The Udwadia?Kalaba equation is a simple, aesthetic, and thought-provoking description of the world
at a very fundamental level. It is about the way systems move. In this paper, we creatively apply
the Udwadia?Kalaba approach to study heavenly bodies? movements (especially on Kepler?s law and the
inverse square law of gravitation). In an alternative way, we show that a heavenly body?s motion
orbit can be an ellipse, a circle, a hyperbola, or a parabola and show the conservation of angular
momentum. Furthermore, by applying the Udwadia?Kalaba approach, we use the constraint of motion
orbit (ellipse, circle, hyperbola, or parabola) and the conservation of angular momentum constraint
(or energy conservation constraint) and easily verify that any heavenly body?s motion complies with
the inverse square law of gravitation. That is, we study Kepler?s law and Newton?s inverse square
law in an analytical way, which makes the dynamicist more clear about the way heavenly bodies move
and also…