Spaceman Speff orbits spherical asteroid X with his spaceship. To ...

[bobbysung]

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 What is the mass of planet X? (G = 6.67  10-11 N  m2/kg2)
 
  A) 4.0  1019 kg
  B) 5.1  1017 kg
  C) 4.0  1016 kg
  D) 5.1  1014 kg

Question 2

Shoot a cannonball horizontally from a cannon at a mountain top and it gains speed as it falls and hits the ground below. But fire the cannonball fast enough for circular orbit and no change in speed occurs. Why?
 
  What will be an ideal response?

[brbarasa]

Answer to Question 1

A

Answer to Question 2

Answer: The slower cannonball has a parabolic trajectory with a component of force in its direction of motion. This increases the speed of the falling cannonball. When it is fired in circular orbit, the trajectory is circular and the force is perpendicular all along the path with no component of force in the direction of motion. Put another way, in circular orbit the force of gravity does no work on the cannonball. Therefore there is no change in speed. When fired at a lower speed, where the cannonball arcs downward, a component of force in the direction of motion exists. Then work is done and the cannonball gains kinetic energy.