I have a hard time imagining physics. For example take a train moving 100 kmh to the north which wants to reverse direction to the south. It has to break and then accelerate again, a very costly operation. Except when the tracks make a turn? But how can a northward momentum change to a southward momentum?
The same confusion I have when trying to imagine satellites going around Earth or slingshot maneuvers. Would an X-Wing turn in space differently than in the atmosphere of Hoth? Would it in space just rotate, but keep its forward (now backwards) momentum instead of turning like a fighter jet?
> The same confusion I have when trying to imagine satellites going around Earth or slingshot maneuvers.
I can't recommend KSP enough. It's a "silly" game with "on rails physics" (so not exactly 100% accurate wrt general relativity stuff) but it's got a very nice interface and it will make you "get" orbital mechanics by dragging stuff around. You'll get an intuition for it after a few hours of gameplay / yt video tutorials. Really cool game.
This is how I now “get” orbital mechanics better than I ever did trying to study it. Play is the best education.
> For example take a train moving 100 kmh to the north which wants to reverse direction to the south. It has to break and then accelerate again, a very costly operation. Except when the tracks make a turn? But how can a northward momentum change to a southward momentum?
Your train is decelerating, and then accelerating southwards. It really is.
If you were on a train that was travelling in a straight line northwards and the driver applied the brakes, it would decelerate, which really is acceleration with a negative value (and I can hear that in my old high school physics teacher's voice, hope you're doing well, Mr Siwek). You would feel yourself being thrown forwards if the acceleration was strong enough because your momentum wants to keep you moving north.
If you were on a train that was travelling around a U-shaped bit of track looping from northbound to southbound, then you'd be thrown towards the outside of the curve. Guess what? The train is not moving north so fast, and your momentum is trying to keep you moving north.
The difference here is that if you brake the train to a stop and throw it in reverse then you're dissipating energy as heat to stop it, and then applying more energy from the drivetrain to get it moving again, but if you go round a U-shaped track the energy going north is now energy going east. You have not added or removed energy, just pointed it a different direction.
Turning around a track definitely dissipates some heat energy through increased friction with the rails. Imagine taking a semicircle turn and making it tighter and tighter. At the limit, the train is basically hitting a solid wall and rebounding in the other direction, which would certainly transfer some energy.
The energy question is this: going from a 100kmh-due-north momentum to a 100kmh-due-south momentum via slowing, stopping, and accelerating again clearly takes energy. You can also switch the momentum vector by driving in a semicircle. Turning around a semicircle takes some energy, but how much - and where does it come from? Does it depend on how tight the circle is - or does that just spread it out over a wider time/distance? If you had an electric train with zero loss from battery to wheels, and you needed to get it from going north to going south, what would be the most efficient way to do it?
There is no "required" energy to change direction, even for a zero-radius change, think of a bouncing ball:
https://www.youtube.com/watch?v=QpuCtzdvix4
This only applies in perfectly elastic systems, where the bodies can convert kinetic energy to potential energy and back with perfect restitution. Which, thanks to the second law of thermodynamics, doesn't exist in reality. It's only a question of how much energy is lost. (Unless, of course, you include the medium into which the energy dissipates as heat into the system itself. But such a model is not useful in almost all practical scenarios.)
A bouncing ball is elastic. There is some loss in the process of storing the energy from the movement into the ball and then releasing it into the opposite direction. Good example though!
> Turning around a track definitely dissipates some heat energy through increased friction with the rails.
No it doesn't, but we're talking about identical spherical frictionless trains in a vacuum.
You are also talking about a track with infinite mass because otherwise the reason train can change direction is because it's pushing the track northwards
Obviously! It goes without saying that the track must be infinitely massive and infinitely stiff, mounted on an entirely inflexible infinite plane.
See, now you're talking real physics!
I feel like none of the answers have addressed you train example correctly. The momentum is exchanged with the Earth. So the Earth+train still have the same total momentum. The energy is mostly conserved (ignoring the friction that's needed to stay on the track). You can do the same by running past a lamp post and extending a hand to grab it - you'll change direction.
In your train example, the rails exert a force on the train as it turns. In orbit, the planets are constantly exerting a force on the satellite.
What's going on here is that your momentum changes whenever you experience a force. Your energy changes whenever you experience a force towards or from the direction that you are traveling.
The force from the rails at all points is at right angles to the direction of motion. So your energy doesn't change. Your momentum is constantly changing. And you're doing it by shoving the Earth the other way. But the Earth is big enough that nobody notices.
Now to the orbital example. In the Newtonian approximation, an orbit works similarly. In a circular orbit, you're exchanging momentum with the planet, but your energy remains the same. The closer the orbit, the more speed you need to maintain this against a stronger gravity, and the faster you have to move.
In an elliptical orbit, you're constantly exchanging momentum with the planet, but now you're also exchanging between gravitational potential energy, and kinetic energy. You speed up as you fall in, and slow down as you move out. Which means that you are moving below orbital speed at the far end of your orbit, and above when you are close.
Now to this paradox. Slowing down causes you to shift which elliptical orbit you are in, to one which is overall faster. Therefore slowing down puts you ahead in half an orbit, and then you'll never stop being ahead.
When you brake you generate a ton of heat.
Doing a U-turn generates less heat, but still quite a bit. The train will have to slow down depending on the radius of the curve, and even then the turn will slow it down some more.
But yeah, less heat generation means kinetic energy is conserved.
Cars have to slow down when they turn because it’s too much to ask of the tires to accelerate (throttle) and turn, since turning is in itself acceleration.
Caveat: when the tires are already at the limit of adhesion (e.g. on an F1 car). In a road car, you are not normally turning at 1g and probably can’t accelerate at 1g so you can turn and accelerate when you have enough margin.
It’s just the average driver doesn’t realize how much margin is available.
A train has momentum in the direction of the track. If the track makes a 180° turn the train will lose some momentum to increased friction with the track during the turn, but essentially the momentum still follows the track.
A fighter jet (or X-Wing in orbit) kind of generates its own "track" with the guiding forces of the wings. You can still do a 180° turn and keep a significant part of your momentum. Though the guiding effects are a lot softer, so your losses are a lot worse
A satellite (or an X-Wing in orbit) has no rails that can go in arbitrary directions. Any momentum is in "orbit direction", but orbits work in weirder ways. If you make your orbit highly elliptical then at the highest point you will have traded nearly all your kinetic energy for potential energy and can make a 180° turn pretty cheaply (because it's only a small change in speed)
What's happening is that you exchange forward momentum for angular momentum. When the track straightens out again, you trade the angular momentum for forward momentum again. The train pays for this in friction losses; the orbital maneuver costs some fuel for steering.
A very related physics issue that boggles my mind is when you roll a disk, like a wheel. You can roll the disk north, and it'll lean, curve, and end up going south. What force changed the direction of the wheel?
I understand it, intellectually. It's pushing sideways against the surface as it leans and spins, but it just doesn't feel right. I have no intuition for it.
If you are talking about the gyroscopic precession effect that happens when you push on a spinning disc, this is the best video I've seen so far that explains it in an intuitive way: youtube.com/watch?v=n5bKzBZ7XuM
You too can change direction easier if there is an object (like a pole or something) you can push/pull against. Try it, maybe it will help your intuition.
Run towards a pole and then try to come back around it, once without touching it and once using it to swing around. That's the role the curved tracks play. You exchange momentum with the object, and in the end with the Earth.
play KSP, it will click after a few days.
> a very costly operation
It's only costly due to the waste heat from breaking. If you captured that energy with perfect regenerative breaking you could return to the same speed in the opposite direction. (In a spherical cow sense anyway.)