Design of Near-optimal Earth Escape Orbits for Solar Sail Spacecraft

With the increase of the interest in solar sailing, it is required to provide a basis for future detailed planetary escape mission analysis by drawing together prior work, clarifying and explaining previously anomalies. In this paper, a technique for escaping the Earth by using a solar sail is developed and numerically simulated. The spacecraft is initially in a geosynchronous transfer orbit (GTO). Blended solar sail analytical control law, explicitly independent of time, are then presented, which provide near-optimal escape trajectories and maintain a safe minimum altitude and which are suitable as a potential autonomous onboard controller. This control law is investigated from a range of initial conditions and is shown to maintain the optimality previously demonstrated by the use of a single-energy gain control law but without the risk of planetary collision. Finally, it is shown that the blending solar sail analytical control law is suitable for solar sail on-board autonomously control system.

Tangent-impulse transfer from elliptic orbit to an excess velocity vector

The two-body orbital transfer problem from an elliptic parking orbit to an excess veloc-ity vector with the tangent impulse is studied. The direction of the impulse is constrained to be aligned with the velocity vector, then speed changes are enough to nullify the relative velocity. First, if one tangent impulse is used, the transfer orbit is obtained by solving a single-variable function about the true anomaly of the initial orbit. For the initial circular orbit, the closed-form solution is derived. For the initial elliptic orbit, the discontinuous point is solved, then the initial true anomaly is obtained by a numerical iterative approach; moreover, an alternative method is proposed to avoid the singularity. There is only one solution for one-tangent-impulse escape trajectory. Then, based on the one-tangent-impulse solution, the minimum-energy multi-tangent-impulse escape trajectory is obtained by a numerical optimization algorithm, e.g., the genetic method. Finally, several examples are provided to validate the proposed method. The numerical results show that the minimum-energy multi-tangent-impulse escape trajectory is the same as the one-tangent-impulse trajectory.

Empirical studies of escape behavior find mixed support for the race for life model

Escape theory has been exceptionally successful in conceptualizing and accurately predicting effects of numerous factors that affect predation risk and explaining variation in flight initiation distance(FID;predator–prey distance when escape begins).Less explored is the relative orientation of an approaching predator,prey,and its eventual refuge.The relationship between an approaching threat and its refuge can be expressed as an angle we call the“interpath angle”or“Φ,”which describes the angle between the paths of predator and prey to the prey’s refuge and thus expresses the degree to which prey must run toward an approaching predator.In general,we might expect that prey would escape at greater distances if they must flee toward a predator to reach its burrow.The“race for life”model makes formal predictions about howΦshould affect FID.We evaluated the model by studying escape decisions in yellow-bellied marmots Marmota flaviventer,a species which flees to burrows.We found support for some of the model’s predictions,yet the relationship betweenΦand FID was less clear.Marmots may not assessΦin a continuous fashion;but we found that binning angle into 445°bins explained a similar amount of variation as models that analyzed angle continuously.Future studies ofΦ,especially those that focus on how different species perceive relative orientation,will likely enhance our understanding of its importance in flight decisions.