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@Colin2B, I am just making use of this thread here to further discuss under the freedom of 'New Theories' a subject that I started on Physics board that @Janus was participating in here:https://www.thenakedscientists.com/forum/index.php?topic=73266.msg541684#msg541684Where I am trying to get to grips with the equatorial bulge. (Back to Shapiro Effect with you as and when you are up for it)----------------------------So repeating the consideration from that thread:+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 slowerhigher GP = +centrifugal force + centripetal speed = time going fasterlower GP = -centrifugal force -centripetal speed = time going slower+mass = time goes slower -mass = time goes fasterEquatorial bulge sea level - Conventionally:1: +mass = time goes slower2: +height = +centrifugal force = time goes faster3: + 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 fasterwithout bulge+height = +centrifugal force = time goes faster+ centripetal speed = time goes slower= time goes fasterSo +mass of equatorial bulge = time goes slower cancelling time going faster = same rate of time at sea level each longitudeHere we are saying that +mass is the same as -centrifugal force.------------------------Now under my theory everything is the same except:+mass = time goes faster-mass = time goes slowerEquatorial bulge sea level:1: +mass = time goes faster2: +height = +centrifugal force = time goes faster3: + mass = -centrifugal force = time goes slower** 4: +centripetal speed = time goes slower= same rate of time at sea level each longitude.= faster, faster, slower, slower= 2 faster, 2 slower.without bulge+height = +centrifugal force = time goes faster + centripetal speed = time goes slower= 'time goes faster'So +mass = time goes faster and +mass = -centrifugal force = time goes slower= 'time goes slower'.Add the above two together and 'time goes faster' and 'time goes slower' cancel= same rate of time at sea level each longitude.Here I am saying that + mass and -centrifugal force are NOT the same thing!Now because where there is more mass/gravity, 'time goes faster', this gives a physical cause and effect description of why GRACE moves faster over the mountain than over the valley.(This theory can be tested by placing a precision clock at LIGO to see how the clock ticks when a gravity wave hits.)
An oblate spheroid adds an additional complication. First consider the scenario with no rotation. This can be look at a like a spherical body with a world girdling "hill" around the equator. In this situation, walking from either pole to the equator is walking "uphill" and you are moving to a higher gravitational potential, where clocks run faster than they do at the poles. If the "hills" were mass-less then you could use the simply version of the gravitational time dilation equation to work out just how much faster. But since they aren't, it is a bit more complicated. The way the mass is distributed will have an effect, and it would take a bit of additional calculation to work out just how much difference this will account for. If the Body is rotating and had no gravity, then someone moving from pole to equator would be effectively moving "downhill" to a lower potential causing clocks to run slower at the equator than at the poles, since the tangential speed is greatest at the equator. If, as we have with the Earth, both effects are in play and the degree oblateness is due to the combination of the Gravity of the body and its rotation due to the plasticity of the body, we get the case where these two time dilation effects combine in such a way that all clocks at mean surface "level" run at the same rate. ( if the surface is bumpy), you'll get variations between depressions and rises.)
So - given that GRACE shows that gravity is stronger at top of mountain than in valley,
Edit: I just looked at the GRACE gravity map again, and it clearly show red at the top of mountains, and it show a graph that suggests that red is equal to stronger gravity. I can't be reading that wrongly, can I?
So where the GRACE anomaly map shows red at top of mountains, and it states that anywhere red is showing a stronger gravitational acceleration, are you saying that that the red areas are not showing stronger gravitational acceleration?Edit: I just looked at the GRACE gravity map again, and it clearly show red at the top of mountains, and it show a graph that suggests that red is equal to stronger gravity. I can't be reading that wrongly, can I?Yes, you are reading the map wrong, In at least one way. You keep wanting to interpret the GRACE readings as the strength of gravity at ground level, When they represent the fluctuations from the mean value of gravity measured at the altitude of the Satellites. To get how gravity changes at ground level, you would have to combine this information with exactly how far ground level is from the center of the Earth at the point of interest. The gravity map supplied by grace doesn't include this second bit of information.Also, your insistent claim that red is at the top of mountains isn't always true. In the GRACE map: There are areas where higher gravity is associated with mountains, bit also areas where it is associated with low spots, such as out in the North Atlantic. You weren't under the impression that the "bumpiness" in the Gravity map represented elevation of the ground at that point were you? It is just a way of "doubling up" on how they represented the gravity measurements. They are shown in both color and and relief. If you want to look for a correlation between the gravity map and geological features, this tectonic plate map is of interest.Note that there is some correlation between where plates meet and high gravity areas( including that region in the North Atlantic.) This is likely due to how local density of the crust is effected. In certain places, this will also correlate with mountian ranges ( West coast of the Americas and the Himalayas, for example), but that is because these meeting points between plates are subduction zones, where mountains tend to be built.
But our Earth is both rotating and has gravity anomalies that differ from the conventional 'gravity potential'......And what I want to do is to calculate the rotational aspects of relative motion time dilation, and the gravity potential anomalies aspects of time dilation together, because that is what we observe occurring on our planet....And I want to do this as a modification of general relativity where the factor of the gravity that clearly holds a clock to the top of a mountain 'is' included. This being because this extra gravity holding the clock to the mountain against the centrifugal force 'is' a factor that exists, isn't it?
@Janus. I think you misunderstand my purpose.I am quite simply interested in calculating time dilation using both the 'relative motion' and the 'gravity potential' equations in order to arrive at a 'contant rate of time' for sea level at each longitude of the equatorial bulge. (this being on basis that the equatorial bulge constitutes both changes in height and changes in speed occurring simaltaniously)That is all I am interested in. You have said that 'adding in' the 'extra mass' of each increase in the equatorial bulge would require some additional calculation.I am saying that 'if you add in' that extra mass that contitutes an increase in height of the bulge from poles to equator, where an aspect of +mass=time goes slower (conventional GR remit) must now be added to the calculation - this will NOT, under the conventional means of calculating, result in a constant rate of time at sea level of each longintude of the equatorial bulge.You may tell me that my understanding is amiss somehow and 'show me how' adding in the extra mass under the remit of +mass=time goes slower WILL result in a constant rate of time at sea level of any longitude...***In which case I will then AGREE with you that there isn't any necessity for a modification of GR.***
Clocks at sea level tick at the same rate no matter how you try to calculate it.
Here is my first paper, now published at Journal of Space Exploration...http://www.tsijournals.com/articles/TSSE-18-2146.pdf