The thing is, those systems are valid. They are valid in that they are capable of mathematically describing the observations. Scribing a set of perfect circles with epicycles can both reflect the movement of the planets we observe from our centered position on Earth. (Venus is the one that sketches out the pentagram).they might well turn out to be no more valid than the epicycles of the Ptolemaic and Copernican models of the Solar System. It might be that computational irreducibility means that approximations are the best we can do to describe reality and there is no neat equation or sets of equations to do the job.
They can also describe ellipses directly.
What those methods don't do is accurately convey any cause.
One issue with those two methods were their tendencies to grow in complexity in order to continue describing the irregular effects of a dynamic system controlled by gravity where every object, beyond the Sun and Earth, affected every other object as they moved. When our powers of observation and recording showed more and more variation from the fundamental models, we kept adding more epicycles upon epicycles to describe them. The simpler mathematics of heliocentric ellipses allowed for more accurate estimations with less steps in the math. Today's models have far outstripped any version of Ptolemaic modeling. Every new inconsistencies we discover are, as in the past, meet with another layer of complexity to the accepted system.
But, what are we to do when we have no other good and consistent ideas to replace them with? One question is, what about tweeking a system we have already abandoned? Perhapse our beliefs in the invalid systems of the past, get in the way of searching a potentially productive avenue to understanding?
-Will