A spaceship with a mass of 2.8 × 10⁶ kg is traveling toward two spherical asteroids,each with a mass of 5.0 × 10¹⁶ kg,that are 40 km apart center-to-center.Its path is perpendicular to the line joining the asteroids and is aimed at the midpoint of that line.What is the sum of the gravitational forces exerted by the asteroids on the spaceship when the spaceship is 30 km away from that midpoint? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)12,000 N B)8,000 N C)16,000 N D)6,200 N E)18,000 N

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Quizplus · Accepted Answer

The gravitational force between two objects is given by the equation F = Gm1m2/r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them. In this problem, the spaceship has a mass of 2.8 × 10^6 kg, and the asteroids each have a mass of 5.0 × 10^16 kg. The distance between the spaceship and the midpoint of the line joining the asteroids is 30 km, or 3 × 10^4 m. The gravitational force between the spaceship and each asteroid is therefore:F = Gm1m2/r^2 = (6.67 × 10^-11 N ∙ m^2/kg^2)(2.8 × 10^6 kg)(5.0 × 10^16 kg)/(3 × 10^4 m)^2 = 12,000 NThe sum of the gravitational forces exerted by the asteroids on the spaceship is therefore 12,000 N.

A Spaceship with a Mass of 2