Ceres, the largest asteroid known, has a mass of roughly 8.7 x1020 kg. If Ceres passes within 12,000km of the spaceship (2.75e4kg) in which you are traveling, what force does it exert on the spaceship?

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Question:

Ceres, the largest asteroid known, has a mass of roughly 8.7 x1020 kg. If Ceres passes within 12,000km of the spaceship (2.75e4kg) in which you are traveling, what force does it exert on the spaceship?

Answers

Answer:11.1 NExplanation:The gravitational force between the asteroid and the ship is given by:[tex]F=G\frac{mM}{R^2}[/tex]where[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1} s^{-2}[/tex] is the gravitational constant[tex]M=8.7\cdot 10^{20} kg[/tex] is the mass of the asteroid[tex]m=2.75\cdot 10^4 kg[/tex] is the mass of the spaceship[tex]R=12,000 km=1.2\cdot 10^7 m[/tex] is the distance between the asteroid and the spaceshipSubstituting numbers into the equation, we find the force[tex]F=(6.67\cdot 10^{-11})\frac{(2.75\cdot 10^4 kg)(8.7\cdot 10^{20} kg)}{(1.2\cdot 10^7 m)^2}=11.1 N[/tex]

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