In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point $L_1$ and the other around $L_2,$ with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to $L_1$ and $L_2$ as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the “interior” and “exterior” Hill’s regions and other resonant phenomena.

Small unmanned aircraft systems (sUAS) are rapidly transforming atmospheric research. With the advancement of the development and application of these systems, improving knowledge of best practices for accurate measurement is critical for achieving scientific goals. We present results from an intercomparison of atmospheric measurement data from the Lower Atmospheric Process Studies at Elevation—a Remotely piloted Aircraft Team Experiment (LAPSE-RATE) field campaign. We evaluate a total of 38 individual sUAS with 23 unique sensor and platform configurations using a meteorological tower for reference measurements. We assess precision, bias, and time response of sUAS measurements of temperature, humidity, pressure, wind speed, and wind direction. Most sUAS measurements show broad agreement with the reference, particularly temperature and wind speed, with mean value differences of 1.6 $\pm 2.6{}^{\circ }$ C and 0.22 $\pm 0.59$ m/s for all sUAS, respectively. sUAS platform and sensor configurations were found to contribute significantly to measurement accuracy. Sensor configurations, which included proper aspiration and radiation shielding of sensors, were found to provide the most accurate thermodynamic measurements (temperature and relative humidity), whereas sonic anemometers on multirotor platforms provided the most accurate wind measurements (horizontal speed and direction). We contribute both a characterization and assessment of sUAS for measuring atmospheric parameters, and identify important challenges and opportunities for improving scientific measurements with sUAS.

We generalize the concepts of finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures to arbitrary Riemannian manifolds. The methods are illustrated for convection cells on cylinders and Möbius strips, as well as for the splitting of the Antarctic polar vortex in the spherical stratosphere and a related point vortex model. We modify the FTLE computational method and accommodate unstructured meshes of triangles and tetrahedra to fit manifolds of arbitrary shape, as well as to facilitate dynamic refinement of the FTLE mesh.

Transition states in phase space are identified and shown to regulate the rate of escape of asteroids temporarily captured in circumplanetary orbits. The transition states, similar to those occurring in chemical reaction dynamics, are then used to develop a statistical semianalytical theory for the rate of escape of asteroids temporarily captured by Mars. Theory and numerical simulations are found to agree to better than $1\%$. These calculations suggest that further development of transition state theory in celestial mechanics, as an alternative to large-scale numerical simulations, will be a fruitful approach to mass transport calculations.