Where Does Earth's Counter Gravity Go in an Expanding Universe?

[AgentSmith]

The rate of expansion is usually defined as $\dot{a}/a$. This rate is currently decreasing and seems to be approaching a constant value (proportional to the square root of the cosmological constant). When you have a differential equation given by:

{\dot{a} \over a} = H_0

where $H_0$ is a constant, then $a(t)$ has exponential growth. The solution is:

a(t) = a(0) e^{H_0 t}

So it's not the rate of expansion that is accelerating, but the distances between objects.

I understand the simple ODE. But the scale factor of the universe, a(t), is not constant, and neither is the Hubble parameter. I don't understand your last sentence.

 

[Chalnoth]

There are two different things here.
1. The rate of expansion is the Hubble parameter. This is decreasing and approaching a constant value.
2. The distances between objects are increasing in an accelerating manner.

 

[Rob Benham]

Is there any effect on for example the Earth, due to its deceleration in all directions simultaneously compared to the 'fixed stars'?

 

[Chalnoth]

The stars aren't fixed. They're orbiting the milky way. Within the milky way, the expansion has no impact at all.

 

[Rob Benham]

The stars aren't fixed. They're orbiting the milky way. Within the milky way, the expansion has no impact at all.

Hence, 'Fixed Stars' being in quotes.

I suppose it's much the same as calling gravity a force. I have to confess I haven't heard the term for a very long time, but it was often used, even in the heavier end of science books for the layman a couple of decades ago. I had a feeling back then that they didn't emphasize the almost 'mechanical isolation' of a galaxy clearly enough.

Anyway, to the point. Surely Earth for example, must be decelerating in all directions simultaneously compared to the bulk of the observable universe, and specifically, not our galaxy. What could be the effects of such relative motion?

 

[phinds]

Hence, 'Fixed Stars' being in quotes.

I suppose it's much the same as calling gravity a force. I have to confess I haven't heard the term for a very long time, but it was often used, even in the heavier end of science books for the layman a couple of decades ago. I had a feeling back then that they didn't emphasize the almost 'mechanical isolation' of a galaxy clearly enough.

Anyway, to the point. Surely Earth for example, must be decelerating in all directions simultaneously compared to the bulk of the observable universe, and specifically, not our galaxy. What could be the effects of such relative motion?

You are confusing recession with proper motion. They have nothing to do with each other. The proper motion of the receding galaxies relative to Earth is trivial compared to the recession speed, which by the way is about 3c for objects at the edge of the Observable Universe. There is no effect due to recession speed (other than that we see them red shifted)

 

[Chalnoth]

Hence, 'Fixed Stars' being in quotes.

I suppose it's much the same as calling gravity a force. I have to confess I haven't heard the term for a very long time, but it was often used, even in the heavier end of science books for the layman a couple of decades ago. I had a feeling back then that they didn't emphasize the almost 'mechanical isolation' of a galaxy clearly enough.

Anyway, to the point. Surely Earth for example, must be decelerating in all directions simultaneously compared to the bulk of the observable universe, and specifically, not our galaxy. What could be the effects of such relative motion?

Talking about this effect in this way doesn't make any sense.

There is a real effect where the expansion of the universe acts as a sort of friction, in that if you have one object which is moving at a high velocity in some direction compared to the background, then it will "catch up" to parts of the universe that are in that direction, becoming slower relative to its nearby surroundings. This has the effect of making the expansion more uniform over time (on very large scales).

But this effect only appears if you are looking at the whole. If you just look at the Earth, or just look at the Milky Way, there is literally no way to know that this is happening at all. There is zero impact.

It gets even worse when you realize that local gravitational attraction dominates over this effect at scales smaller than a few million light years.

 

[Rob Benham]

You are confusing recession with proper motion.

Not so much confusing, as failing to make clear the question details. It's just that an accelerated object, in my limited understanding, undergoes a change in the direction of motion. I wondered what the effects might be on something that was decelerating in all directions simultaneously relative to the total mass of all matter in the Universe.

I find it fascinating that such a phenomenon, in any event, would not be detectable.

The difference in types of motion: Do you used the terms 'Co-moving velocity' and 'actual motion'? Also that the movement of the galaxy through the expanding Universe is often called the 'Peculiar velocity'?

At this point, I'm not addressing the problem of the latter being too small to have any significant effect.

 

[phinds]

Not so much confusing, as failing to make clear the question details.

Hm ... didn't seem that way to me, but OK.

It's just that an accelerated object, in my limited understanding, undergoes a change in the direction of motion.

then your understanding is incorrect. Acceleration does not require a change in direction, just speed. A change in direction does imply acceleration but acceleration does not imply a change in direction.

I wondered what the effects might be on something that was decelerating in all directions simultaneously relative to the total mass of all matter in the Universe.

I have no idea what you could possibly mean by that concept.

 

[Rob Benham]

[QUOTE="phinds, post: 5225841, member: 310841

then your understanding is incorrect. Acceleration does not require a change in direction, just speed. A change in direction does imply acceleration but acceleration does not imply a change in direction.[/QUOTE]

Oh dear. Goes to show how careful one has to be.

What I failed to say was 'undergoes a change when accelerated along the line that it is traveling'. I was intentionally not using terms like 'Length contraction', but I did mean shortened in the direction of motion, or contracted. I also avoided using the term 'Lorentz contraction' as it would be pretentious to do so. But, what I am questioning is the possibility of any physical body in the Universe undergoing what is in effect, the reverse of such a change in all directions simultaneously.

I can well understand your reaction to such a concept.

 

[phinds]

What I failed to say was 'undergoes a change along the line that it is traveling'.

OK, yes that would be acceleration.

... what I am questioning is that any physical body in the Universe is undergoing the reverse of such a change in all directions simultaneously.

Such a change requires that a force be applied. What force is it that you think is being applied to the Earth in all directions simultaneously, that causes it to move in all directions simultaneously ?

The "reverse of such a change" in this case just means "no change at all" and your theory does not seem to me to hold water.

EDIT: When I say the opposite of "reverse" in this case means "none" what I mean is that you cannot decelerate in all directions at once any more than you can accelerate in all directions at once so you can only be talking about no acceleration.

 

[Rob Benham]

What force is it that you think is being applied to the Earth in all directions simultaneously, that causes it to move in all directions simultaneously ?

That's a good question.

I visualize a line from a point at the centre of the Earth going through a particle at the surface, and on to a distant or fixed star*. Take this to mean a visible object not in our galaxy. I assume the surface particle is moving away from that distant object for the two separate reasons mentioned earlier. I also assume that velocity is increasing.

Now construct such a line through every particle on the surface of our planet. I can only see that it is decelerating in all directions simultaneously. What affect that might have is what I've been curious about for a very long time. *Now I remember where that term came from. It was used by us old timer airline skippers when answering papers on gyros and astral navigation. It occurs to me now that we were unaware that we were only pointing our sextants at stars within our galaxy. )

 

[phinds]

I can only see that it is decelerating in all directions simultaneously.

And I can only say again that such a concept makes no sense. You cannot accelerate (or decelerate, which is just negative acceleration) "in all directions simultaneously". Motion is relative. Acceleration is not. In the Earth's frame of reference, the Earth is not moving.