The accessibility of the Near Earth Asteroids

In 1925, the German engineer Walter Hohmann published a book, “The Attainability of Celestial Bodies”, in which he lays the foundations of modern interplanetary traveling. He was the first to consider the problem of reaching a planet, and specifically Venus and Mars because at that time space travel was conceivable only with humans on board a spaceship. The basic problem dealt with was the choice of the trajectory that the spacecraft had to follow in order to reach the target planet. Hohmann noticed that Keplerian motion could be used to this end, thus finding “a new use for an old object: the ellipse”. The so-called “Hohmann transferstrategy” consists of connecting the orbit of the Earth to the orbit of the target planet with an elliptic trajectory tangent to both orbits. To actually carry out theorbital transfer a spacecraft has to perform two maneuvers, one to leave Earth’sorbit and the other upon arrival at the planet’s orbit. Because a maneuver produces a change of velocity, Hohmann introduced a quantity, the total ΔV, given by the sum of the velocity variations resulting from the two orbital maneuvers,which is a measure of the accessibility of a celestial body: the higher the ΔV, the less accessible the body. Hohmann focused on the accessibility of the planets and therefore he assumed that the target orbits were coplanar to that of the Earth and that the planets moved on circular orbits. In what follows the possibility of applying the Hohmann transfer strategy to the study of the accessibility of the near-Earth asteroids (NEAs) is discussed. Note that in this case the Hohmann original assumptions are not met because NEAs can have large inclinations and eccentricities. The interest on the accessibility of NEAs has grown in the last decades due to the operation of all-sky surveys, which increased dramatically the NEA discovery rate allowing to detect also small objects with physical properties interesting for both scientific and exploration missions. After giving an overview of the classical Hohmann transfer and of its possible extension, we will see how it can be used in NEA space mission design.