Maximum Latitude Difference for Equal Centripetal and Gravitational Acceleration

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Discussion Overview

The discussion centers around the question of the maximum latitude difference between two locations on Earth where the total centripetal and gravitational accelerations are equal. It explores the theoretical implications and variations in measurements due to various factors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants suggest that the maximum latitude difference depends on accuracy and sensitivity, noting that no two different latitudes in one hemisphere have identical values.
  • There is a belief that a standard weight measured over the Earth's surface would vary continuously, although some participants acknowledge that geological factors and elevation also influence gravity.
  • One participant posits that while variations due to geology might be negligible, the relationship between centripetal force and variations in radius and asymmetry could lead to equal weights at different latitudes, contingent on specific models of the Earth's shape.
  • Another participant expresses curiosity about the question, finding it aesthetically intriguing to consider how widely separated points could have the same magnitude of acceleration.
  • A suggestion is made to reference external resources for further information on the topic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the maximum latitude difference, and multiple competing views regarding the factors affecting gravitational and centripetal acceleration remain present throughout the discussion.

Contextual Notes

The discussion highlights limitations related to the assumptions about geological influences, the dependence on specific models of the Earth's shape, and the unresolved nature of the mathematical relationships involved.

Loren Booda
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In either the northern or southern hemisphere, what is the maximum difference in latitude between two places measuring the same total centripetal and gravitational accelerations?
 
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... it depends on your accuracy/sensitivity. No two different latitudes on one hemisphere have the exact same values.
 
I thought a standard weight measured over the Earth's surface would vary continuously.
 
Gravity is also a function of geology, elevation, and time (due to the movement of celestial bodies).

I don't know the answer but I am curious ... Why do you ask the question?
 
Loren Booda said:
I thought a standard weight measured over the Earth's surface would vary continuously.
For the most part yes, absolutely. The correction due to the centripetal force is pretty simple, and for any given model of oblate-ness, you can correct for that. Most likely variations due to geology (etc) would be entirely negligible, but again, it depends on your situation and sensitivities.

Actually, depending on the particular nature of the obliquity, it is possible that at different latitudes your weight would be the same (finding different balances between centripetal force and variations due to radius and asymmetry)---but it would depend on the particular models.
 
billiards said:
I don't know the answer but I am curious ... Why do you ask the question?
I find it aesthetically intriguing how two most widely separated points would have the same magnitude of acceleration as mapped on the Earth's surface.
 
Hmm at this point maybe a reference to http://www.csr.utexas.edu/grace/science/ would help?

[URL]http://www.csr.utexas.edu/grace/gallery/animations/ggm01/ggm01-200.gif[/URL]
 
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