Velocity of a given planet relative to the Galactic Center

[Entropix]

TL;DR Summary

Trying to understand how fast a planet can moves relative to the Galactic Center.

Long time had this question about how fast a planet, dwarf or not or even a rogue asteroid can move relative to the core of the Galaxy, where, if my understanding is correct it has to be a supermassive black hole.

Knowing satellites revolves around a planet and this system circles around a star and the star itself circles the Galactic Center, do we know how fast satellites or other fast moving asteroids can be relative to the Galactic Core?

A second question would be: does the centrifugal force pushes out energy or matter from the black hole core or from let's say it's proximity or slowly (or not) moves inward due to the immense Black Hole Gravity that swallows everything around?

Is there any way that by moving or accelerating a satellite around the Moon to be enough to exceed the light velocity of that fast moving rocket relative to the center of Galaxy? Any better insights about this would be greatly appreciated.

Also would be interesting to find how faster a rocket should be to 'exceed' light velocity vs GC.

Tnx in advance for any better clues on this topic.

 

[phinds]

TL;DR Summary: Trying to understand how fast a planet can moves relative to the Galactic Center.

Well, take our sun as an example. You should be able to look up how long it takes it to make one orbit and what its radius is from the black hole, so the calculation is trivial.

A second question would be: does the centrifugal force pushes out energy or matter from the black hole core or from let's say it's proximity or slowly (or not) moves inward due to the immense Black Hole Gravity that swallows everything around?

I find that paragraph completely incoherent and have no idea what you are asking.

Also would be interesting to find how faster a rocket should be to 'exceed' light velocity vs GC.

Nothing moves faster than light.

 

[renormalize]

Well, take our sun as an example. You should be able to look up how long it takes it to make one orbit and what its radius is from the black hole, so the calculation is trivial.

Yes, and to save the OP the modicum of effort, here's one relevant link: https://public.nrao.edu/ask/orbital-period-of-the-sun-in-the-milky-way-galaxy :

... the Sun takes about 226 million years to orbit the center of our Galaxy, and it orbits at a speed of about 230 km/s. The distance from the Sun to the center of our Galaxy ... is about 8 kilo-parsecs (kpc) ...

 

[Entropix]

@phinds Velocities adds up when taking the GC and the faster moving rocket around the moon as references. If you have a mosquito inside your car that flies with the v1 considering your car as a reference it doesn't move with the car velocity alone vs a ground based reference it moves with v1+v2.

So taking v1+v2+v3+v4 idk if we still talk about only 230km/s. Those celestial bodies permanently moves relative one another.

I find that paragraph completely incoherent and have no idea what you are asking.

The question is if centrifugal force of the spinning black hole (BH) in the core of the galaxy has an influence on the galaxy general motion and if this general motion blue shifts or red shifts or it's simple none but rather fixed when taking the BH as reference. Adding some context, I've read that slowly the Moon increases its distance relative to the Earth so it rather red shifts (it moves outward slightly over time). It was not incoherent was rather let's say in a too 'condensed' form.

 

[phinds]

@phinds Velocities adds up when taking the GC and the faster moving rocket around the moon as references. If you have a mosquito inside your car that flies with the v1 considering your car as a reference it doesn't move with the car velocity alone vs a ground based reference it moves with v1+v2.

Motion addition in Relativity doesn't work that way and your asked about exceeding the speed of light. Nothing exceeds the speed of light.

The question is if centrifugal force of the spinning black hole (BH) in the core of the galaxy has an influence on the galaxy general motion and if this general motion blue shifts or red shifts or it's simple none but rather fixed when taking the BH as reference.

My understanding is that some rotating black holes do what is called "frame dragging" which has an effect on space-time in its immediate vicinity but not on the rest of the galaxy.

Adding some context, I've read that slowly the Moon increases its distance relative to the Earth so it rather red shifts (it moves outward slightly over time).

I seriously doubt that that red shift is measurable (but you are right that it exists, at least theoretically).

It was not incoherent was rather let's say in a too 'condensed' form.

I disagree. I'm sure YOU understood what you were asking, but ot me it was incoherent.

 

[PeroK]

@phinds Velocities adds up when taking the GC and the faster moving rocket around the moon as references. If you have a mosquito inside your car that flies with the v1 considering your car as a reference it doesn't move with the car velocity alone vs a ground based reference it moves with v1+v2.

