The gravitational acceleration g

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Discussion Overview

The discussion revolves around the concept of gravitational acceleration, denoted as g, and its derivation from Newton's law of gravitation. Participants explore the relationship between gravitational force and acceleration, particularly in the context of Earth.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that gravitational acceleration g can be derived from the equation F=GMm/r^2, where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the Earth.
  • Others suggest that by substituting the known values of Earth's mass, radius, and G into the equation, one can calculate g and compare it to the commonly accepted value of approximately 9.8 m/s².
  • A participant notes that while GM/r² is exactly equal to 9.8 m/s² at only one specific point, it remains approximately valid for most practical heights experienced on Earth.
  • There is a reiteration of the relationship between gravitational force and acceleration, emphasizing the equivalence of Newton's law of gravitation and Newton's second law of motion.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical relationship between gravitational force and acceleration but express varying degrees of precision regarding the value of g and its applicability at different heights. The discussion remains unresolved regarding the exact conditions under which g equals 9.8 m/s².

Contextual Notes

There are limitations regarding the assumptions made about the uniformity of gravitational acceleration at different heights and the specific conditions under which the value of g is considered accurate.

manimaran1605
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Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)
 
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Why don't you look up the mass of the earth, the radius of the earth, and G and plug them into Gm/r^2 and see what you get? Is it close to the usual value of g?
 
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GMm/R2

Usually

M = mass of planet
m = mass of object/particle

but Newton also says..

F = mg

You can do the rest.
 
manimaran1605 said:
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)
At the surface of the earth, Gm/r^2= g using m= mass of the earth, r= radius of the earth.
 
At only one point is GM/r^2 exactly equal to 9.8. However, since r only changes slightly with respect to its value at heights we experience, for all intents and purposes, g=9.8m/s^2.
 
manimaran1605 said:
Suppose a particle of mass M is under gravitational attraction. The Newton's law of gravitation says that F=GMm/r^2, and the part Gm/r^2 is g (acceleration due to gravity how?)

Like noted above, you get it by equating Newton's gravity law with Newton's second law.
You can plug in some numbers here: Earth's Gravity.
 

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