voko said:There is a formula relating the orbital angle and the orbital radius, and so one can easily get the x/y components versus the angle. Dependence on time, however, is implicit.
Cartesian orbit refers to a mathematical representation of an object's position and velocity in 3-dimensional space, using the x, y, and z coordinates. Keplerian orbit, on the other hand, refers to a description of an object's motion around a central body using its orbital elements such as eccentricity and inclination.
Cartesian coordinates can be transformed into Keplerian coordinates using mathematical equations. This allows for a more intuitive understanding of an object's orbital motion and can be helpful in predicting future positions of the object.
Cartesian coordinates are easier to work with mathematically and can be used for more complex orbital scenarios such as multiple-body systems. They also provide a direct representation of an object's position and velocity, making it easier to visualize the orbit.
Kepler's laws describe the motion of planets around the sun in an elliptical orbit. Keplerian orbit uses these laws to represent the motion of any object around a central body, not just planets. The orbital elements used in Keplerian orbit calculations are based on these laws.
Yes, Keplerian orbit can be used to describe the motion of objects in elliptical, parabolic, and hyperbolic orbits. The eccentricity of the orbit determines its shape, with a circular orbit having an eccentricity of 0 and a parabolic or hyperbolic orbit having an eccentricity of 1 or greater.