So taking v1+v2+v3+v4 idk if we still talk about only 230km/s. Those celestial bodies permanently moves relative one another.The question is if centrifugal force of the spinning black hole (BH) in the core of the galaxy has an influence on the galaxy general motion and if this general motion blue shifts or red shifts or it's simple none but rather fixed when taking the BH as reference. Adding some context, I've read that slowly the Moon increases its distance relative to the Earth so it rather red shifts (it moves outward slightly over time). It was not incoherent was rather let's say in a too 'condensed' form.

You have some serious misconceptions about the theory of relativity. Most notably, you cannot exceed the speed of light by velocity addition.

In addition, you can't study a rotating black hole by applying Newton's laws and the concept of centripetal force. Not least because a black hole is a vacuum.

 

[Entropix]

You have some serious misconceptions about the theory of relativity. Most notably, you cannot exceed the speed of light by velocity addition.

Ok, my understanding was that only the INFORMATION can not exceed light speed not necessarily that two objects can not exceed light speed thru velocities addition relative to one another. Previously I thought that because our universe expands in an accelerated fashion some distant galaxies that moves relative to our solar system faster than the speed of light and so we can not see nor have any information about them since the information can not move faster than c. I mean my guess was that accelerating an 'object' for 14 bn years it has to go pretty fast.

Isn't it possible that the reason we can not see the galaxy core that we perceive it as being black/or a dark spot it's because basically no information/light can reach us but not necessarily because information can not escape BH huge gravity but because thru velocity addition of things inside/or on the BH relative to us exceed speed of light hence information/light can not reach us? And how fast a BH spins anyway?

So you guys say that two rockets both traveling let's say with the 3/4 of the light speed towards each other those move only with c and not 1.5 times c?

In addition, you can't study a rotating black hole by applying Newton's laws and the concept of centripetal force. Not least because a black hole is a vacuum.

BH is vacuum? Wow that really I didn't know, I thought it has some really mind blowing dense matter in it.

But tnx for the clarification.

 

[Nugatory]

So you guys say that two rockets both traveling let's say with the 3/4 of the light speed towards each other those move only with c and not 1.5 times c?

If A is moving at at speed $u$ relative to me and B is moving at speed $v$ relative to me, then the speed of A relative to B (and B relative to A) is not the $u+v$ we expect from your example with the mosquito in the car. It is $(u+v)/(1+uv)$ measuring time in years and distances in light years so that $c=1$. Google for “relativistic velocity addition” for more.

 

[Drakkith]

Ok, my understanding was that only the INFORMATION can not exceed light speed not necessarily that two objects can not exceed light speed thru velocities addition relative to one another.

Information is 'encoded' in matter and light. We don't detect information with a camera, we detect light. The information is contained in the pattern the light makes on the detector. So if no light or matter can travel faster than c, neither can information.

Previously I thought that because our universe expands in an accelerated fashion some distant galaxies that moves relative to our solar system faster than the speed of light and so we can not see nor have any information about them since the information can not move faster than c. I mean my guess was that accelerating an 'object' for 14 bn years it has to go pretty fast.

Mind-blowing fact: those distant galaxy were not accelerated away from us like a rocket accelerates. No force is being applied to them. They have been in free-fall the whole time. And from their point of view, we have moved away from them while they were stationary.

Isn't it possible that the reason we can not see the galaxy core that we perceive it as being black/or a dark spot it's because basically no information/light can reach us but not necessarily because information can not escape BH huge gravity but because thru velocity addition of things inside/or on the BH relative to us exceed speed of light hence information/light can not reach us?

This is difficult to understand, but I think the answer is no. Nothing escapes from beyond the event horizon of a black hole unless you want to start talking about hawking radiation (which doesn't really 'escape' from beyond the event horizon, but is produced outside of it). But that an entirely different subject and wouldn't change the answer to your question.

And how fast a BH spins anyway?

That depends on the size and some other factors. One black hole in our galaxy is spinning at around 1150 rotations per second, nearly the upper limit.

So you guys say that two rockets both traveling let's say with the 3/4 of the light speed towards each other those move only with c and not 1.5 times c?

