3 ms·
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
by eesmith 1y ago
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.
- nandomrumber 1y ago1040 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.
- nandomrumber 1y agoIn light of the error in the parent comments math, I retract my previous comment and substitute the following bit of awkward silence: …
- defrost 1y agoWe 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.
- nandomrumber 1y agoOops. 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
- dalke 1y agoImagine how I feel every time I see "Dalek" instead of my surname.
- ars 1y ago90 m/s? Way too slow, it's more like 70km/s (or 90) - seems you left out a k.
- eesmith 1y agoYes, that was my error - thanks!
- perihelions 1y agoI 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]
- eesmith 1y agoMy mistaken use of m/s instead of km/s, in a squared term, indeed gives a HUGE difference. Thanks!
- Voultapher 1y agoBased on the corrected 90 km/s instead of m/s it should be 52 pt (peta-ton) impact.
- eesmith 1y agoLet'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-history-mauna-kea 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.