An undiscovered planet, many light-years from Earth, has one moon, which has a nearly circular periodic orbit. The distance from the center of the moon to the surface of the planet is 2.120 × 105 km and the planet has a radius of 3275 km and a mass of 6.55 × 1022 kg.
The gravitational constant is 6.67 × 10-11 N.m2/kg2.
How long T, in days, does it take the moon to make one revolution around the planet?
A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds.
Assume that the asteroid is approximately spherical, with an average density ρ = 24110 g/m3 and volume V = 2.63 × 1011 m3. Recall that the universal gravitational constant is G = 6.67 × 10-11 N-m2/kg2.
With what minimum initial speed vesc will the rocks need to be thrown in order for them never to fall back to the asteroid?
vesc = m/s