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Aug 7, 2021 at 14:50 comment added wizzwizz4 @DescheleSchilder No – but near-light-speed can be achieved a (tiny) distance away.
Aug 7, 2021 at 8:28 comment added Deschele Schilder Do you think there is a limit of the speed increase if the planets are black holes? I mean, can lightspeed be achieved at a distance away from the horizons?
Aug 7, 2021 at 8:18 comment added Raffles @RossPresser you are right that it will decrease as speed increases if you maintain a fixed distance from the object each time you pass it. However if you move closer to the object each time you pass it, so that you exactly compensate for the speed increase, you will get the same deflection. This is borne out by the escape velocity formula which is inversely proportional to the distance... which I was not aware of when I posted the question, but thanks to you fine people I have now come across :-) en.wikipedia.org/wiki/Escape_velocity
Aug 5, 2021 at 13:11 comment added Ross Presser @Raffles The amount of the deflection decreases with your initial speed. Consider that a planet is so deflected by the sun that it stays in orbit though it's millions of miles away, while a light beam actually grazing the surface of the sun is barely deflected by less than a degree.
Aug 5, 2021 at 10:19 comment added AI0867 Assuming a spherical body, the lowest possible altitude is the radius of the object. At that altitude, there will be a certain gravitational acceleration. Above that altitude, the acceleration will be lower. For every encounter velocity, you will pass through the gravity well in a certain amount of time, the time being shorter for larger velocities. This gives you a very loose upper bound of time-spent-in-gravity-well * accceleration-at-object-radius = velocity-gained. This value will clearly be lower at higher encounter velocities. There's probably a website that can give you actual numbers.
Aug 5, 2021 at 7:28 comment added Raffles I don't think this is true. Gravity bends space, so you always get a deflection, even travelling at the speed of light (although in that case of course there is no increase in speed!). See en.wikipedia.org/wiki/Gravitational_lens. The question is, how deep down the gravity well do you need to go in order to come back out the way you need to? You can't go so deep that you actually crash into the planet, so what is the limit that you can (safely) go to, and what speed can you achieve? It's that limit that I'm after in asking the question. Thanks
Aug 4, 2021 at 21:48 history edited uhoh CC BY-SA 4.0
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Aug 4, 2021 at 20:09 history answered PearsonArtPhoto CC BY-SA 4.0