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Karl Schwarzschild’s landmark paper revealed the first ever exact solution to Einstein’s gravitational field equation. This was a major scientific achievement. However, his solution for the metric of a spherically symmetric spacetime is different than the one found in textbooks today— because Schwarzschild assumed, like in Newtonian gravity, that only one singularity could exist. Given the newness of Einstein’s general theory of relativity and the existing paradigm of Newtonian gravity, his assumption was natural. While other authors have previously pointed out this shortcoming and corrected it, the contribution of this paper is to show how Schwarzschild might have discovered it himself. A simple geometric proof indicates how Schwarzschild, with a different assignment of a single constant of integration, would have arrived at the metric found in textbooks today. [ABSTRACT FROM AUTHOR]

Interstellar space missions will require spacecraft that travel at relativistic speeds. Furthermore, their trajectories will be influenced by gravitational sources. Accordingly, this paper applies to interstellar missions a recently developed formulation of relativistic mechanics that predicts a spacecraft's trajectory when it passes by a gravitational source at a relativistic speed. The formulation, called spacetime impetus, is unique in that it employs a relativistic universal law of gravitation that does not explicitly require general relativity while producing precisely the same results. Based on these developments, an analyst can now update nonrelativistic mission planning codes to give them general relativistic capabilities. It requires augmenting the code with relativistic velocities and relativistic accelerations, the replacement of the universal law of gravitation with a relativistic universal law of gravitation, and setting up Lorentz transformations between frames. [ABSTRACT FROM AUTHOR]

This article tests the hypothesis that "the likelihood that the species will react and level at which they do to the unmanned aerial vehicle (UAV) is related to the altitude, number of passes, sound intensity, type of UAV, takeoff distance, and species." This paper examined the behavioral responses of a group of free ranging ungulate species (Oryx, Kudu, Springbok, Giraffe, Eland, Hartebeest, and Impala) found in an animal reserve in Namibia to the presence of different in-flight UAV models. The study included 397 passes (trials) over 99 flights at altitudes ranging from 15 to 55 meters in three categories of response level: No response, Alert, and Movement. The ungulates were unhabituated to the UAVs and the study was conducted in the presence of stress-inducing events that occur naturally in the environment. Certain species were found to be more reactive than others, in addition to several displaying different response levels in single or mixed herd environments. Zebras were found to be less responsive in mixed herd environments while Oryx were present, as compared to when the Oryx were not; suggesting that some species may respond based on other species perception of threat or their relative fitness levels. The UAVs also produced inconsistent response rates between movement and alert behavior. The reference vehicle, Phantom 3 was much more likely than the Mavic to induce an alert response, while both having similar probabilities of inducing a movement response. Furthermore, the Custom X8 showed significantly more alert and movement responses than the other UAVs. This shows there may be several aspects to the UAVs that affect the responses of the ungulates. For instance, the sound intensity may alert the species more often, but close proximity may induce a movement response. More generally, the data shows that when the UAV is flying above 50 meters and has a measured sound intensity below 50 dB, the likelihood of inducing a movement response on an ungulate species is below 6% regardless of the vehicle on the first pass over the animals. Additionally, with each subsequent pass the likelihood of response dropped by approximately 20 percent. The results suggest a stronger correlation between flight altitude and response across the different ungulates, and the evidence suggests rapid habituation to the UAVs. [ABSTRACT FROM AUTHOR]

A novel method was developed for locating and allowing gliders to stay in thermals (convective updrafts). The method was applied to a 5 kg, glider, called ALOFT (autonomous locator of thermals), that was entered in the 2008 Montague Cross-Country Challenge held on 13-15 June 2008 in Montague, California. In this competition, remote-controlled gliders in the 5 kg class competed on the basis of speed and distance. ALOFT was the first known autonomously soaring aircraft to enter a soaring competition and its entry provided a valuable comparison between the effectiveness of manual soaring and autonomous soaring. ALOFT placed third in the competition in overall points, outperforming manually-flown aircraft in its ability to center and use updrafts, especially at higher altitudes and in the presence of wind, to fly more optimal airspeeds, and to fly directly between turn points. The results confirm that autonomous soaring is a bona fide engineering subdiscipline, which is expected to be of interest to engineers, who might find that this has some utility in the aviation industry. DOI: 10.2514/1.C000287