Question

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.

Answer 1

g =
`0.1m/s^2`

Step-by-step explanation:

From the law of atmosphere

`Nv(y) = n0*e^(-mgy/Kb*T)`

Given:

Kb = Boltzmann's constant =
`1.38*10^-23 J/K`

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 =
`0.1m/s^2`