Accepted value of G with longitude

  • Context: High School 
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Discussion Overview

The discussion revolves around the accepted value of gravitational acceleration (g) and its variation with respect to longitude and latitude. Participants explore how to determine g at a specific location, the significance of significant figures in measurements, and the implications of geological variations on the values of g.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant requests clarification on the accepted value of g at their longitude, indicating a potential misunderstanding of terms like longitude and latitude.
  • Another participant suggests a general value of "10 m/s²" for g, while also questioning the distinction between centripetal and gravitational acceleration in the context of the experiment.
  • A link is provided to additional resources related to gravitational potential.
  • There is a discussion about the accepted value of g being approximately 9.7803267714 m/s², with a clarification that the equation mentioned pertains to latitude, not longitude.
  • One participant emphasizes that geological variations can significantly affect the value of g beyond a few decimal places, suggesting caution in quoting precise figures.
  • A participant challenges the use of excessive significant figures in the context of measuring changes in g, questioning the mass associated with a very small change in g.
  • Another participant provides a calculation using Newton's equation of gravitation to illustrate the mass corresponding to a small change in g, concluding that it would be a relatively large pebble.

Areas of Agreement / Disagreement

Participants express differing views on the relevance of longitude in determining g, with some asserting that latitude is the more pertinent factor. There is no consensus on the implications of significant figures in the context of the measurements discussed.

Contextual Notes

Participants note that geological variations can have a larger effect on the value of g than theoretical calculations beyond a certain precision. The discussion also highlights the potential confusion between longitude and latitude in the context of gravitational measurements.

Who May Find This Useful

This discussion may be useful for students and researchers interested in gravitational measurements, the effects of geographical location on gravity, and the importance of significant figures in scientific calculations.

B-80
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Hey I have a lab write up due, and on it I need the accepted value of g and to get it at my longitude, any idea what this means, and how I can figure it out
 
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Your longitude [by which, we'll pretend you actually said latitude]? Do you mean altitude, or do you have some experiment that can distinguish centripetal acceleration from gravitational acceleration (without being sensitive to geological variations specific to your location)?

I suggest "10ms^-2".
 
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Here is a link:

http://geophysics.ou.edu/solid_earth/notes/potential/igf.htm
 
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thanks man so its 9.7803267714 right? and then the other equation next to it with lambda is to fix for longitude?
 
No lambda is latititude, there is no theoretical reason to fix for longitidue.
Note that the equation is an avaerage over the earth, after about the 3rd decimal place the local geology has a larger effect, so you probably don't want to quote more sig figures.
 
Can someone knock up a quick example to show the OP how ridiculous the number of SF he has used there is?

What kind of mass corresponds to a 0.0000000001 m/s/s change in g? A pebble? A boulder?

It's something i'd be interested to know. And I think that it's important that the OP has it hammered home how carefully you have to handle SF.
 
Using Newton's equation of gravitation g = -(Gm) / r^2

G = Gravitational Constant r = Distance from centre of body g = "Force" due to gravity m = mass

Assuming the radius of the object is 1 meter

0.0000000001 = (6.67300 × 10 ^ -11 x mass) / ( 1 ^ 2)

Mass = 0.0000000001 / 6.67300 × 10 ^ -11

Mass = 1.4985763 kg

So yeah a large pebble...
 

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