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 net gravitational force 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 net gravitational force on the spaceship is the vector sum of the gravitational forces exerted by the two asteroids. The gravitational force exerted by each asteroid is given by:$$F = G \frac{m_1 m_2}{r^2}$$where:* G is the gravitational constant (6.67 × 10^-11 N ∙ m^2/kg^2)* m_1 is the mass of the asteroid (5.0 × 10^16 kg)* m_2 is the mass of the spaceship (2.8 × 10^6 kg)* r is the distance between the asteroid and the spaceship (30 km = 30,000 m)The net gravitational force is:$$F_net = F_1 + F_2 = G \frac{m_1 m_2}{r^2} + G \frac{m_1 m_2}{r^2} = 2G \frac{m_1 m_2}{r^2}$$Plugging in the values, we get:$$F_net = 2(6.67 × 10^-11 N ∙ m^2/kg^2) \frac{(5.0 × 10^16 kg)(2.8 × 10^6 kg)}{(30,000 m)^2} = 12,000 N$$Therefore, the correct answer is A.

A Spaceship with a Mass of 2