Orbiting bodies move under the influence of gravity on circular or elliptic orbits. The central body that exerts the force on the orbiting body sits at one of the focal points of the ellipse.
The easiest way to understand the interplay between kinetic and potential energy along such an orbit is to realize that the potential energy increases radially from the central body with increasing distance. If you look in the plane of the elliptic orbits, lines of constant pontential are circles. During the course of its motion, if the orbiting body comes closer to the central body, it reduces its potential energy in the gravitational field, i.e., the gravitational force performs acceleration-work on the orbiting body. 246
This work, or loss in potential energy is converted into kinetic energy, i.e., the body gets faster. After moving through the point of the orbit closest to the central body, the orbiting body increases its distance from the central body again, which increases its potential energy in the gravitational field at the cost of kinetic energy, so the work conserved in the form of kinetic energy is given back.
In total, energy is conserved during this kind of motion, because the involved gravitational force is a conservative force. A conservative force $\vec{F}$ can be expressed as the gradient of position ($\vec{r}$) dependent potential energy $V(\vec{r})$, i.e, $$ \vec{F} = -\nabla V(\vec{r}).$$
If you start from <PERSON>'s equation of motion $$ m\frac{d\vec{v}}{dt} = \vec{F} = -\nabla V, $$ you multiply both sides of the equation with velocity $\vec{v}$, you obtain on the left hand side $$ m\frac{d\vec{v}}{dt}\vec{v} = \frac{d}{dt}\left(\frac{1}{2}m\vec{v}^2\right),$$ and on the right hand side $$ -\nabla V\cdot \vec{v} = -\frac{d}{dt}V(\vec{r}),$$ such that $$ \frac{d}{dt}\left(\frac{1}{2}m\vec{v}^2 + V(\vec{r})\right) = 0.$$ This means that for conservative forces, the sum of kinetic and potential energies is always time-independent, i.e., conserved. All a mechanical system can do in such a situation is to shuffle energy back and forth between kinetic and potential energy. They cannot consume energy (in physics we would say, they do not dissipate energy).
This is what happens during orbital motion in a gravitational field, where the potential energy is given by $$ V(\vec{r})\propto -\frac{1}{|\vec{r}|},$$ if the central body sits in the origin. 766