a circular orbit

A circular orbit is the simplest kind of orbit: the satellite stays at a constant distance from the body it circles, tracing a perfect circle at a steady speed. Picture a ball on a string whirled around your head at fixed radius, except here the string is invisible and made of gravity. It is the neatest picture of orbiting to start from, before we allow orbits to stretch into ovals.

For the circle to hold, gravity must supply exactly the centripetal force needed to keep bending the motion inward: G M m / r^2 = m v^2 / r. This fixes the speed at v = sqrt(G M / r) for a given radius r, and the period at T = 2 pi sqrt(r^3 / G M). Because the distance never changes, the object's speed never changes either, and its gravitational potential energy stays constant too. A circular orbit is really just the special case of an ellipse whose two foci have merged into one centre, an eccentricity of exactly zero.

In practice a perfectly circular orbit is an idealization; real orbits are at least slightly elliptical, and thin atmosphere, an uneven planet, and the pull of other bodies keep nudging them. But the circular case is the workhorse model: it gives clean formulas and good first estimates for satellites and moons, and it is the target for many communications and imaging satellites that want a constant altitude.