Re: Earth decreased speed?
Yes it’s all about momentum change, a gravity assist doesn’t just ‘speed up’ a spacecraft but also changes its trajectory. I think the best, grounded analogy I ever heard was this.
Imagine I stand at the side of a railway track, in my hand I hold a tennis ball and with the best will in the world I could throw this ball at, say 10 metres per second, a train is approaching say moving at 100 metres per second. At a critical point I throw the ball at the front of the train, no directly, not head-on (I would need to be standing on the track to do that), but at an angle. The ball hits the front of the moving train and rebounds away.
Now from the perspective of the train driver, they see the ball approach, quite fast, depending on how fact the train is going, how fast I can throw the ball, and the angle, the ball hits and the driver sees it rebound away at a different angle but apparently the same speed - so nothing has happened!
But from my perspective, the ball bounces off the front of the train in a totally different direction but moving a lot faster. If I could carefully measure the trains speed, I would find that it has slowed down, but as the train is, what, millions of times more massive than the ball, this is just not relevant.
Replace the tennis ball with a space probe, replace the train with a planet, replace the driver with someone standing on the surface of that planet with a really good telescope, and most importantly, replace the person standing by the rail track with the sun! Now, obviously the probe doesn’t literally ‘bounce’ off the planet, it’s a gravitational interaction, the closer you can get to the centre of the planet, the greater the effect will be. So from the point of view of someone standing on the planet, the probe approaches, getting faster and faster and then swings by the planet and gets slower again as the planets gravity acts to pull it back. But from the viewpoint of someone standing on the sun (yes, OK, I know), the probe accelerates towards the planet, swings by and departs, in a totally different direction, and much faster. The planet ever so slightly slows down, but it’s completely imperceptible.
And you can go the same in reverse, and ‘lose’ speed (with respect to the sun) - in this analogy, you can throw the ball faster than the train is going and you throw it at the back of the train as it passes, in this case the ball slows down (with respect to you), and transfers momentum to the train.
Something mentioned above was the Oberth effect. Imagine you have a spacecraft in an elliptical orbit, so at one point it is close to its primary (say the Earth) and at the other point it is far away. You want to raise your orbit, well at least raise the apogee, in effect ‘add energy’ to the space craft. You have fuel on board to burn and impart energy to the probe. The question is, at what point in the orbit is it most advantageous to burn the fuel?
And the answer is at perigee, the lowest point, which can sound counter-productive, surely that’s when the Earth’s gravity is at its strongest? But think of it like this.
The probe has a mass of say 1000kgs, and you intend to burn 100kgs of fuel. At apogee, the highest point of the orbit, the entire mass has maximum gravitational potential energy and minimum kinetic energy, as it fall down to perigee, it trades potential energy for kinetic energy until at perigee it’s moving as fast as it will. Now imagine that it was possible to burn all 100kgs of fuel instantaneously (you can’t but run with it), suddenly the probe is 100kgs less massive, but the mass of the fuel had itself kinetic energy, and now it’s gone. Where? Over and above the impulse from burning the fuel, the probe now gains additional energy - momentum is conserved, the fuel and the momentum it had, has to go somewhere, and it goes to increasing the speed of the probe. This is the Oberth effect, the maximum ‘delta-V’, ie a change in velocity will happen if you burn fuel at the bottom of the gravitational potential well! *
Orbital mechanics is really not intuitive - I’ll leave you with a question. You have two spacecraft in identical orbits but one is 100km behind the other. You want to close the distance in advance of docking, so on the trailing spacecraft, you fire thrusters at the ‘back’ of the craft and increase speed. What happens?
* yes I know I’m interchanging energy and momentum, and yes I know they are not remotely the same, but for the purpose of explaination, give me a break eh?