Thus the nondimensionalization is not all that important to properly understand the timescales of the solution. In problems that we will do later on there are multiple timescales and in this case a good choice of reference quantities to nondimensionalize is important to both clarify the timescales and suggest simplifying approximations, i.e., terms which can be dropped without significantly increasing degrading the accuracy of the model. We will therefore use the 2 body problem as an exercise in nondimensionalization. We will start with the general equations for the 2 body problem and go through a complete nondimensionalization. Furthermore in any model it is important to indicate exactly what approximations and what assumptions are made so that you can easily see the limitations of the model.
Assumptions Suppose the mass of the sun is and the mass of the planet is .
It will be the case that although we will not use that. Finally, assume that the motion of the planet is confined to a plane so that only 2 coordinates need to be specified. Notation A next component of constructing a model is to set up meaningful notation. Also, let Notice that we are using to denote dimensional quantities. Here we will assume some knowledge of Newtonian physics.