The gravitational acceleration g

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SUMMARY

The gravitational acceleration, denoted as g, is derived from Newton's law of gravitation, expressed as F = GMm/r². By substituting the mass of the Earth (M), the radius of the Earth (r), and the gravitational constant (G) into the equation, one can calculate g, which is approximately 9.8 m/s² at the Earth's surface. This value remains consistent for practical purposes, as variations in r due to altitude changes are minimal. The relationship between gravitational force and acceleration is established by equating Newton's law of gravitation with Newton's second law, F = mg.

PREREQUISITES
  • Understanding of Newton's law of gravitation
  • Familiarity with gravitational constant (G)
  • Knowledge of mass and radius of the Earth
  • Basic principles of classical mechanics
NEXT STEPS
  • Calculate gravitational acceleration using different planetary masses and radii
  • Explore variations of g at different altitudes and locations on Earth
  • Study the implications of gravitational acceleration in orbital mechanics
  • Investigate the effects of gravitational forces on objects in free fall
USEFUL FOR

Students of physics, educators teaching classical mechanics, and anyone interested in understanding gravitational forces and their calculations.

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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