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Cerrena [4.2K]
3 years ago
10

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid

Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids? Show all work and circle answe
Physics
1 answer:
mariarad [96]3 years ago
4 0

Answer:

0.05806

Explanation:

m_x = Mass of asteroid x

m_y = Mass of asteroid y

r_x = Distance from asteroid x = 140 km

r_y = Distance from asteroid y = 581 km

m = Mass of asteroid

Force of gravity between asteroid x and the astronaut

F_1=\frac{Gm_xm}{r_x^2}\\\Rightarrow F_1=\frac{Gm_xm}{140^2}

Force of gravity between asteroid x and the astronaut

F_2=\frac{Gm_ym}{r_y^2}\\\Rightarrow F_2=\frac{Gm_ym}{581^2}

Here these two forces are equal as they are in equilibrium

\frac{Gm_xm}{140^2}=\frac{Gm_ym}{581^2}\\\Rightarrow \frac{m_x}{140^2}=\frac{m_y}{581^2}\\\Rightarrow \frac{m_x}{m_y}=\frac{140^2}{581^2}\\\Rightarrow \frac{m_x}{m_y}=0.05806

The ratio of the masses of the asteroid is 0.05806

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