Celestial Mechanics

Is this a homework question?
You have to at least try and answer it, describe what you know and any ideas you have about the solution

 

It's not impossible, but the energy expenditure would be ridiculous. If you're referring to ballistic orbits, I suspect that it's because an orbital period of less than 80 minutes would put the object inside the atmosphere. (Although, I haven't actually heard of that limit before.)

edit: Sorry, Mgb; didn't mean to step on your toes here. I started this response before seeing yours. It didn't occur to me that it might be a homework problem.

 

Because the centrifugal force would be greater than gravitational, unless you compensate it some other way. Computing this you get the minimal period something about 84 minutes.

 

Surely the definition of an orbit is that centrifugal force equals the gravitational.

If you calculate the height necessary for an 84min orbit and compare it to the height of the atmosphere / density of the atmosphere at that height you will see why a satelite orbiting at that height isn't going to last long.

you could orbit the Earth at sea level if you had an air free pipe to avoid air resistance.