Right, but as I explained, it’s the how that doesn’t make sense to me - the explanation that you “fall for longer” doesn’t make sense, since 1. with how orbits work, it takes the same energy and time to “fall” as it does to ascend, and 2. at these scales you can use the planet as an inertial frame of reference, so the angle of approach doesn’t matter for how “long” you “fall”, it’ll be the same regardless of whether you’re moving towards or away from the planet.
You mentioned “from the perspective of the planet” before, and I think perhaps that’s the key, from the planet’s perspective you fall and rise with equal velocities and equal accelerations, but crucially the planet is moving relative to other things and curves your orbit, so whilst you might might have the same falling and rising speeds relative to it, they’re not in the same direction, so your velocity has changed, and from an external perspective you’ve gained velocity from it.
Imagine you start stationary relative to the sun, with Jupiter barrelling towards you (not on a collision course!). From Jupiter’s perspective you fall towards it, and so from the suns perspective you gain velocity opposite jupiters orbit, but you’re not directly head on so it twists your course (let’s say 90 degrees to keep things simple) then as you leave Jupiter it indeed decelerates you relative, but crucially you’re in a different direction now, (from jupiters perspective) you’re pointed right towards the sun, so as you pull away Jupiter is decelerating you in the sun direction (aka accelerates you away from the sun). So you were both accelerated in the anti-Jupiter-orbit direction and then again in the anti-sun direction. Added together those give you a vector which is non-zero, so you’ve gained speed from Jupiter.
If your orbit didn’t curve (eg if you could pass straight through the middle of Jupiter without colliding) I think perhaps it’d cancel out its own effects on your velocity, though I’d need to check to be certain…
I’m sorry, but this comment thread genuinely makes me feel like I’m going insane. You seem to have explained exactly the same thing as me, with the same example, and none of it includes the “fall for longer before you catch up” bit.
As for the orbit not curving, yeah, I think you’re right - the obvious case is if you’re sitting stationary on the planet’s orbit, but the curious case is if you’re approaching from the sun, with the planet’s velocity plus velocity away from the sun. If I’m not mistaken, in that case you’d end up with the same velocity (minus what you might have lost to the sun’s gravity), but on the other side of the planet’s gravity well, which means you still gained energy.
I guess the original claim works if you imagine it along a specific axis only (1 dimensionally) in that perspective you either fall quickly then leave slowly or fall slowly and leave quickly, matching up to a change in velocity along that axis.
As others have said, you are stealing kinetic energy from the planet to go faster. Or giving kinetic energy back to the planet to go slower.
So, relatively, you slow down and the planet speeds up or the planet slows down and you speed up.
Right, but as I explained, it’s the how that doesn’t make sense to me - the explanation that you “fall for longer” doesn’t make sense, since 1. with how orbits work, it takes the same energy and time to “fall” as it does to ascend, and 2. at these scales you can use the planet as an inertial frame of reference, so the angle of approach doesn’t matter for how “long” you “fall”, it’ll be the same regardless of whether you’re moving towards or away from the planet.
You mentioned “from the perspective of the planet” before, and I think perhaps that’s the key, from the planet’s perspective you fall and rise with equal velocities and equal accelerations, but crucially the planet is moving relative to other things and curves your orbit, so whilst you might might have the same falling and rising speeds relative to it, they’re not in the same direction, so your velocity has changed, and from an external perspective you’ve gained velocity from it.
Imagine you start stationary relative to the sun, with Jupiter barrelling towards you (not on a collision course!). From Jupiter’s perspective you fall towards it, and so from the suns perspective you gain velocity opposite jupiters orbit, but you’re not directly head on so it twists your course (let’s say 90 degrees to keep things simple) then as you leave Jupiter it indeed decelerates you relative, but crucially you’re in a different direction now, (from jupiters perspective) you’re pointed right towards the sun, so as you pull away Jupiter is decelerating you in the sun direction (aka accelerates you away from the sun). So you were both accelerated in the anti-Jupiter-orbit direction and then again in the anti-sun direction. Added together those give you a vector which is non-zero, so you’ve gained speed from Jupiter.
If your orbit didn’t curve (eg if you could pass straight through the middle of Jupiter without colliding) I think perhaps it’d cancel out its own effects on your velocity, though I’d need to check to be certain…
I’m sorry, but this comment thread genuinely makes me feel like I’m going insane. You seem to have explained exactly the same thing as me, with the same example, and none of it includes the “fall for longer before you catch up” bit.
As for the orbit not curving, yeah, I think you’re right - the obvious case is if you’re sitting stationary on the planet’s orbit, but the curious case is if you’re approaching from the sun, with the planet’s velocity plus velocity away from the sun. If I’m not mistaken, in that case you’d end up with the same velocity (minus what you might have lost to the sun’s gravity), but on the other side of the planet’s gravity well, which means you still gained energy.
I guess the original claim works if you imagine it along a specific axis only (1 dimensionally) in that perspective you either fall quickly then leave slowly or fall slowly and leave quickly, matching up to a change in velocity along that axis.
But yeah, I wouldn’t have explained it that way.