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 radius of the asteroid. Plugging in the given values, we get: 14.6 km/s = sqrt(2 * 6.67 × 10^-11 N ∙ m^2/kg^2 * M / (6371 km + 2300 km)). Solving for M, we get: M = 1.8 × 10^24 kg.

A Satellite Is in Circular Orbit at an Altitude of 2300