Acceleration due to gravity
August 12, 2016 6:46 AM Subscribe
How close could you get to the speed of light due to acceleration by falling into or being in a decaying orbit around a large gravity well (black hole?)
Obviously you wouldn't want to cross the event horizon of the black hole. But before you got to that point, could you get close to c?
Obviously you wouldn't want to cross the event horizon of the black hole. But before you got to that point, could you get close to c?
You only get ripped apart by tidal forces if you approach a small black hole Static Vagabond. You could (probably) cross the event horizon of the black hole at the centre of the galaxy just fine, because the tidal forces at the boundary are small.
blue_beetle: It ’s not entirely clear what you’re asking. Is it: “If I fall into a black hole, will I get up to the speed of light as I approach it?” or is it “If I have enough energy available, could I orbit the black hole at a speed close to the speed of light?” (or possibly some other variant)
Since black hole orbits are weird the answer is complicated & depends on exactly what you’re asking!
posted by pharm at 7:16 AM on August 12, 2016
blue_beetle: It ’s not entirely clear what you’re asking. Is it: “If I fall into a black hole, will I get up to the speed of light as I approach it?” or is it “If I have enough energy available, could I orbit the black hole at a speed close to the speed of light?” (or possibly some other variant)
Since black hole orbits are weird the answer is complicated & depends on exactly what you’re asking!
posted by pharm at 7:16 AM on August 12, 2016
I don't have equations for you, but since gravity is inversely proportional to the square of distance, even strong gravity fields have a relatively short range. I would surmise that you wouldn't have enough time under the influence of a black hole's gravity to accelerate anywhere near to c before you got close enough to be swallowed up (or dodged nimbly to the side and bypassed it).
posted by ejs at 7:18 AM on August 12, 2016
posted by ejs at 7:18 AM on August 12, 2016
(You can, for instance, set up an orbit which whips around the event horizon an arbitrary number of times in a very *nearly* circular orbit & then hurls you out to ∞. This is quite odd.)
posted by pharm at 7:18 AM on August 12, 2016
posted by pharm at 7:18 AM on August 12, 2016
if we ignore tidal effects on a "real person", ignore quantum mechanics, are not bothered about whether you cross the horizon and assume that there's no angular momentum to complicate things, then you get closer and closer (arbitrarily close) to the speed of light as "you" fall into the hole.
this is because the gravitational potential well, given those assumptions, is infinite (that's roughly what "singularity" means).
in practice, exactly how close you get to the speed of light is going to depend on the details of what is "inside" a black hole, which we do not know.
[disclaimer: am at the border of my knowledge here.]
posted by andrewcooke at 7:47 AM on August 12, 2016
this is because the gravitational potential well, given those assumptions, is infinite (that's roughly what "singularity" means).
in practice, exactly how close you get to the speed of light is going to depend on the details of what is "inside" a black hole, which we do not know.
[disclaimer: am at the border of my knowledge here.]
posted by andrewcooke at 7:47 AM on August 12, 2016
Response by poster: Not to threadsit, but I'm trying to determine if gravitational acceleration is a viable method for accelerating something (a craft or projectile) to high relativistic velocities. For example, could we accelerate a probe to a significant percentage of c to explore the universe in a (slightly) more compressed timeframe than convential means?
Is there a formula for calculating maximum gravitational slingshot effect? Given no other requirement than maximum speed, what could we achieve with Jupiter or the Sun?
posted by blue_beetle at 8:17 AM on August 12, 2016
Is there a formula for calculating maximum gravitational slingshot effect? Given no other requirement than maximum speed, what could we achieve with Jupiter or the Sun?
posted by blue_beetle at 8:17 AM on August 12, 2016
Forces in physics do not describe a change in velocity, they describe a change in a quantity called momentum. So the force of gravity doesn't change your velocity, it changes your momentum.
At low velocities like we deal with in everyday life, your momentum is just your mass, how heavy you are, times your velocity. This means that when you're just dealing with human scale things, gravity accelerates you, i.e. changes your velocity, at a constant rate.
This is not true, though, once you start going really, really fast, like near the speed of light. At these "relativistic" speeds, the relationship between your momentum and your velocity gets more complicated. Your momentum has no limit, but your velocity does. Doubling your momentum just gets you just some fraction closer to the speed of light, but you never quite get there.
So what happens is that, as you approach light speed, gravity accelerates you less and less despite the fact that the force of gravity remains the same and your momentum is still changing at the same rate. You never quite reach the speed of light.
Of course this is glossing over a lot of tricky things that matter in real life, (particularly that gravitational acceleration varies with distance but also possible general relativistic effects from a strong gravitational field) but it is the basic idea.
posted by Zalzidrax at 8:23 AM on August 12, 2016 [1 favorite]
At low velocities like we deal with in everyday life, your momentum is just your mass, how heavy you are, times your velocity. This means that when you're just dealing with human scale things, gravity accelerates you, i.e. changes your velocity, at a constant rate.
