For a circular orbit, we can resolve the forces acting on it along the radial and tangential axes. However, along which orthogonal axes should I resolve the forces acting on a body traveling in an elliptical orbit? Also, for many formulas of gravitation along an elliptical orbit, it seems like the radius (from the circular motion equations) are replaced with the length of the semi-major axis. Why is this so?
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1$\begingroup$ Try to have a look here basics.altervista.org/test/Math/analitic_geometry/… for conics in gravitation, and here basics.altervista.org/test/Math/analitic_geometry/conics.html as the main page about conics (Cartesian and polar coordinates, cone sections, conics in gravitation and optics) $\endgroup$– basicsCommented Feb 1 at 11:17
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$\begingroup$ The tangent and radial vectors are only ever orthogonal at perihelion and aphelion. Generally, elliptical orbit problems are solved by clever manipulation of the radial, tangent, angular momentum and Laplace-Runge vectors. The point of commonality between all the conic orbits is that the force is central and proportional to the inverse square. $\endgroup$– Albertus MagnusCommented Feb 1 at 15:25
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On an elliptic Orbit the Center of Gravity is one of the focal points. So there are three forces addingup to Zero. The Gravitation pull, the centrifugal force outward perpendicular to the Tangente, and the Rest, tangential, changing the tangential velocity. This term vanishes in the axis Points.