Their closing velocity is 1.5c as viewed from an observer at rest with their 'midpoint', but that is not a physical velocity. Each rocket would see the other as traveling at 0.96c.

BH is vacuum? Wow that really I didn't know, I thought it has some really mind blowing dense matter in it.

It is unknown what lies beyond the event horizon, but it is likely that the majority of it is a vacuum or close to it. What happens near the singularity is unknown entirely.

 

[Entropix]

Ok, thank you all for these clarifications and better explanations of how things might/or do happen down there at a more refined scale than my previous understanding.

I've just read an article that said and I quote: 'One black hole, at the heart of galaxy NGC 1365 is turning at 84% the speed of light. It has reached the cosmic speed limit, and can’t spin any faster without revealing its singularity.'

Didn't knew a BH can spin that fast. Another quote that I've found (same article) related to this topic: 'Imagine the event horizon of a black hole as a sphere in space, and then surrounding this black hole is the ergosphere. The faster the black hole spins, the more this ergosphere flattens out.'

So this somewhat same/similar thought made me raise the question of centrifugal force as influencing the motion of galaxy knowing that the galaxy also has a flat or a disk like shape.

To give a comparison, when a drag racing car suddenly accelerates, its tires due to centrifugal force start dramatically flattening out, scaling things up and spinning such massive BH object at 84% from the c that indeed can influence the shape of a galaxy knowing that there must be more BHs near the GC.

I'll return when I fully digest all the info you guys provided maybe with another question.

Tnx once again

 

[sophiecentaur]

TL;DR Summary: Trying to understand how fast a planet can moves relative to the Galactic Center.

Long time had this question about how fast a planet, dwarf or not or even a rogue asteroid can move relative to the core of the Galaxy, where, if my understanding is correct it has to be a supermassive black hole.

Isn't it possible that the reason we can not see the galaxy core that we perceive it as being black/or a dark spot it's because basically no information/light can reach us but not necessarily because information can not escape BH huge gravity but because thru velocity addition of things inside/or on the BH relative to us exceed speed of light hence information/light can not reach us? And how fast a BH spins anyway?

It appears that the extension of a 'Solar System type model' to the orbits of the stars around the galactic centre just doesn't work, unfortunately. It doesn't behave as if there's a single massive attractor at the centre (whatever its internal structure). You need to use the total mass of all the stars PLUS a lot of dark matter to explain the observed paths and velocities. And you have to remember that it's only inside or near the Schwartschild radius (pretty damn close in) that a black hole's gravitational effect is any different from any other huge mass. Orbiting stars will stay in place and not be 'sucked in' because Gravity works the same way for black holes, same as for other masses.

This may be a bit off-topic but the Esa Gaia project has mapped millions of stars in the galaxy and their individual characteristics (velocities and chemistry) suggest strongly that our galaxy has in fact formed by cannibalising many other smaller galaxies. This happened 10By ago but the individual merged galaxies still retain much of their original characteristics and it's predicted that a 'thorough mixing' will take several tens of By. So . . . .the motions of some groups of stars are more to do with their original galaxy than with the Milky Way. Unsurprisingly, it's not a simple model.

 

[PeroK]

Ok, my understanding was that only the INFORMATION can not exceed light speed not necessarily that two objects can not exceed light speed thru velocities addition relative to one another. Previously I thought that because our universe expands in an accelerated fashion some distant galaxies that moves relative to our solar system faster than the speed of light and so we can not see nor have any information about them since the information can not move faster than c.

Things get more complicated when you include the expansion of space itself. But, that's not directly related to observations within our galaxy.

I mean my guess was that accelerating an 'object' for 14 bn years it has to go pretty fast.

If you want to understand more about the expanding universe, try this excellent insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[Entropix]

This may be a bit off-topic but the Esa Gaia project has mapped millions of stars in the galaxy and their individual characteristics (velocities and chemistry) suggest strongly that our galaxy has in fact formed by cannibalising many other smaller galaxies. This happened 10By ago but the individual merged galaxies still retain much of their original characteristics and it's predicted that a 'thorough mixing' will take several tens of By. So . . . .the motions of some groups of stars are more to do with their original galaxy than with the Milky Way. Unsurprisingly, it's not a simple model.

