'Oumuamua (1I/2017 U1) is the first known object of interstellar origin to have entered the Solar System on an unbound and hyperbolic trajectory with respect to the Sun. Various physical observations collected during its visit to the Solar System showed that it has an unusually elongated shape and a tumbling rotation state and that the physical properties of its surface resemble those of cometary nuclei, even though it showed no evidence of cometary activity. The motion of all celestial bodies is governed mostly by gravity, but the trajectories of comets can also be affected by non-gravitational forces due to cometary outgassing. Because non-gravitational accelerations are at least three to four orders of magnitude weaker than gravitational acceleration, the detection of any deviation from a purely gravity-driven trajectory requires high-quality astrometry over a long arc. As a result, non-gravitational effects have been measured on only a limited subset of the small-body population. Here we report the detection, at 30σ significance, of non-gravitational acceleration in the motion of 'Oumuamua. We analyse imaging data from extensive observations by ground-based and orbiting facilities. This analysis rules out systematic biases and shows that all astrometric data can be described once a non-gravitational component representing a heliocentric radial acceleration proportional to r or r (where r is the heliocentric distance) is included in the model. After ruling out solar-radiation pressure, drag- and friction-like forces, interaction with solar wind for a highly magnetized object, and geometric effects originating from 'Oumuamua potentially being composed of several spatially separated bodies or having a pronounced offset between its photocentre and centre of mass, we find comet-like outgassing to be a physically viable explanation, provided that 'Oumuamua has thermal properties similar to comets.

Given the benefits of coupling low-thrust propulsion with gravity assists, techniques for easily identifying candidate trajectories would be extremely useful to mission designers. The computational implementation of an analytic, shape-based method for the design of low-thrust, gravity-assist trajectories is described. Two-body motion (central body and spacecraft) is assumed between the flybys, and the gravity-assists are modeled as discontinuities in velocity arising from an instantaneous turning of the spacecraft's hyperbolic excess velocity vector with respect to the flyby body. The method is augmented by allowing coast arcs to be patched with thrust arcs on the transfers between bodies. The shape-based approach permits not only rapid, broad searches over the design space, but also provides initial estimates for use in trajectory optimization. Numerical examples computed with the shape-based method, using an exponential sinusoid shape, are presented for an Earth-Mars-Ceres rendezvous trajectory and an Earth-Venus-Earth-Mars-Jupiter flyby trajectory. Selected trajectories from the shape-based method are successfully used as initial estimates in an optimization program employing direct methods.

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We consider low-thrust orbit transfers around a central body, where specified changes are sought in orbit elements except true anomaly. The desired changes in the remaining five elements can be arbitrarily large. Candidate Lyapunov functions are created based on analytic expressions for maximum rates of change of the orbit elements and the desired changes in the elements. These functions may be thought of as proximity quotients because they provide R measure of the proximity to the target orbit. The direction of thrust needed for steepest descent to the target orbit is also available analytically. The thrust is shutoff if the effectivity of the thrust at the current location on the osculating orbit is below some threshhold value. Thus, the equations of motion can be numerically integrated to obtain quickly and simply a transfer to the target orbit. A series of transfers can be easily computed to assess the trade-off between propellant mass and flight time. Preliminary comparisons to optimal solutions show that the method, while sub-optimal, performs well. *Senior Member of the Engineering Staff, Navigation and Mission Design Section, Mail-Stop 301-14OL. Member AIAA. Member AAS.

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