Direct solar radiation pressure on the orbits of small near–Earth asteroids: observable effects?

We consider the perturbations of Near–Earth Asteroid orbits due to direct solar radiation pressure (both the absorption and the reflection components). When the body is spherical and the surface albedo homogeneous the effect is small (and only short–periodic). However, when at least one of these restrictive and unrealistic assumptions is relaxed, long–term orbital effects appear and they may potentially lead to observable displacement of the orbit. We illustrate this conclusion by computing the orbital perturbations due to radiation pressure for objects with an odd–zonal distribution of albedo and for objects with ellipsoidal shape. Especially in the first case the effects are large, due to the long–term perturbations of the semimajor axis. For high–eccentricity orbits observed over a long interval of time, the (v/c)–correction of the direct radiation pressure, known as Poynting–Robertson effect, should be also considered. As an example we demonstrate that for the asteroid 1566 Icarus, during its next close approach to the Earth, the orbit displacement due to the direct solar radiation forces might be, under reasonable assumptions, comparable to the orbit determination uncertainty, thus potentially observable.