# North Korea’s ICBM test Succeeds

The distance of the impact point, 430 miles, is irrelevant. The height it reached, 1245 miles (=2000km), indicates it was a test of of part of an ICBM.

Physics for poets: You can travel 430 miles in a rowboat. It requires little of what physics calls “work.” But how high can you jump? The height requires energy, which is roughly proportional to the height reached by the missile. North Korea tested the energy of the missile by launching it almost straight up.

We can tell how much energy the missile had by the height it reached. This then tells us how fast it would have flown in the more horizontal trajectory of an ICBM.  Your precocious high school physics student will tell you to use this relationship: P.E. = K.E., potential energy = kinetic energy.

An ICBM does not have to reach orbital velocity. It needs to reach about 15,000 mph = 24000km/hr = 6.7 km/second The energy required by an ICBM is about 65% that of a missile that achieves orbital trajectory.

Did the missile have enough potential energy at the peak height of 2000 km to qualify as an ICBM? Equating kinetic energy with potential energy, which we know from the height, let’s calculate the height the missile could reach if it were an ICBM with a speed of 24000 km/hr:

1/2*m*v^2 = m*g*h. Spelling out,

1/2 X (mass of missile) X velocity of missile squared =

mass of missile X gravitational constant X height

where

“m”, what you might call the “weight” of the missile, cancels out. It makes no difference.

g is the gravitational constant, 9.8 meters/second squared.

h = the height the missile reached.

v^2 = 2*g*h. Now solve for h.

h = 2290  km, which is very close to the reported height of 2000km. It indicates a missile with enough range to reach some targets in the U.S. A little faster, and it could hit anywhere.

Conclusion: North Korea has tested a rocket which, for all intents and purposes, the “practical truth” of journalism, is an ICBM.

Pundits will probably try to buy us a few more minutes of peace by pointing out that it has not been demonstrated with all the pieces in place, an “end-to-end” test. That will happen when the missile is fired in a flatter trajectory. It may also reveal the uncomfortable truth about missile defense systems: none of them satisfy a benefit analysis.

To clarify, let’s make it concrete. Suppose the calculation is for a bitter war in which you are attempting to defend the battlefield from a missile attack. Since this is war, your forces might be attrited (reduced) by 50% in a week, or, in the case of nuclear war, in a day. In this case, a missile defense that works 90% of the time can markedly reduce the attrition of your forces, so that at least some of your soldiers are alive when those of the enemy are mostly dead.

Now consider what 90% means with New York City. Every time the enemy lobs a missile, there is a 10% chance NY will be destroyed. We solved this problem better with the various doctrines related to MAD, “mutual assured destruction.” But the assumptions of MAD require that the adversary is more like us than different.

About an ICBM test, Donald Trump said, (NY TImes) “It  won’t happen.”

Now it has.