> 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.

> 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.

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.

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.

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.

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)

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.

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.

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.

Yeah, it's amazing. With enough docking and maneuvering practice I developed some kind of intuition for moving in space. I could maneuver without meticulously planning the burns.

Still can't leave Eve though...

I tried to teach a group of HS students about orbital mechanics as a high school physics teacher using KSP. It was... difficult. Not impossible. But I agree it's an excellent learning tool.

I'm a professional astrodynamicist and I owe my base level understanding of orbital mechanics to KSP. It's a fantastic resource for learning the basics of Keplerian motion.

Also, obligatory XKCD: https://xkcd.com/1356/

I wish ksp 2 hadn't been a boondoggle

I doubt SpaceX could put a satellite in orbit with KSP physics. Just the absence of realistic thermal conduction would prevent it. The outer skin temperature typically peaks around 300–600 °C during the densest part of the atmosphere. If you calculate those forces wrong the rocket has a bad day. Best case it is over engineered and has a reduced payload. They might as well do their calculations with pi equal to 3.

https://archive.is/

Paste link, good to go. https://archive.is/qrP0p

There is the small, tiny issue of people commenting just based on title, without even reading the article.

In this case I expected it just links to https://www.youtube.com/watch?v=bcvnfQlz1x4 and didn't even notice in links to Wired.

Allowing paywalls vs not been discussed for a long time. Latest comment from dang about it seems to be this:

> The answer is that paywalls are allowed when there are workarounds (such as archive links) which allow ordinary readers to read the article without paying or subscribing, while hardwalled domains (i.e., without such workarounds) are banned. - https://news.ycombinator.com/item?id=43876575

https://hn.algolia.com/?dateRange=all&page=0&prefix=true&que...

Or in the words of Larry Niven (The integral trees)

East takes you Out

Out takes you West

West takes you In

In takes you East

Down is where the enemy gate is.

Slow is smooth, smooth is fast.

How so?

Obligatory: https://xkcd.com/1356/