Although the search for extra-solar co-orbital bodies has not had success so far , it is believed that they must be as common as they are in the Solar System .
Co-orbital systems have been widely studied , and there are several works on stability and even on formation .
However , for the size and location of the stable regions , authors usually describe their results but do not provide a way to find them without numerical simulations , and , in most cases , the mass ratio value range is small .
In the current work , we study the structure of co-orbital stable regions for a wide range of mass ratio systems and built empirical equations to describe them .
It allows estimating the size and location of co-orbital stable regions from a few system’s parameters .
Thousands of massless particles were distributed in the co-orbital region of a massive secondary body and numerically simulated for a wide range of mass ratios ( \mu ) adopting the planar circular restricted three-body problem .
The results show that the horseshoe regions upper limit is between 9.539 \times 10 ^ { -4 } < \mu < 1.192 \times 10 ^ { -3 } , which correspond to a minimum angular distance from the secondary to the separatrix between 27.239 \degree and 27.802 \degree .
We also found that the limit to exist stability in the co-orbital region is about \mu = 2.3313 \times 10 ^ { -2 } , much smaller than the value predicted by the linear theory .
Polynomial functions to describe the stable region parameters were found , and they represent estimates of the angular and radial widths of the co-orbital stable regions for any system with 9.547 \times 10 ^ { -5 } \leq \mu \leq 2.331 \times 10 ^ { -2 } .