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Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed, that G is independent of the density of the attracting body.
But you could also change x to get the same result, so the observed frequency isn't a function of M alone but of the gravitational potential -GM/x.
Your thought experiment seems ambiguous to me.
You say the gravitational potential is the same for two points of the same position of altitude from the centre of the earth.
That is an aproximation that doesn't take into account local densities. It you add them to the equation, you will find a higher gravity then higher gravitational potential in the denser location.
However, the difference is so small that I don't think it you can measure any effect on clocks.
But you say that in the denser region clocks will tick faster.
What is the reason and what would be the magnitude of the effect?
Quote from: alancalverd on 20/04/2017 09:10:10Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed, that G is independent of the density of the attracting body.A BH actually proves that statement incorrect.The difference between a black hole and regular mass is frequency is not possible in a black hole. The frequency produced in a spherical planet is reduced to the center of a planet if atomic clocks follow frequency. A correlation has been established. Time continues to tick slower to the center of a planet if we extend the observed tests.
Gravity potential energy is pe=mgh, where pe stands for potential energy, m is a body of mass in relation to Mearth, g is the strength of the g-field at h, and h 'can' be the height from the centre of the earth.
Alan - you seem to have fallen into the very common trap of believing that you have nothing left to learn.Quote from: alancalverd on 20/04/2017 09:10:10Henry Cavendish established in 1797, and practically every national laboratory and astronomical observation since then has confirmed, that G is independent of the density of the attracting body.The program "Gravity and Me: The force that shapes us" is really very informative and entirely disagrees with you on this point.It takes you on a journey around Britain with a set of laboratory scales and a laboratory weight and quite clearly shows one by how many Newtons that laboratory weight changes due to locational position and conditions.
Under the remit of conventional physics a clock in the greater gravity field will be observed to run slower.
......as predicted and proved by experiment, many times!We know gy = gmax - w2Rcos2ywhere gmax is g at the poles, w is the angular velocity of the earth, R the radius of the earth, and y is the latitude.It is surprising that a shift of only 2 degrees of latitude was distinguishable from the subterranean density effect, but the above equation is sufficiently accurate over small variations in y that it can indeed be used for locating geological anomalies like ore and oil deposits. Fortunately, national laboratories that maintain time standards are aware of the local value of g and hence can account for the difference between, say, WWV time signals (from Colorado) and MSF (from Cumbria). Now it seems that your hypothesis is that two clocks operating in the same value of g would run at different rates if their local geology was different. Very spooky. What mechanism do you think tells the clock whether it is sitting over sand, or over granite but under a lead roof, if g is the same in both cases?
if clocks were placed at locations of differing geological density but at the same height from centre of earth, and at same radius of centripetal motion,
For the 2 clocks of the suggested experiment - placed at locations of equal radius of centripetal motion, (to equalise SR effects) and at equal altitude, but at locations of differing geological density *and therefore at locations of differing g* - the clock in the denser location (compared to the clock in the less dense location) will have an increased m,