Hippasos said:I guess there is generalization to 3D as well somewhere...
Or is that really necessary?
An elliptical orbit is a type of orbit in which an object, such as a planet or satellite, travels around another object in an oval or elliptical path. This path is determined by the gravitational pull of the larger object and the speed and direction of the smaller object.
The focus of an elliptical orbit is determined by the distance between the center of the larger object and the center of the smaller object. This distance, known as the semi-major axis, is half of the longest diameter of the elliptical orbit.
The focus of an elliptical orbit is one of the two fixed points inside the orbit, while the center is the midpoint of the line connecting the two focus points. The center of an elliptical orbit does not necessarily coincide with the center of the larger object it is orbiting around.
An object's speed in an elliptical orbit is not constant. It is fastest at the closest point to the larger object, known as the perihelion, and slowest at the furthest point, known as the aphelion. This is due to the conservation of angular momentum and the varying strength of the gravitational force.
Yes, it is possible for an object to have an elliptical orbit around more than one object. This is known as a three-body or n-body problem and can be seen in some planetary systems, where a planet orbits around two stars or a moon orbits around a planet and a larger moon.