The conics (the
orbits solution of the 2body problem) were found by Newton, who
invented the infinitesimal calculus to solve this precise
problem. But to determine in which orbit the body will lie, it is
necessary to introduce another concept: the binding Energy of the
object.
First of all, it is necessary to understand
that no physical process can happen without spending some energy
(heating a house, walking, etc). In other words, energy can be
seen as a veritable money, with different currency that can be
changed.
In particular, the binding
energy E is a measure of how much a body is tied
to another : it corresponds to the work necessary to
bring the two bodies at an infinite distance. This energy
can be negative if the two bodies are gravitationally
bound (as in the case of closed orbits, such as the
circle or the ellipse) or positive if the two bodies are
not bound, and the orbit is opened.
The value of the binding energy E is inversely
proportional and of opposite sign of the major axes. This
means that a very little semiaxis corresponds to a
strongly negative energy and therefore to a very bound
orbit. 
