A new point of view about a biparametric family of anomalies in the elliptic motion

Abstract

One of the main problems in celestial mechanics is the wellknown two-body problem. This problem can be studied by analytical and numerical methods. In the elliptical case, the performance of the numerical method is good if the eccentricity value is not high. The main problem, in this case, is the distribution of the points over the orbit. Given a fixed temporal step size, most points are located in the apoapsis region, while few are in the periapsis region. This paper tries to define a new temporal variable so that the point distribution is higher over the periapsis region than on the apoapsis region. It is also desirable to obtain a higher concentration of points with greater curvature. To this aim, we intend to study a modification of the biparametric family of anomalies.