Acceleration in elliptical orbits
A planet is orbiting a star in an elliptical path. At the instant shown in the diagram, find the direction of the net acceleration of the planet.
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Since the distance from the center of the orbit is non-uniform because it is an ellipse rather than a circular orbit, there is a tangential acceleration as well as a centripetal acceleration because the velocity is non-zero. The magnitude of the acceleration can be given by the Pythagorean Theorem, using the square root of the sums of the squares of both the centripetal and tangential accelerations. Drawing a vector diagram of this resulting vector will show that dir(a) points towards S.