The Palermo Technical Impact Hazard Scale P is used to quantify the risk associa

Question

The Palermo Technical Impact Hazard Scale P is used to quantify the risk associated with the impact of an asteroid collidig with the earth:

P = log(PiE0.8/0.03T)

where Pi is the probability of impact occuring in T years and E is the energy of impact (in megatons of TNT). The risk is greater that a random event of similar magnitude if P > 0 (asteroids observed in 2006 have P <= -2, indicating low risk).

1) Calculate dP/dT, assuming that Pi = 2 x 10-5 and E = 2 megatons.

2) Use the derivative to estimate the approximate change in P if T increases to 26 years.

Explanation / Answer

a. dP/dT = [.03*T/(ln10*p*E^.8)]*[-p*E^.8/(.03*T^2)]
= 1/(ln10*.03*T)

b.For a change in T of 26 years, P will change by 1/(ln10*.03*26) = .55679

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