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An astronaut, whose mission is to go where no one has gone before, lands on a spherical planet in a distant galaxy. As she stands on the surface of the planet, she releases a small rock from rest and finds that it takes the rock 0.540 s to fall 1.90 m. If the radius of the planet is 8.60×107 m, what is the mass of the planet?

Respuesta :

Answer:

The mass of the planet is [tex]M_{planet} =[/tex] 144.5 × [tex]10^{25}[/tex] kg

Explanation:

We know that g for the planet is given by

[tex]g = G \frac{M_{planet} }{r^{2} }[/tex]

[tex]M_{planet} = \frac{gr^{2} }{G}[/tex] --------- (1)

Acceleration is given by

[tex]a = \frac{2(y_2-y_1)}{t^{2} }[/tex]

[tex]a = \frac{2(1.90)}{0.54^{2} }[/tex]

[tex]a = g = 13.03 \frac{m}{s^{2} }[/tex]

Radius of the planet R = 8.6 × [tex]10^{7}[/tex] meter

Now put the value of g  & R in equation (1)

[tex]M_{planet} = \frac{(13.03)(8.6)^{2}(10^{14} ) }{6.67 (10^{-11} )}[/tex]

[tex]M_{planet} =[/tex] 144.5 × [tex]10^{25}[/tex] kg

Therefore the mass of the planet is [tex]M_{planet} =[/tex] 144.5 × [tex]10^{25}[/tex] kg

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