In Orbit You Have to Slow Down to Speed Up

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

Still can't leave Eve though...

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.

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.

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.

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.

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 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)

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.)

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.

East takes you Out

Out takes you West

West takes you In

In takes you East

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

> 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...

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.

There's a reason why his nickname among the other astronauts is Doctor Rendezvous.

[0] https://dspace.mit.edu/handle/1721.1/12652

[1] https://history.howstuffworks.com/historical-figures/buzz-al...

Imagine writing this 6 years before you were literally standing on the moon.

More commonly we push away propellant, but pushing on the other craft is an option.

> If the rendezvous was in orbit does that mean departing from rendezvous pushes both crafts out of orbit?

Assuming we're pushing on the other craft, it means both crafts will change orbits, but in opposite directions. If we're talking about an instantaneous push in the direction of travel one craft will move to an orbit where it is closer to earth one half rotation later, and the other craft will move to an orbit where it is farther from earth one half rotation later.

Both, either, or neither craft could exit orbit like this, but one would be exiting orbit by crashing into the thing its orbiting around (e.g. earth) and the other would exit by reaching escape velocity and flying off into the distance.

> I ask because Earth is an third body scenario between the sun and Jupiter. Jupiter has enough gravity to occasionally pull the Earth slightly (not significantly) out of orbit from the Sun, but Earth's orbit to the Sun is self-correcting due to the difference in mass between the Sun and Jupiter. Quick web searching reveals Jupiter's pull on Earth is only approximately 0.005% of the Sun's after accounting for both mass and distance, but that number rises to 0.011% after accounting for syzygy with the moon.

Yes, Jupiter constantly (not occasionally) perturbs earths orbit, and technically earth constantly perturbs jupiters orbit (though the influence in that direction is completely negligible), but as you note its not enough for either to reach escape velocity or crash into the sun, and it appears to more or less even out over time.