On an asteroid, the density of dust particles at a height of 3 cm is ~30% of its value just above the surface of the asteroid. Assuming the temperature is 20 K and the average dust-particle mass is 10^-19 kg, estimate the gravitational acceleration on the asteroid.

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dannwaeze45 dannwaeze45 · Answer 1 · 2019-12-24T13:23:10+01:00

Answer:

g =[tex] 0.1m/s^2 [/tex]

Explanation:

From the law of atmosphere

[tex] Nv(y) = n0*e^(-mgy/Kb*T) [/tex]

Given:

Kb = Boltzmann's constant = [tex] 1.38*10^-23 J/K [/tex]

temperature T = 20K

Mass M = 10^-19 kg

Since it is 30% of value above surface, therefore Nv = 0.3n0

Rearranging equation (I) to make g subject of the formula,

g = [ (Kb*T)*in(0.3n0 / n0) ] / (m*y)

Substituting each of the values given in the equation, we obtain

g =[tex] 0.1m/s^2 [/tex]