I am trying to figure out how an object could achieve a perfectly circular orbit. Given a mass for the planet or other body the object is orbiting and a distance from the center of mass, how fast would the object have to be moving perpendicular to the center of mass?
My initial assumption was it would have to be travelling horizontally (relatively speaking) as fast as it was falling towards to center of mass. Is this a correct assumption? I guess I am confused because it is easy to calculate the acceleration towards the center of mass given the distance and mass of the body, but I have no idea how you would go about calculating the velocity necessary.