**Ask a monkey a physics question thread**

[Eric]

Thought Experiment: The black hole at the center of the Milky Way instantly disappears.

How long does it take for things to change for our solar system and our planet such that they no longer orbit around the center of the galaxy? How are gravity waves part of the change?

[MadMojoMonkey]

Thought Experiment: The black hole at the center of the Milky Way instantly disappears.

How long does it take for things to change for our solar system and our planet such that they no longer orbit around the center of the galaxy? How are gravity waves part of the change?

The solar system, i.e. everything inside the sun's sphere of influence, wouldn't really notice the difference aside from the dramatic changes in the appearance of the Milky Way as it expands and diffuses across the sky. The Earth is orbiting the sun, and so it doesn't really feel the gravity of the galactic center. There will be tidal forces, but at the distance the sun is from the galactic core, those are negligible. I mean, the moon's tidal forces are quite noticeable on Earth, but the tidal forces on Earth due to the sun are difficult to measure.

The sun will cease to orbit the galactic center ~27,000 years after the black hole annihilates, as it is ~27,000 light years from the center and gravity waves propagate at a rate of 1 light year per year (I.e. the speed of light).

Gravity waves are kinda like this:
Think of a trampoline. (Yeah, this again.)
I'm not re-stating all the pros and cons of this thought experiment; be aware that this is just a basic visual aid,

The galactic core is like a huge weight in the center of the trampoline. The weight sags down and sits at the bottom of a very curved pit in the trampoline. This curvature represents the effect of mass on space-time.

For the purposes of this visualization, replace the weight with a taught rope pulling down on the trampoline from the other side.
Then cut the rope.

The trampoline sheet will spring up. The wave of this up-springing will travel out from the center at the speed of sound in the trampoline sheet.

This is like the way the curvature of space-time would respond to the annihilation of mass. It springs back to the state of having no source of curvature. It overshoots that equilibrium position and then experiences a decaying oscillation as it settles down.
This creates ripples moving spherically outward.

I can't help but think of the ripples in a still pond, if I were to throw a rock into it. At first, the rock displaces the surface into a bowl shape, but then it releases that pull. The resulting waves (not of the impact, but of the release) are probably not a terrible way to visualize 3-d waves in 2-d. You just have to remember that space-time is 3-d and these waves are how the space-time stretches and compresses.

[MadMojoMonkey]

@ong: how about this little tidbit:

note: You can scan back to some of the earliest discussions in this thread to brush up on the relativistic gamma factor, but it works like this:
The faster you go, the more space is contracted in front of you, the more time is dilated all around you, and the more force it takes to accelerate you. That last one is known as the increase in relativistic mass.

As an object's speed approaches the speed of light, that object's relativistic gamma factor approaches infinity. Meaning that the amount of force needed to accelerate it AT ALL is approaching infinity. The result is that nothing with mass > 0 could possibly ever be accelerated to the speed of light, as it would require more energy than the universe (or any universe) can produce by any fathomable means.

Furthermore, if anything which has mass > 0 is actually moving at the speed of light, then it has infinite relativistic mass, and would exert infinite gravitational effect on the universe.


If photons have non-0 mass, then they MUST travel at less than the speed of light.
QED

In order to argue that photons do not move at the speed of light in vacuum, then you need to unravel Einstein's GR. GR is widely accepted as the most elegant theory in all of human history. It is entirely built on the most basic and simple assumptions and it gives us so many predictions. Plenty of these predictions were considered absolutely not physical 100 years ago. Yet, 1 by 1, every one of the predictions to be explored has turned out to be an observable physical phenomenon.

This is not to discourage you. It's to tell you where to start on that Nobel Prize you'll earn for getting this right.

[Eric]

The solar system, i.e. everything inside the sun's sphere of influence, wouldn't really notice the difference aside from the dramatic changes in the appearance of the Milky Way as it expands and diffuses across the sky.

How quickly would the dramatic changes in the appearance of the Milky Way happen?

[MadMojoMonkey]

How quickly would the dramatic changes in the appearance of the Milky Way happen?

You wouldn't see anything for 27,000 years. Same as the time it takes to notice anything at all that is 27,000 light years away.

I've looked into some numbers and I'm now a bit skeptical how dramatic the changes would be. In fact, let me take back all the stuff I said about this earlier. I was comparing it to the "solar system w/o a sun" scenario and that's just no good here.
mass of Milky Way: ~10^12 solar masses
mass of Sagitarius-A: ~4.3(10)^6 solar masses

Sagitarius-A is the name of the suparmassive black hole in the center of the Milky Way. It's only 4 millionths the mass of the Milky way. This is really not even close to our previous discussion. The sun is well over 99% of the total mass of the solar system. Given this, I think most of the objects in the galaxy would remain gravitationally bound to each-other as a galaxy.

The objects bound tightly to the core would likely be flung out, but it seems not very likely that many of them would have escape velocity of the now less massive galaxy. They would have to be quite near escape velocity already.

My current guess as to what we'd actually see in the night sky is that the bulge in the Milky Way toward it's center would become slightly bigger and less bright as the objects orbiting the center would acquire more eliptical orbits as they responded to the change in gravitational potential.

[Eric]

You wouldn't see anything for 27,000 years. Same as the time it takes to notice anything at all that is 27,000 light years away.

Right, I understand that we won't see a change in something that is 27,000 light years away for another 27,000 years. I guess the question should be, how quickly would the changes in the geography of the Milky Way happen? In other words, suppose a given star is 15,000 light years from the center of the Milky Way. Will it start drifting out more then 15,000 light years from the center the very second the black hole disappears or will it take longer for it to lose its gravitational attraction and drift out?

[MadMojoMonkey]

Right, I understand that we won't see a change in something that is 27,000 light years away for another 27,000 years. I guess the question should be, how quickly would the changes in the geography of the Milky Way happen? In other words, suppose a given star is 15,000 light years from the center of the Milky Way. Will it start drifting out more then 15,000 light years from the center the very second the black hole disappears or will it take longer for it to lose its gravitational attraction and drift out?

It will take 15,000 years for it to lose the gravitational attraction.

[Eric]

It will take 15,000 years for it to lose the gravitational attraction.

Makes sense, thanks for the clarification. Today I re-read a 2003 New Scientist article that reports on the 2002 measurement involving Jupiter:

The speed of gravity has been measured for the first time. The landmark experiment shows that it travels at the speed of light, meaning that Einstein’s general theory of relativity has passed another test with flying colours.


Ed Fomalont of the National Radio Astronomy Observatory in Charlottesville, Virginia, and Sergei Kopeikin of the University of Missouri in Columbia made the measurement, with the help of the planet Jupiter.