15,652 research outputs found

    Qualitative Criterion for Interception in a Pursuit/Evasion Game

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    A qualitative account is given of a differential pursuit/evasion game. A criterion for the existence of an intercept solution is obtained using future cones that contain all attainable trajectories of target or interceptor originating from an initial position. A sufficient and necessary conditon that an opportunity to intercept always exist is that, after some initial time, the future cone of the target be contained within the future cone of the interceptor. The sufficient condition may be regarded as a kind of Nash equillibrium.Comment: 8 pages; revsions and corrigend

    1I/2017 U1 (`Oumuamua) is Hot: Imaging, Spectroscopy and Search of Meteor Activity

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    1I/2017 U1 (`Oumuamua), a recently discovered asteroid in a hyperbolic orbit, is likely the first macroscopic object of extrasolar origin identified in the solar system. Here, we present imaging and spectroscopic observations of \textquoteleft Oumuamua using the Palomar Hale Telescope as well as a search of meteor activity potentially linked to this object using the Canadian Meteor Orbit Radar. We find that \textquoteleft Oumuamua exhibits a moderate spectral gradient of 10%±6% (100 nm)−110\%\pm6\%~(100~\mathrm{nm})^{-1}, a value significantly lower than that of outer solar system bodies, indicative of a formation and/or previous residence in a warmer environment. Imaging observation and spectral line analysis show no evidence that \textquoteleft Oumuamua is presently active. Negative meteor observation is as expected, since ejection driven by sublimation of commonly-known cometary species such as CO requires an extreme ejection speed of ∼40\sim40 m s−1^{-1} at ∼100\sim100 au in order to reach the Earth. No obvious candidate stars are proposed as the point of origin for \textquoteleft Oumuamua. Given a mean free path of ∼109\sim10^9 ly in the solar neighborhood, \textquoteleft Oumuamua has likely spent a very long time in the interstellar space before encountering the solar system.Comment: ApJL in pres
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