instead of m/s it should be 52 pt (peta-ton) impact.

Let's see if I get this math right.

Mauna Loa is about 95,000 km3 in volume says https://www.usgs.gov/volcanoes/mauna-kea/science/geology-and... . Density of TNT is 1.6g/cm3:

  95000 km3 * (1000m/km)**3 * 1600 kg/m3 = ~1.5E17 = 150 pt.

1/3rd of the mountain in TNT.

Nope, I can't conceive of that much energy.

…and after just a few million years to settle down again, we’ll be ready to visit blue sky on Mars!

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