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miv72 [106K]
3 years ago
10

Suppose the average mass of each of 20,000 asteroids in the solar system is 1017 kg. Compare the total mass of these asteroids t

o the mass of Earth. Assuming a spherical shape and a density of 3000 kg/m3, estimate the diameter of an asteroid having this average mass.
Physics
1 answer:
blondinia [14]3 years ago
6 0

Answer:

The mass of the asteroids is 0.000334896182184 times the mass of the Earth.

39929.4542466 m

Explanation:

Total mass of the asteroids

m_a20000\times 10^{17}=2\times 10^{21}\ kg

m_e = Mass of Earth = 5.972\times 10^{24}\ kg

The ratio is

\dfrac{m_a}{m_e}=\dfrac{2\times 10^{21}}{5.972\times 10^{24}}\\\Rightarrow \dfrac{m_a}{m_e}=0.000334896182184

The mass of the asteroids is 0.000334896182184 times the mass of the Earth.

Volume is given by

V=\dfrac{m}{\rho}\\\Rightarrow \dfrac{4\pi}{3\times 8} d^3=\dfrac{m}{\rho}\\\Rightarrow d^3=\dfrac{3\times 8}{4\pi}\dfrac{m}{\rho}\\\Rightarrow d=(\dfrac{3\times 8}{4\pi}\dfrac{m}{\rho})^{\dfrac{1}{3}}\\\Rightarrow d=(\dfrac{3\times 8}{4\pi}\dfrac{10^{17}}{3000})^{\dfrac{1}{3}}\\\Rightarrow d=39929.4542466\ m

The diameter is 39929.4542466 m

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