Ascience fiction story i once read had the premise that a small, heavy piece of rock could orbit a planet at a height of 1.5 m. because of this, the natives would always duck down when walking across the small moon's path, a behavior that seemed inexplicable to the explorers who had recently arrived but who didn't know about the moon. if air resistance weren't a problem, and such a situation existed on earth, (a) how fast would the moon travel and (b) how long would the orbital period be

Explanation:

The force of gravity between the Earth, of mass and a rock of mass m orbiting at a distance that would be the radius of the Earth R=6371000m (1.5m is insignificant) would be:

Where is the gravitational constant.

Under this force, the rock experiments a (centripetal) acceleration given by:

Putting all together:

Which for our values is:

And since the circumference of the orbit would be , the time taken to travel it would be:

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west