A satellite is in circular orbit at an altitude of 2300 km above the surface of a nonrotating asteroid with an orbital speed of 5.9 km/s.The minimum speed needed to escape from the surface of the asteroid is 14.6 km/s,and G = 6.67 × 10^-11 N ∙ m²/kg².The mass of the asteroid is closest to A)1.8 × 10²⁴_kg. B)8.9 × 10²³_kg. C)1.3 × 10²⁴_kg. D)2.7 × 10²⁴_kg. E)3.6 × 10²⁴_kg.

Question

Quizplus · Accepted Answer

The correct answer is A because the mass of the asteroid can be calculated using the formula for the escape velocity: v = sqrt(2GM/r), where v is the escape velocity, G is the gravitational constant, M is the mass of the asteroid, and r is the distance from the center of the asteroid to the surface. Plugging in the given values, we get: 14.6 km/s = sqrt(2 * 6.67 × 10^-11 N ∙ m^2/kg^2 * M / (2300 km + 6371 km)). Solving for M, we get: M = 1.8 × 10^24 kg.

A Satellite Is in Circular Orbit at an Altitude of 2300