TABULA/samples/Asteroid Impact

This is SAMPLE2. To work with this sample, enter $2

Asteroid Impact
┌ {1}   2.500 m          asteroid radius
├ {2}   90000 mph        speed=
├ {3}       1 /          relative density=
└>{4}   0.883 Hiroshima  asteroid impact energy

Rationale

A spherical asteroid of radius 2.5 m (2.5 metres, or 8.202 feet) hits the earth, releasing all its kinetic energy. It is travelling at 90,000 miles per hour. How big a bang would it make?

This t-table estimates the resulting bang as almost as big as the world's first combat nuclear bomb Little Boy, dropped on Hiroshima, Japan, on 6 August 1945.

Let's call the energy of such a bang the asteroid impact energy, expressed in Hiroshimas. Define 1 Hiroshima to be 6E13 J (6 times 10^13 Joules).

This is only an estimate of the bomb's yield, since precise measurements were not made at the time. (But our unit of energy is precise, because that is how we define it.)

Question 1. What radius of asteroid would deliver precisely 1 Hiroshima, all other things being equal?

Question 2. Alternatively, to deliver precisely 1 Hiroshima, how fast would the original 2.5 m radius asteroid need to be travelling?

Question 3. To deliver precisely 1 Hiroshima, what relative density would a 2.5 m radius asteroid travelling at 90,000 miles per hour need to be?

Try it out

Select line {1} and enter 3

line {4} changes to 1.525 Hiroshima. That's too great.

You could try entering different numbers until line {4} becomes 1. But there's a quicker way…

Select line {4} and change its value to 1

line {1} changes to 2.606 m. That's the value {1} needs, to make {4} become 1.

That answers Question 1… 2.606 m

Notice these things

a slight increase in radius increases the asteroid impact energy a lot. (Why?)
when you altered {4}, only {1} changed. That's because lines {2} and {3} have been held.

Answer Question 2

Go back to the original sample (enter $2)

Hold line {1} and unhold line {2}.

Select line {4} and enter: 1

line {2} becomes (approx) 95791.9

Answer Question 3

Go back to the original sample (enter $2)

Hold lines {1} and {2}, and unhold line {3}.

Select line {4} and enter: 1

line {3} becomes (approx) 1.133.

Build this t-table

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