The author concludes that, according to Newtonian theory, we don’t need a theory of the structure/constitution of the Sun/planets in order to calculate their orbits. Why?

Because according to Newtonian theory, gravitational force between two bodies depends exclusively on mass/distance, and does not depend on what the bodies are made of.

The conclusion brings up a new concept — what’s required to “calculate orbits.” The premises don’t say anything about what’s required or not required to calculate orbits. So, at a minimum, we know the correct answer must include something about what’s required or not required to calculate orbits.

To go further, we can try to anticipate a more specific connection between the premise and the conclusion. The premise establishes that to calculate gravitational force, we don’t need to consider “what the bodies are made of.” That part supports the idea that, in order to calculate graviational force, we don’t need to consider the structure/constitution of a body (because structure/constitution concerns what bodies are made of).

But what if calculating the orbits of bodies involves more than just calculating gravitational force between them? That opens the possibility that structure/constitution could be important for other factors that are relevant to calculating orbits. We want to eliminate this possibility. We want to establish that in order to calculate orbits, we don’t need anything else besides calculating gravitational force.