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Oberth Effect in deep space

Does the Oberth effect only apply when in orbit of a planet or would a rocket generate more and more thrust (if kept on) even in deep space? Wikipedia explains that the faster the rocket goes, the ...
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Is the fuel burn for a satellite launch affected by the position of the moon relative to the launch site?

The gross mass of a satellite rocket is tiny compared to that of Earth, and Luna. Between them, however, the two bodies set up tides in bodies of water which itself is again considerable mass. At ...