[Janus]

No, it doesn't.   GRACE is measuring the local field strength at a fixed altitude.  From this, you could calculate the field strength at any other fixed altitude (say, Mean Sea Level).   This means that the map does not represent the value of g at the actual physical surface,  But the difference in measured g at the same altitude for different parts of the globe. 

So are you saying that when GRACE takes these measurements over the top of the mountain (or valley), that gravity is not reducing by the inverse square law within the distance between the mountain top (or valley) and GRACE's position of altitude?
That gravity is somehow weaker at the mountain top than GRACE actually reads, and stronger in the valley than GRACE actually reads?

I am saying that GRACE is not measuring the strength of gravity at the mountain top or valley floor, but the strength of gravity at the altitude of where GRACE is and to determine the actual local strength of gravity at the Mountain top or valley floor, you do have to take into account fact that gravity falls off by the square of distance and that the valley floor is closer to the center of the Earth than the Mountain top.    Put another way.  If we were to use the Grace data to calculate the local value of g at 6 km above MSL over Western Australia, you would get a slightly smaller value than it would if you used it to calculate the local g on a 6 km altitude mountain peak in the Andes.    But as you continue downward from 6 km above MSL to ground level in Western Australia, the local measurement of g would increase as you got closer to the center of the Earth, and this increase would overwhelm the small difference in g at 6 km above MSL in the two locations.

[timey (OP)]

Since sea level automatically follows the surface of equipotential, clocks at MSL would be subject to the same equipotential, and would run at the same rate.  So the reason why sea level settles where it does, and why clocks at this level all run at an equal rate is one and the same.

Ok - yes I understand this. But what I'm looking for is the mathematical division or percentage of which time effect is doing what.

As the equitorial bulge gets higher, (at sea level) there is more mass between clock and centre of earth. GRACE shows where there is more mass between centre of earth and surface as red. (stronger gravity)
As the equitorial bulge increases in height, clocks will tick faster due to elevation, but slower due to increased centripetal speed (yes I know, minute differences), and the result is that clocks tick at same rate at each longitude (sea level) from pole to equator.

What I want to understand is by how much does the increased 'mass' between centre of earth and surface (equatorial bulge) contribute to cancelling out the increase in time due to the increase in height* - With respect to how much the increase in cenripetal speed caused by the increase in height (causing a slowing of time) contribute to cancelling out the increased tick rate that is due to the increase in height.
(*we observe that raising a clock 'without' increasing surface height will also increase a clocks tick rate)

[timey (OP)]

I am saying that GRACE is not measuring the strength of gravity at the mountain top or valley floor, but the strength of gravity at the altitude of where GRACE is and to determine the actual local strength of gravity at the Mountain top or valley floor, you do have to take into account fact that gravity falls off by the square of distance and that the valley floor is closer to the center of the Earth than the Mountain top.

Ok - I will take what you say on board - but if I imagine how GRACE manages their data it kind of goes like this:

Got a gravity reading.
Where are we?
What distance to surface?

Use of square (? terminology check "as opposed to inversed square") places gravity strength at top of mountain as ? Places gravity at bottom of valley as?
But perhaps my imagination doesn't serve me well, and I am mistaken?

[Janus]

I am saying that GRACE is not measuring the strength of gravity at the mountain top or valley floor, but the strength of gravity at the altitude of where GRACE is and to determine the actual local strength of gravity at the Mountain top or valley floor, you do have to take into account fact that gravity falls off by the square of distance and that the valley floor is closer to the center of the Earth than the Mountain top.

Ok - I will take what you say on board - but if I imagine how GRACE manages their data it kind of goes like this:

Got a gravity reading.
Where are we?
What distance to surface?

Use of square (? terminology check "as opposed to inversed square") places gravity strength at top of mountain as ? Places gravity at bottom of valley as?
But perhaps my imagination doesn't serve me well, and I am mistaken?

GRACE Consists of two satellites following each other closely in orbit.   The gravitational variations are mapped by carefully measuring how the distance between the two satellites change as they pass over different points of the globe.   This tells the satellites how much the Earth's gravitational field varies.  And this variation is what the map represents.  It is not a map of how local gravity changes at local ground level.    You could work this out from the Grace data and the topological data, But Grace doesn't, because that's not what the research is about, but rather the general "shape" of the Earth's gravity field.  It is about how mass distribution caused by a number a factors (crustal thickness and density for example) effects the measurement of g from point to point on the Earth,  Without worrying about the local changes due to local altitude.  In the case of this study, those variations in " on the spot" measurements in g caused by differences in altitude at ground level is noise to be ignored in order to get to the more interesting data underneath.   

