Spaceman Speff orbits spherical asteroid X with his spaceship.To remain in a circular orbit at 421 km from the asteroid's center,he should maintain a speed of 80 m/s. What is the mass of planet X?
(G = 6.67 × 10^-11 N • m²/kg²)

Question

Quizplus · Accepted Answer

The correct answer is A because the mass of the planet can be calculated using the formula for centripetal force, which is F = mv^2/r. In this case, the force is provided by the gravitational force between the planet and the spaceship, which is F = G * m1 * m2 / r^2. Setting these two forces equal to each other and solving for m1, the mass of the planet, gives m1 = v^2 * r / G * m2. Plugging in the given values, we get m1 = (80 m/s)^2 * 421 km / (6.67 × 10^-11 N • m^2/kg^2) * m2. Since the mass of the spaceship is negligible compared to the mass of the planet, we can simplify this to m1 = (80 m/s)^2 * 421 km / (6.67 × 10^-11 N • m^2/kg^2). Evaluating this expression gives m1 = 4.0 × 10^19 kg.

Spaceman Speff Orbits Spherical Asteroid X with His Spaceship