I read that if some spacecraft's trajectory is carefully planned, i.e. if it can slingshot (at loss of a better word) a massive body like a planet, it can gain speed. Is that correct ?
Does solar system actually lose some energy to such a space craft in this way ?
In order for this question to make sense you need to define which reference frame the spacecraft should gain speed in. Conservation of energy implies that the spacecraft gains no speed in the frame of reference in which the planet is stationary, but it can change its velocity (ie trajectory is changed). If you move that back to the reference frame where the Sun is stationary, you find that the spacecraft's speed may have in fact increased. Total energy of spacecraft and planet is unchanged, making the interaction an elastic collision. But the kinetic energies of individual bodies does change and the planet looses some energy (although being so large the change is entirely negligible).