[timey (OP)]

GRACE Consists of two satellites following each other closely in orbit.   The gravitational variations are mapped by carefully measuring how the distance between the two satellites change as they pass over different points of the globe.   This tells the satellites how much the Earth's gravitational field varies.  And this variation is what the map represents.  It is not a map of how local gravity changes at local ground level.    You could work this out from the Grace data and the topological data, But Grace doesn't, because that's not what the research is about, but rather the general "shape" of the Earth's gravity field.  It is about how mass distribution caused by a number a factors (crustal thickness and density for example) effects the measurement of g from point to point on the Earth,  Without worrying about the local changes due to local altitude.  In the case of this study, those variations in " on the spot" measurements in g caused by differences in altitude at ground level is noise to be ignored in order to get to the more interesting data underneath. 

So when I look at the GRACE gravity map, if I want to know local gravity on top of the Andes I need to take on board that actually gravity is weaker at the top of mountains and stronger in the valleys, and that the reality of gravity on the ground is (kind of) the inverse of what GRACE data shows... Gotcha.

[alancalverd]

The only way to measure g at a point, is to take a gravimeter there.

The way to measure gravitational potential at a point is to take a clock there.

[timey (OP)]

The only way to measure g at a point, is to take a gravimeter there.

https://www.nasa.gov/audience/foreducators/k-4/features/F_Measuring_Gravity_With_Grace.html

"As the lead satellite passes over an area on Earth of slightly stronger gravity, it detects an increased gravitational pull and speeds up ever so slightly, thus increasing its distance from the trailing satellite. Conversely, the lead satellite slows down when it passes over an area of slightly weaker gravity, decreasing the distance between the two satellites."

Nothing to do with a gravimeter, and everything to do with gravitational acceleration at that location.

[timey (OP)]

Anyway @Janus
To wrap up my GRACE observation, it is interesting that if one inverses the GRACE gravity map so that there is weaker gravity at top of mountain - then the faster rate of time in weaker gravity describes the acceleration GRACE observes...(Bc an object's speed will be increased by an increase in the rate of time)

But this does leave one scratching one's head as to why there is weaker gravity at position of greater depth from surface to center earth.

Clearly, as you have outlined in above posts, at ground level earth, the centripetal force will have an effect on the amount of downward attraction that a body feels, and this contributes to a weaker gravity at the top of mountains due to extra centripetal speed at the greater height.

Without the factor of centripetal force, GRACE is showing us the opposite.

Again I find myself straight back to wanting to know 'the percentage' by which the slowing of time due to centripetal speed, and 'the percentage' by which the slowing of time due to stronger gravity field, are together responsible for cancelling out the speeding up of time due to weaker gravity at height - with respect to time being uniform at sea level of evey longitude of the equatorial bulge...

[timey (OP)]

OK - so @Janus, I haven't been able to find anyone to run me through the exact mathematics of the equatorial bulge, but have come up with some equatorial bulge considerations:

+relative speed, or centripetal speed = time going slower.

-minus relative speed, or centripetal speed = time going faster

+centrifugal force = time goes faster
-centrifugal force = time goes slower

higher GP = +centrifugal force + centripetal speed = time going faster

lower GP = -centrifugal force -centripetal speed = time going slower

+mass = time goes slower
-mass = time goes faster

Equatorial bulge sea level - Conventionally:

1: +mass = time goes slower
2: +height = +centrifugal force = time goes faster
3: + mass = -centrufugal force = time goes slower**
4: +centripetal speed = time goes slower
= same rate of time at sea level each longitude.

=slower, faster, slower, slower

= 3 slower + 1 faster


without bulge:

+height = +centrifugal force = time goes faster
+ centripetal speed = time goes slower
= time goes faster

So +mass of equatorial bulge = time goes slower cancelling time going faster = same rate of time at sea level each longitude

Here we are saying that +mass is the same as -centrifugal force?

--------------------------

At this juncture I am now swapping over to this thread on New Theories in order that I may talk further on this subject outside of the remit of Physics Board speak...

https://www.thenakedscientists.com/forum/index.php?topic=69800.msg542632#msg542632

[yor_on]

Actually that's a rather profound definition Janus.
Although the gravity is 'null' (presumably:) at 'Earths inner center' as observed by someone there, his clock still will tick slower than a clock at the surface, if both was synchronized with each other (same frame of reference) at some earlier time and place. Makes a really good argument for SpaceTime being the culprit.

[Zer0]

Off - Topic Post. (subjective)

A sound Advice for any Guests/Amateur or Beginner level newbies wannabes Physicists. (subjective opinion)

If you are following this discussion & reading it word to word, using a scientific dictionary side by side.

And if all that heavy technical jargons & scientific verbiage is making your head spin or dizzy.
If all of a sudden, for no reason you start humming the song " amazing GRACE how sweet the sound, that saved a wretch like me ".

Then Ladies & Gentlemen, now would be a good time to take a Break.
Shut the door n lock it, close all the windows n pull the curtains, switch off the lights, remove all your clothes n just dance like nobody's watching.
(Trust me, you need this) 👍

Copyrights, Thanks & Credits - CCMusicFactoryVEVO(channel)/YouTube.

Enjoy!
✌

P.S. - timey & Janus how about you both meet up n get a room n have a GRACEfull conversation in the name of Science. 👌