This is not true, though, once you start going really, really fast, like near the speed of light. At these "relativistic" speeds, the relationship between your momentum and your velocity gets more complicated. Your momentum has no limit, but your velocity does. Doubling your momentum just gets you just some fraction closer to the speed of light, but you never quite get there.
So what happens is that, as you approach light speed, gravity accelerates you less and less despite the fact that the force of gravity remains the same and your momentum is still changing at the same rate. You never quite reach the speed of light.
Of course this is glossing over a lot of tricky things that matter in real life, (particularly that gravitational acceleration varies with distance but also possible general relativistic effects from a strong gravitational field) but it is the basic idea.
posted by Zalzidrax at 8:23 AM on August 12, 2016 [1 favorite]
while what zalzidrax says above is correct, there is a technique called "gravitational slingshot" that you may have heard about, and which may be what has prompted your question. that actually "uses" the motion of the planet. so it doesn't depend so much on the mass (although mass is important) as the velocity of the planet.
you could slingshot using a black hole, just as you could with a planet. but because it's the speed that's important, you would need a black hole that is going in the direction you want.
having said that, i have never done the maths and perhaps there is some detail i am unaware of. more details on wikipedia
posted by andrewcooke at 9:06 AM on August 12, 2016
you could slingshot using a black hole, just as you could with a planet. but because it's the speed that's important, you would need a black hole that is going in the direction you want.
having said that, i have never done the maths and perhaps there is some detail i am unaware of. more details on wikipedia
posted by andrewcooke at 9:06 AM on August 12, 2016
Oh right, I see.
Sure, you can do that. You need a pair of massive merging black holes though :)
posted by pharm at 10:29 AM on August 12, 2016
Sure, you can do that. You need a pair of massive merging black holes though :)
posted by pharm at 10:29 AM on August 12, 2016
Just considering the extreme case of "how velocity would you get to if you fell from the height of the moon?", There are a couple problems. First, before you get further away than the moon, the gravity of other bodies, especially the sun, complicate the seemingly easy business of falling. Second, you already have e velocity that makes falling straight, or at all, difficult. Not east for an eRtbly thing to fall into the sun, for example.
But to answer the simple question, I think the speed you can get to with a simple fall is the same as the escape velocity which from the earth's surface is a little over 11 km/s. 618km/s from the sun.
posted by SemiSalt at 2:37 PM on August 12, 2016
But to answer the simple question, I think the speed you can get to with a simple fall is the same as the escape velocity which from the earth's surface is a little over 11 km/s. 618km/s from the sun.
posted by SemiSalt at 2:37 PM on August 12, 2016
Thinking more along the lines of my last answer, since the escape velocity of a black hole at the event horizon is the speed of light, the Newtonian physics answer would be that if you fell toward a black hole from the other side of the universe, you would reach the speed of light at the event horizon. However, things get very non-Newtonian as you approach c, so to get a better answer than mine, find a better physicist than me, e.g. college physics major or better.
posted by SemiSalt at 11:07 AM on August 13, 2016
posted by SemiSalt at 11:07 AM on August 13, 2016
If you want to accelerate things to a high velocity to explore the universe, falling into a gravity well isn't going to help you. The reason for this is as you fall, you exchange gravitational potential energy for kinetic energy, but if you want to escape the gravity well at any point (i.e. to stop orbiting / falling towards the black hole in your example) you're going to have to transfer all of that kinetic energy into gravitational potential energy. This leaves you back where you started. It's conservation of energy, there's no way around it.
Ok then what about graviational slingshots? It turns out that if the black hole or whatever is moving in the right direction you can extract a bit of energy from the kinetic energy of the black hole. For a handwavey explaination, the way this works is that you fall into a gravity well, but by the time you want to start climbing out, the "trough" of the well has moved, so it's not as difficult to get out as it is to fall in. In the classical approximation, the limit on how much velocity you can get out of this is twice the velocity of the black hole (the wikipedia covers it pretty well). Obviously relativistic subtleties apply if you want to accelerate to a significant fraction of c, but the principle applies that you need an astronomical body moving relative to earth at high speed.
posted by Ned G at 6:43 AM on August 17, 2016
Ok then what about graviational slingshots? It turns out that if the black hole or whatever is moving in the right direction you can extract a bit of energy from the kinetic energy of the black hole. For a handwavey explaination, the way this works is that you fall into a gravity well, but by the time you want to start climbing out, the "trough" of the well has moved, so it's not as difficult to get out as it is to fall in. In the classical approximation, the limit on how much velocity you can get out of this is twice the velocity of the black hole (the wikipedia covers it pretty well). Obviously relativistic subtleties apply if you want to accelerate to a significant fraction of c, but the principle applies that you need an astronomical body moving relative to earth at high speed.
posted by Ned G at 6:43 AM on August 17, 2016
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posted by Static Vagabond at 6:53 AM on August 12, 2016 [3 favorites]