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Calculating Earth-surface gravity by integration
According to analyses stretching back to Isaac Newton, the surface gravity of a planet can be calculated assuming all the mass of a planet is at its centre. This zomb seeks, instead, to calculate the surface gravity of the Earth using the data in PREM (Preliminary Reference Earth Model), in particular variation of density with depth. Any method of calculation may be used, the attached file gives one suggestion. If catchers are aware of such a calculation done previously and its result, a reward of Q100 will be paid instead for the first response. The Earth and all its internal layers may be assumed spherically shaped, and the reference point at sea level. (ZBL#158). See also attached file ZBL158X.pdf.
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The successful response to this zomb, as in the attached file, shows that calculating the surface gravity on a spherically symmetrical Earth by any integration method gives the same result as assuming all the mass of the Earth is at its centre.
Here there may be starting point for studies of how surface gravity may be affected by situations where spherical symmetry does not apply -- for instance, the Inner/Outer Core boundary has been claimed to be irregular in parts.
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