Gravity in General Relativity and Earth's Surface

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SUMMARY

In General Relativity (GR), the proper acceleration at the surface of the Earth is definitively 9.8 m/s². This value corresponds to the acceleration experienced by a stationary observer in a spherically symmetric vacuum, expressed mathematically as a = m/(r²√(1-2m/r)). When the radius (r) is significantly greater than the mass (m), this approximation aligns closely with Newton's gravitational constant. The discussion highlights the relationship between GR and classical mechanics, confirming the consistency of gravitational acceleration values.

PREREQUISITES
  • Understanding of General Relativity principles
  • Familiarity with proper acceleration concepts
  • Basic knowledge of spherically symmetric vacuum solutions in GR
  • Mathematical proficiency in calculus and differential equations
NEXT STEPS
  • Explore the implications of proper acceleration in General Relativity
  • Study the derivation of gravitational acceleration in spherically symmetric vacuum
  • Learn about the differences between General Relativity and Newtonian gravity
  • Investigate the effects of mass and radius on gravitational fields
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the applications of General Relativity to gravitational phenomena.

Jerry Friedman
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Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?
 
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Yes. The proper acceleration of the surface.
 
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Jerry Friedman said:
Is there something in General Relativity whose value is 9.8 m/s2 at the surface of the Earth?

The acceleration of the stationary observer in the spherically symmetric vacuum according to GR is ##a=\frac{m}{r^2\sqrt{1-2m/r}}## (up to a sign).

If ##r>>m## this is very close to Newtons value.
 
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Thank you, Orodruin and Mentz114. I may be back with another question.
 

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