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Alecsey [184]
3 years ago
11

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. A

ssuming the temperature is 20 K and the average dust-particle mass is 10-19 kg. Estimate the gravitational acceleration on the asteroid.a. 2 m/s^2b. 10 m/s^2c. 0.1m/s^2
Physics
1 answer:
Anvisha [2.4K]3 years ago
4 0

From the law of atmosphere

N_v(y) = n_0*e^{-\frac{mgy}{Kb*T}}

Where

n_0 = constant and is number density where the height y = 0cm

n_V = Number density at height y=3cm

Kb = Boltzmann constant = 1.38*10^{-23}J/K

T=20K

m = 10^{-19}kg

Re-arranging the equation to have the value of the gravity,

\frac{N_v(y)}{n_0} = e^{-\frac{mghy}{KbT}}

ln(\frac{N_v(y)}{n_0}) = -\frac{mgy}{KbT}

Since it is 30% of value above surface, therefore N_v = 0.3n_0

ln(\frac{0.3n_0}{n_0}) = -\frac{mgy}{KbT}

g = -\frac{KbT ln(0.3)}{my}

g = -\frac{(1.38*10^{-23}J/K)(20K)(Ln(0.3))}{10^{-19}(3*10^{-2})}

g = \frac{1.38*2*ln(0.3)*10^{-22}}{3*10^{-4}}

g = 1.104*10^{-1}m/s^2

g = 0.1m/s^2

Therefore the correct answer is C.

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