APOD: Falcon 9 Boostback (2020 Mar 12)

[APOD Robot]

Falcon 9 Boostback

Explanation: Short star trails appear in this single 84 second long exposure, taken on March 6 from a rotating planet. The remarkable scene also captures the flight of a Falcon 9 rocket and Dragon cargo spacecraft over Cape Canaveral Air Force Station shortly after launch, on a resupply mission bound for the International Space Station. Beginning its return to a landing zone about 9 kilometers from the launch site, the Falcon 9 first stage boostback burn arcs toward the top of the frame. The second stage continues toward low Earth orbit though, its own fiery arc traced below the first stage boostback burn from the camera's perspective, along with expanding exhaust plumes from the two stages. This Dragon spacecraft was a veteran of two previous resupply missions. Successfully returning to the landing zone, this Falcon 9 first stage had flown before too. Its second landing marked the 50th landing of a SpaceX orbital class rocket booster.

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[neufer]

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<<River bifurcation (from Latin: furca, fork) occurs when a river flowing in a single stream separates into two or more separate streams (called distributaries) which continue downstream. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior. A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. In continuous systems, this corresponds to the real part of an eigenvalue of an equilibrium passing through zero. In discrete systems, this corresponds to a fixed point having a Floquet multiplier with modulus equal to one. In both cases, the equilibrium is non-hyperbolic at the bifurcation point. The topological changes in the phase portrait of the system can be confined to arbitrarily small neighbourhoods of the bifurcating fixed points by moving the bifurcation parameter close to the bifurcation point (hence 'local').>>

Period-halving bifurcations (L) leading to order, followed by period doubling bifurcations (R) leading to chaos.

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[orin stepanek]

crs20_boostback1024.jpg

Awsome; that's the way it was done in old movies!

[heehaw]

See you later, bifurcator!