Cobos, my former professor of Mechanics and Waves I would fill several boards to explain why the orbits are elliptical and as such, represent the minimum energy of an object that orbits another, that is … everyone.
This, formerly, except for Kelpler who mathematically “wrote” to mortals, the rest, they care a cucumber even when no GPS coverage, mainly because they do not realize because of our limited memory (visual).
But taking a picture with a camera on the moon at perihelion (the closer) and apogee (the farther) from its orbit and comparing them is fully observable by the size difference. In fact, the difference is around 30%, which indicates where the focus of the orbit and who is in this focus, the Earth.
Thanks to Kepler could easily calculate the orbital period of the stars (ease and precision fuck) just by knowing the distance of the semi-major axis (remember that is an ellipse with two axles and that this period does not depend on the eccentricity of the orbit. Hence the speed bag is the body depends on the distance to the focus being quicker to lower this distance. Come on, it runs faster when it is closer and slows down, the farther this. All this because the sweeping the body area should be equal regardless of the distance and the only way this is accomplished.
By studying the orbits of Kepler, Newton could make mathematically formulate the laws of universal gravitation known to all.