[geordief (OP)]

Imagine two scenarios.
A: There is a black hole merger  ,let's say 1000 lys away
B:a rogue planet or sun  makes its way towards  the same  observer again some 1000 lys away.

Now A causes gravitational waves that  curve spacetime  when they reach the observer but B 's  long journey also ,over time must ,I think alter the  spacetime curvature at the observer.

Does B accomplish a comparable result to A  without the "use" of gravitational waves?

ps I realize I  have probably mangled  this question .I wonder where I have slipped up this time ;-)

[Kryptid]

I don't think option B would be detectable at LIGO at all. LIGO detects changes in the distance between mirrors. When a gravitational wave passes through the detector, it causes an alternating expansion and contraction of the distances between the mirrors. The frequency of that alternation increases as two black holes come closer and closer to each other in their orbits until they merge. A rogue planet wouldn't replicate that.

[geordief (OP)]

I don't think option B would be detectable at LIGO at all. LIGO detects changes in the distance between mirrors. When a gravitational wave passes through the detector, it causes an alternating expansion and contraction of the distances between the mirrors. The frequency of that alternation increases as two black holes come closer and closer to each other in their orbits until they merge. A rogue planet wouldn't replicate that.

Thanks.I can see that any changes would be undetectable (it was /remains amazing  that the gravitational waves were detected at Ligo so to imagine any changes madr by the rogue planet are entirely theoretical.
But  the theoretical changes  (I am assuming the planet never accelerates) would be incremental  over trillions of years.

If there was a theoretical way to calculate  the spacetime curvature  where the observer was  compared to what it would have been  had the rogue planet never existed  then  could that be done?

And might  the  theoretical changes bear any comparison at all with the changes in scenario A?

[Kryptid]

If there was a theoretical way to calculate  the spacetime curvature  where the observer was  compared to what it would have been  had the rogue planet never existed  then  could that be done?

You can calculate the difference in force with pretty straightforward arithmetic, but the fact that Jupiter itself doesn't seem to be screwing with LIGO, despite being millions of times closer than the hypothetical rogue planet and changing its distance from us at a much higher rate would strongly suggest that it wouldn't produce a detectable signal of any kind.

And might  the  theoretical changes bear any comparison at all with the changes in scenario A?

In theory, a massive object approaching us should cause an incredibly teeny, tiny change in the distance of the mirrors over time. Even if you could detect it, it would be happening at a rate many orders of magnitude slower than what gravitational waves would cause. Also, the effect on the mirrors would be different. LIGO has two arms oriented at 90 degrees from each other for a reason: gravitational waves will affect each arm in a different and predictable way. That wouldn't be the case for a rising gravitational force from an approaching rogue planet.

[geordief (OP)]

If there was a theoretical way to calculate  the spacetime curvature  where the observer was  compared to what it would have been  had the rogue planet never existed  then  could that be done?

You can calculate the difference in force with pretty straightforward arithmetic, but the fact that Jupiter itself doesn't seem to be screwing with LIGO, despite being millions of times closer than the hypothetical rogue planet and changing its distance from us at a much higher rate would strongly suggest that it wouldn't produce a detectable signal of any kind.

And might  the  theoretical changes bear any comparison at all with the changes in scenario A?

In theory, a massive object approaching us should cause an incredibly teeny, tiny change in the distance of the mirrors over time. Even if you could detect it, it would be happening at a rate many orders of magnitude slower than what gravitational waves would cause. Also, the effect on the mirrors would be different. LIGO has two arms oriented at 90 degrees from each other for a reason: gravitational waves will affect each arm in a different and predictable way. That wouldn't be the case for a rising gravitational force from an approaching rogue planet.

Is it correct to describe the effect on the  distance between the two mirrors as being caused by a change in the curvature of spacetime at that (those) moment(s)? -caused by the arrival of the gravitational wave.

And secondly ,when the effect of something like an approaching rogue planet travelling for trillions of years before it reaches the observer is calculated mathematically  is it necessary to account for any quantum effects  or is there no limit  to the smallness of the size of the effect that can be calculated by purely classical means?

[Kryptid]

Is it correct to describe the effect on the  distance between the two mirrors as being caused by a change in the curvature of spacetime at that (those) moment(s)? -caused by the arrival of the gravitational wave.

It is indeed a change in space. It is an expansion of space in one axis with a simultaneous contraction of space on an axis ninety degrees offset from the first. Followed by the opposite: a contraction on the first axis and expansion on the second. Followed by another expansion and contraction again and again in sequence: https://en.wikipedia.org/wiki/Gravitational_wave#/media/File:Quadrupol_Wave.gif

And secondly ,when the effect of something like an approaching rogue planet travelling for trillions of years before it reaches the observer is calculated mathematically  is it necessary to account for any quantum effects  or is there no limit  to the smallness of the size of the effect that can be calculated by purely classical means?

I'm actually not sure about the answer to this question. If it gets small enough, a theory of quantum gravity might be needed.

[geordief (OP)]

 

   "It is indeed a change in space. It is an expansion of space in one axis with a simultaneous contraction of space on an axis ninety degrees offset from the first. Followed by the opposite: a contraction on the first axis"

I hope this is not just pedantry but would it be correct  to describe those movements (btw is it movements of  just space or spacetime as I assumed?) as changes in the curvature of spacetime?

In other words do  gravitational  waves propagate along 3 axes or (with time) 4 axes ?

[Halc]

I hope this is not just pedantry but would it be correct  to describe those movements (btw is it movements of  just space or spacetime as I assumed?) as changes in the curvature of spacetime?

No.  Spacetime is fixed, and does not 'change' anywhere since it is not set in time, but rather has time as part of it. The state of space changes over time. Gravitational waves move through space (at speed c) over time, so space changes size over time, which is what LIGO detects.

LIGO detects vibrations (sensitive from about 10 to 10k Hz) in that size change over time, or rather the ratio of two axes set 90? apart. It cannot detect say the expansion of space since 1) such expansion does not affect the ratio of those two orthogonal distances, and 2) the expansion of space, like the moving distant massive body, has no resonant frequency to it.

Oddly enough, that 10-10k Hz range, if doubled, is pretty much the range of human sound sensitivity, which means they can listen live to LIGO without modification, unlike say night-vision goggles which must translate IR frequencies into higher range where human sight is sensitive.