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The Shkadov thruster
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One of the simplest examples of stellar engine is the Shkadov thruster (named after Dr. Leonid Shkadov who first proposed it), or a Class A stellar engine.

Such an engine is a stellar propulsion system, consisting of an enormous mirror/light sail—actually a massive type of solar statite large enough to classify as a megastructure—which would balance gravitational attraction towards and radiation pressure away from the star. Since the radiation pressure of the star would now be asymmetrical, i.e. more radiation is being emitted in one direction as compared to another, the 'excess' radiation pressure acts as net thrust, accelerating the star in the direction of the hovering statite. Such thrust and acceleration would be very slight, but such a system could be stable for millennia. Any planetary system attached to the star would be 'dragged' along by its parent star. For a star such as the Sun, with luminosity 3.85 × 10^26 W and mass 1.99 × 10^30 kg, the total thrust produced by reflecting half of the solar output would be 1.28 × 10^18 N. After a period of one million years this would yield an imparted speed of 20 m/s, with a displacement from the original position of 0.03 light-years. After one billion years, the speed would be 20 km/s and the displacement 34,000 light-years, a little over a third of the estimated width of the Milky Way galaxy.

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The Shkadov thruster/@Futurycon

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Leonid Mikhailovich Shkadov

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Leonid Mikhailovich Shkadov (1927–2003) scientist, engineer in aircraft development and optimisation, one of the TsAGI deputy directors (1986-2003), Doctor of Engineering, professor, recipient of the USSR State Prize (1977).