I've wondered something for a while that perhaps you can answer. How can space probes etc. use planets to slingshot to a higher speed (perhaps the MSM just reports wrong)? I understand using a planet to execute a turn, but increasing speed seems impossible, as gravity should have the same effect outbound as inbound.
Planets are not standing still. They can be used to pull the probe along.
Elementary (but clever) calculus.
"slingshot" orbital speedups are gained by having the spacecraft fly by a planet or moon starting at exactly the right place that the planet gives up energy from its forward orbital motion to the spacecraft. What this means is that every time we use Jupiter to speed up a probe, the planet slows down slightly. if we sent a really, really large number of probes by Jupiter this way, we could get it to fall into the Sun.
The probe's "final" (i.e. when it's far enough away for the planet's gravity to become insignificant) inbound and outbound speeds relative to the planet are equal. However, what's important for slingshot trajectories is speed relative to the sun, which can be increased or decreased depending on how the probe's trajectory and the planet's orbit interact.
Of course, the momentum and energy don't appear out of nowhere -- the planet loses the same amount that the probe gains. The planet is a lot bigger, so the effect on its orbit is miniscule.
Momentum is conserved. Some of the momentum of the large body is transferred to the smaller body, which if it is Jupiter versus Voyager 1 won't matter much to Jupiter.
Remember the planet is moving in its assigned orbit as well. You end up adding part of the velocity of the planet to your spacecraft as you do the flyby. However, you cannot get something for nothing. The Planet loses the same energy that was gained by the spacecraft. (Albeit imperceptible)
The tennis ball comes over the net at you, and is slowing down. You hit it with your moving racket, which is heavier than the tennis ball and send the ball back over the net at speed greater than it had before you hit it. In the probe planet case the probe spends more time in the planets gravitational field inbound than outbound due to the initial relative motion of the planet, so more momentum is transferred by gravity to the probe.