This I think isn't off-topic cos it provides an essential context given the fact that dark matter has such important role and Esa Gaia project not only confirmed this but additionally revealed this 'cannibalism' process between galaxies.

Hope the big league scientist at the top that have dark matter under their radar to give more clues about this mysterious kinda matter.

If you want to understand more about the expanding universe, try this excellent insight:

Tnx for pointing this resource, I'm gonna check it out.

Each rocket would see the other as traveling at 0.96c.

Yeah from the cockpit of one rocket the other rocket will have 0.96c but still in fact rockets approach with the velocity perceived by the observer at rest with their 'midpoint'. If let's say there's 1 light year in between the rockets those gonna met/collide in the midpoint faster (at ~ 0.5 light year from the start) and not after 1 light year, m I right?

To make it it more clear to me and please correct me in case I'm getting it wrong, if there are two planets 1 light year apart and in the middle there's a space station and simultaneously two radio signals leave both planets, information from both planets reach the space station twice as fast. So in the middle we gonna know what happened 0.5 light year from the first planet but also what happened to the other planet in that same 0.5 light year and not in 1 light year. Is this correct?

@Nugatory that's some serious/fairly complicated thing you've just pointed out thank you very much for that I'll look it up more closely.

 

[PeroK]

Yeah from the cockpit of one rocket the other rocket will have 0.96c but still in fact rockets approach with the velocity perceived by the observer at rest with their 'midpoint'. If let's say there's 1 light year in between the rockets those gonna met/collide in the midpoint faster (at ~ 0.5 light year from the start) and not after 1 light year, m I right?

To make it it more clear to me and please correct me in case I'm getting it wrong, if there are two planets 1 light year apart and in the middle there's a space station and simultaneously two radio signals leave both planets, information from both planets reach the space station twice as fast. So in the middle we gonna know what happened 0.5 light year from the first planet but also what happened to the other planet in that same 0.5 light year and not in 1 light year. Is this correct?

Yes, of course. Both radio signals travel at $c$. No velocity exceeds the speed of light in that scenario.

This is sometimes called "separation" speed. And, of course, the maximum separation speed is $2c$.

 

[Drakkith]

To make it it more clear to me and please correct me in case I'm getting it wrong, if there are two planets 1 light year apart and in the middle there's a space station and simultaneously two radio signals leave both planets, information from both planets reach the space station twice as fast.

I think you mean half the time, not twice as fast. 'Twice as fast' refers to velocity.

So in the middle we gonna know what happened 0.5 light year from the first planet but also what happened to the other planet in that same 0.5 light year and not in 1 light year. Is this correct?

That's right. The distance between each planet and the station is 0.5 ly, so it only takes 0.5 years for the signals to reach the station. Note that each planet would have to wait a full year for that information to reach them.

 

[Drakkith]

So this somewhat same/similar thought made me raise the question of centrifugal force as influencing the motion of galaxy knowing that the galaxy also has a flat or a disk like shape.

To give a comparison, when a drag racing car suddenly accelerates, its tires due to centrifugal force start dramatically flattening out, scaling things up and spinning such massive BH object at 84% from the c that indeed can influence the shape of a galaxy knowing that there must be more BHs near the GC.

For starters, I'm not sure there are more black holes near the galactic center. I'd guess there are more in the disk than the center thanks to the vastly larger number of stars and stellar material in the disk than the galactic center. But that's just a guess.

Second, stars and gas in a galaxy are not rigidly connected to each other like the molecules in a tire. So centrifugal force doesn't really come into play here. We could speed up the rotation of the stars near the center of the galaxy and it wouldn't do anything at all to the rest of the stars in the galaxy. The same is true of the black hole at the galactic center. The ergosphere extends a short distance from the event horizon, but the rotation of the black hole does nothing to objects beyond that distance.

The disk shape of galaxies arises due to conservation of angular momentum during their formation, not from centrifugal force.

 

[Entropix]

The disk shape of galaxies arises due to conservation of angular momentum during their formation

Well yeah but to have an angular momentum it means that we have a solar system or a star that has a mass, a tangential velocity and some orbit with a certain radius but the question would be what makes them having all that? Also if centrifugal forces of the BHs do not change the motion of the galactic disk what it does then, nothing, only that ergosphere thing? Isn't that too little?

