gravitation waves vs. gravity (supernewbie)

Hmmmm ..... it's essentially change with time. Try this:

Let's go far far away from anything else. Put a single mass in place and make it something quite big - say around planet size or so. Now take another somewhat smaller mass - say 100kg - and call this the test mass. Actually we'll make it you suitably suited and provisioned. Being much smaller than the first you won't have a significant influence on the planet. But if we move Merle about we could measure effects on you and 'map' out the gravitational field. This can be described by a vector ( an arrow, with a direction and a length ) at each point in space.

Closer in to the central mass the field is stronger [ vectors are longer ], further out the field is weaker [ vectors are shorter ]. Also the field points toward our central body, indicating that gravity is attractive, so the vectors are pointing toward the central mass. If the planet is made of something suitable and reasonably arranged, the vectors will point to it's exact [ geometrical ] centre. If you examine the length of those vectors versus the distance from the centre of the planet then they will go like 'inverse square' - so if Merle goes out to double some previous distance then the field strength goes down by a factor of four ( ie. to 25% ), or move in three times closer and the strength increases by a factor of nine.

( Aside: we could also note that there is something that goes like the square of distance from a central point in three dimensional space - the surface area of a sphere centred on that point ).

Now let's choose other central masses and see what happens to our measured field ( assume we stay outside the substance of the planet ie. above ground ). It will retain all of the above characteristics but the strength at any previously measured point now increases linearly with the central mass. Double the mass, double the field - a quarter of the mass gives 25% - etc.

Kepler, Newton and others defined this pretty well ( though not in our modern language ). However this is all static meaning that we didn't measure the field during any period when the central body changed.

Suppose, Merle, we left you out there while the planet's mass was being doubled, over say a ten-second time period. Then the field goes up to double it's previous magnitude - at each point the vectors stretch to twice their length - over those ten seconds. This could be called a monopole change in the field, meaning that even though the magnitude increased, all those vectors still point back to the same single original point at the planet's centre. This actually can't happen because it would require the creation/destruction of mass ( or equivalently energy ) to/from nothing. To date no one has seen any violation of the principle of conservation of mass/energy - you can interchange via the famous E = mc^2, but no free lunches ( or disappearing ones ).

OK, now let's try another change to the planet. Let's move the whole thing sideways by 100m to your right and further away from Merle while you remain in place ( for the moment let's ignore how to be sure of what 'in place' means ). Then you will experience a change in both the strength ( down a bit, shorter vector ) and direction of the field ( over a bit to the right ) at your position. If you plot these changes with time on some chart then it will, naturally, look like a transition between being in the presence of one planet followed later by being in the presence of an identical one ( but 100m to your right ). This could be called a dipole change in the field. This can't actually happen either, as in this case we have no 'reacting' mass. To get the planet to move we would have to influence it with another 'something' to shift it. If it did 'magically' displace sideways then we would violate another of Newton's Laws - the 'equal and opposite action and reaction' one - or equivalently the conservation of momentum if you like. Like the conservation of mass/energy, no violations have been observed to date.

Phew! Are you still with me?

So how do we get a change in the field? How do we get a time variation in the field - which would propagate out with the speed of light as positions further out 'feel' the changes - and thus have 'waves'?

It turns out that a 'non-spherically symmetric' change will do it. A good example is the Earth going around the Sun - we could examine this two body system without altering it by moving Merle about as a test mass. At any given moment the Earth/Sun system has an axis to it - the line between the two - and can't be described by a monopole field change or a dipole field change. A 'quadrupole' field fits the bill here. Think of one second's worth of change from Merle's viewpoint, floating out there somewhere and still suited and provisioned! During that second the Earth has moved between two points ( a dipole change ), but so has the Sun ( another dipole change ). So it is, sort of, two dipoles making a quadrupole ( four mass ) field change. ( You might consider the reasonableness or otherwise of tripolar, or any other odd-polar, field changes ...... ). Note that the Sun does move too, just not as much as the Earth. They both orbit around a common centre which lies well within the Sun - not at the Sun's centre.

So now we have gravity waves from a solar type system! Merle will note a rhythm in the field changes as each full orbit restores the system to ( nearly ) the same state - the waves have a regular period ( guess how long? ). Because of the feebleness of gravity, relative to other forces, a suitably place LIGO ( at say our second nearest star system of Alpha Centauri ) will have to be pretty good to pick this up. Note that these waves moving away from the system cause it too lose energy, hence each orbit brings them slightly closer.

To get the waves really rocking one has to :
(A) - choose a system with really big masses all round. Try binary star systems with either or both members neutron stars or black holes.
(B) - choose a system with quicker changes. Try one of type A above, but have them close in to each other and orbiting fast.
(C) - choose a system which is really changing fast. Try one of type B above, but where the time scale is well within our lifetimes, energy is draining rapidly from the system, the members are moving closer together quite noticeably and will collide and merge. These are the 'inspirals' ( ie. spiralling in ) sought for as part of E@H.

