Question

2. A strange spherical asteroid has a density of 5200. kg/m2 with an outer radius of 200.0 km, Symmetricalily in the center of the asteroid is a spherical cavity 75.0 km in diameter. A 2500. kg spacecraft from Earth orbits the asteroic 25.0 km above its surface in a circular orbit. What is the orbital period (in hours) of the spacecraft? Ignore the gravity of all other bodies.

Answer 1

Given data, A strange spherical asteroid has a density of 5200 kg/m^3 with an outer radius of 200.0 km. symmetrically in the center of the asteroid is a spherical cavity 75.0 km in diameter. A 2500 kg space craft from earth orbits the asteroid 25.0 km above its surface in a circular orbit. the orbital period (in hours) of the space craft. from earth orbit Ignore the gravity of all other bodies Density of the asteroid p = 5200 kg/m^3 outer radius R = 200 km Inner radius r = 75/2 = 37.5 km Mass of the spacecraft m = 2500 kg Height of the spacecraft from the surface of asteroid h = 25 km Now the mass of the asteroid is \r\n M = pv = 5200 times 4/3 pi (R^3 - r^3) m = 1.73 times 10^20 kg Now using the force motion condition M (R + h) w^2 = GMM/(R + h)^2 w^2 = GM/(R + h)^3