Final answer:
In an elliptical orbit, the highest speed is at the perihelion or perigee, while the slowest speed is at the aphelion or apogee, governed by the laws of conservation of angular momentum and energy.
Step-by-step explanation:
The speed of an object in an elliptical orbit varies depending on its position in that orbit. According to Kepler's second law, sometimes referred to as the law of equal areas, a line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means that when a planet or satellite is closer to the body it is orbiting, it travels faster, and when it is farther away, it travels slower.
The points where the speed is fastest and slowest have specific names: the fastest point is called the perihelion for an orbit around the Sun, and perigee for an orbit around Earth. Conversely, the slowest point is called the aphelion and apogee, respectively. The orbital speed is greatest at perihelion/perigee where the gravitational potential energy is least, and slowest at aphelion/apogee where the gravitational potential energy is greatest.
In terms of conservation laws, the changes in speed are dictated by the conservation of angular momentum and the conservation of energy. As the satellite or planet moves closer to the object it is orbiting, it speeds up to conserve angular momentum, and as it moves away, it slows down. These principles not only help us understand orbits in our solar system but are also essential in designing satellite trajectories and understanding planetary motions.