After reading that some bh spins with the 84% of the c doesn't that mean that the speed itself increases the mass of the bh knowing that closer to relativistic velocities, mass starts to increases while it drains more and more energy to do that?

 

[PeroK]

After reading that some bh spins with the 84% of the c doesn't that mean that the speed itself increases the mass of the bh knowing that closer to relativistic velocities, mass starts to increases while it drains more and more energy to do that?

The concept of relativistic mass is generally a dead end, although still actively emphasised in popular science sources. In particular, gravitational mass does not increase with relative velocity.

That said, the angular momentum of a black hole, contributes to the spacetime curvature. See, for example, the Kerr metric.

 

[sophiecentaur]

The disk shape of galaxies arises due to conservation of angular momentum during their formation, not from centrifugal force.

It is also worth noting that the arms of a spiral galaxy are not spinning like the solid spokes of a rotating wheel. The visible arms are, in fact patterns of varying density that occur because of the stars' mutual interactions as they orbit around the galaxy. Rather like ocean waves travel over the surface of the sea but the water actually may go nowhere. Stars seen in one of the arms may well end up in a gap, after a few million years.

Well yeah but to have an angular momentum it means that we have a solar system or a star that has a mass, a tangential velocity and some orbit with a certain radius but the question would be what makes them having all that?

Beware of relying on virtually any intuitive picture of anything cosmological; a personal model is almost sure to be misleading about what's actually going on.

You seem to be seeing as different the angular momentum that's observable in, say, a solar system with the same quantity of angular momentum that existed in the primordial nebulae in which the stars were formed. Same quantity, just re-arranged over the eons. Any random nebula will (must ) have non-zero total angular momentum and the total doesn't change. You can't dismiss angular momentum as if it's just something that's around at the moment. Read around about the formation of stars in nebulae; it's fascinating and there are some great simulations (using hours of super computer time).

PS Hats off to all the calculations, made from millions of observations and the resulting models that have been developed in the last hundred years or so. (We've only been aware for a century or so that our Milky Way is not the sum total of our universe.)

 

[Drakkith]

Well yeah but to have an angular momentum it means that we have a solar system or a star that has a mass, a tangential velocity and some orbit with a certain radius but the question would be what makes them having all that?

No, rigid bodies in clear, differentiated orbits are not required. A giant gas cloud with enough self gravity to hold itself together has angular momentum in every one of its particles. The total angular momentum of the cloud is the sum of the angular momentum of each particle.

Also if centrifugal forces of the BHs do not change the motion of the galactic disk what it does then, nothing, only that ergosphere thing? Isn't that too little?

Centrifugal force does nothing in the context of a black hole. The ergosphere is not the result of centrifugal force. It is the result of the spinning of the black hole twisting spacetime, an effect known as frame dragging. Why should centrifugal force do anything at all? What would even be generating the centrifugal force? Remember that centrifugal force is a fictitious force, a force that only appears in a rotating frame of reference. From our non-rotating frame of reference outside the black hole there is no centrifugal force at all.

After reading that some bh spins with the 84% of the c doesn't that mean that the speed itself increases the mass of the bh knowing that closer to relativistic velocities, mass starts to increases while it drains more and more energy to do that?

Just to clarify, mass doesn't increase for an object moving linearly at high velocities. Otherwise objects would turn into black holes and collapse in on themselves just because some subatomic particle is moving at close to the speed of light relative to them (because then they are moving at near c relative to the particle).

However, mass does increase if you spin up an object, so a black hole that is slowed down should lose some of its mass as it does so.

I don't know what you mean about draining energy though.

 

[phinds]

However, mass does increase if you spin up an object, so a black hole that is slowed down should lose some of its mass as it does so.

I think that's wrong. The mass stays the same. It's the energy that changes, thus the stress-energy tensor changes.

 

[Drakkith]

I think that's wrong. The mass stays the same. It's the energy that changes, thus the stress-energy tensor changes.

I don't think so. It seems that you can extract energy from the Penrose process, reducing the mass of the BH. Unless I have misunderstood this process that is.

 

[phinds]

I don't think so. It seems that you can extract energy from the Penrose process, reducing the mass of the BH. Unless I have misunderstood this process that is.

I think we're saying the same thing. You extract ENERGY, thus reducing the stress-energy tensor. You don't extract mass.