There are other non-spherically symmetric arrangements too. I've glossed over some finer details purists may object to. I haven't really melded relativistic time distortions in either. The full General Relativity treatment I don't actually grasp in toto [ who does ? :-) ]. But I'm having a quiet Sunday morning so I thought I give it a whiz.... :-)

Cheers, Mike.

It does spin around it's own axis, which goes through it's centre from 'North' to 'South' .... I was referring to the orbit of the Sun and the Earth around each other. Think of it like two dancers ( Torville and Dean on ice say ) - they hold hands and swing around each other ( orbit about a point between them ), but each can spin separately around themselves ( revolve around a line from head to toe ).

Because the Sun is such a fatty compared to Earth then the point around which they orbit ( that is follow a closed path in space, close enough to an ellipse shape or slightly flattened circle ) is within the Sun itself. As it's mass is some 330,000 odd times that of the Earth, and about 150,000,000 kilometres from Earth - then this common orbital centre ought be about 500km off the Sun's centre.

Mind you the real solar system has Jupiter et al, so the actual dance is somewhat more complicated. The centre of mass ( or barycentre ) which I've been describing is still well within the Sun, as it has about 98% of the total mass in the system.

Cheers, Mike.

Because Earth and other planets pull the Sun with their gravitational fields
and as a result the Sun wobbles. Actually by measuring such wobbles of others stars scientists were able to detect and calculate the orbits of a number of extra-solar planets

I enjoy giving them! Except if I err ...... :-)

Ok, we have a see-saw, we know it's total length and the weight of the people either end - so where do we place the pivot such that it balances?

mass1 * distance1 = mass2 * distance2

so that distance1 / distance2 = mass2 / mass1

( an inverse relationship, meaning the heavier mass is closer, the lighter further out )

and

distance1 + distance2 = const

now ( about ) mass of Earth = 81 * mass of Moon

and Earth/Moon separation ( about ) = 384000 km

so 384000/(81 + 1) = 4680km ( ie. about 5000km )

radius of Earth = 6350 ( about )

barycenter distance from surface = 6350 - 4680 = 1670km ( ie. about 1500km )

I concur, give or take a tad!

Good old Wiki! - Earth and Moon.

So as we speak we are all orbiting that barycentre! Last night the Moon was overhead DownUnder so I was on the Moon's side of that point. Today I've moved round that point to the side opposite the moon, and herein lies an interesting tale.....

I'm constrained to attempt to comply with two 'dances'.

- I'm following the surface of the Earth as it rotates about it's own axis which goes through the geometric centre of the Earth.

- I'm orbiting with the Earth around the barycentre common to the Moon.

- because those centres are distinct by about 5000km then I have varying forces upon me : which I interpret as tides!

Yup, we are all tidally affected but not in a way that is 'everyday' noticeable. I'd need to have some large spatial extent and be somewhat more fluid to obviously distort from this effect. Being middle aged I do have some spread, which my daughter labels as 'bouyancy', but I'm not actually an ocean ..... :-)

In fact the LIGO's have to account for this, merely one of the blizzard of effects to be accounted for ( then subtracted away ) to finally get to the General Relativity effects of primary interest. The Earth's surface has some plasticity and will rise and fall with the Moon's tidal influence, the Sun also, and probably the other planets if we look hard enough.

If you go to the detector logs, say Hanford's ( User name: 'reader', Password: 'readonly' ), then check out the 'Site Overview' graphic/screenshot ( expand/zoom if needed ) you'll see in the lower left area a 'TIDAL' section which indicates the corrections/offsets required in the arms.

Cheers, Mike.

Outstanding point!

What saves the whole enterprise is that most disturbances ( things wiggling the detector other than the astronomical events we seek ) do not have a preference in trend. Take 'shot noise', a limiting factor at the higher frequency end of the LIGO band. This is due to a bunch of photons arriving at once at a mirror - so for a brief period an above average number of hits occurs. This is part of the quantum mechanical uncertainty of photon behaviour. But, like a good bookie, then by waiting the odds will swing - in that fewer ( than average ) photons will arrive at other moments. This does of course get those mirrors wobbling but after a while that effect averages out.

My analogy is like a seashore, alot of stuff transient/momentary going on, wind/waves/birds/sand/weather, but if you wait the tide comes and goes. Many of the desired astronomical signals are cyclic but you generally need some expected waveform/template to search for. There is a probabilistic/confidence aspect to this. The E@H effort is largely trying to bring out signal from noise.

Mind you there are plenty of disturbances with a 'trend' in the same direction as our interest. The Livingstone logs show two trains and an earthquake earlier this week which threw the detector out of science mode lock for hours - you can only toss that time away alas. But having several separated detectors ( planet wide ) will filter out quite alot of that sort of stuff, or at least 'park' the disturbance in a known region of the dataset.

Cheers, Mike.