in simplification, you could derive that curvature of the orbit is basically the force between objects, with radius, from the centre of mass. Once you know curvature at a point, you ca define a series of curves fitting, and substitute with other postions to find all constants. And what is curvature? you can find online, that curvature is just a function of second order derivative, and you just have to solve a second degree differential equation.
in simplification, you could derive that curvature of the orbit is basically the force between objects, with radius, from the centre of mass. Once you know curvature at a point, you ca define a series of curves fitting, and substitute with other postions to find all constants. And what is curvature? you can find online, that curvature is just a function of second order derivative, and you just have to solve a second degree differential equation.