Vipul: Created page with "==Definition== '''Acceleration due to gravity''' refers to the value of the acceleration on one body due to another that ''would'' arise as a result of the [[gravitational force..."

2011-08-24T15:48:06Z

Created page with "==Definition== '''Acceleration due to gravity''' refers to the value of the acceleration on one body due to another that ''would'' arise as a result of the [[gravitational force..."

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==Definition==

'''Acceleration due to gravity''' refers to the value of the acceleration on one body due to another that ''would'' arise as a result of the [[gravitational force]] between the bodies, ''if'' there were no other forces on that body. In other words, that body is in [[free fall]].

===The case of the earth or a large planet===

Consider the [[earth]] and an object near the surface of the earth, so that, for practical purposes, the distance between their [[center of mass|centers of mass]] can be taken to be the radius of the earth. If <math>M</math> is the [[mass]] of the earth, <math>R</math> is the radius of the earth, and <math>m</math> is the mass of this other object, then the magnitude of gravitational force exerted by the earth on the object is:

<math>F_{\operatorname{grav}} = \frac{GMm}{R^2}</math>

where <math>G</math> is the [[gravitational constant]]. ''If'' the body with mass <math>m</math> were in [[free fall]], [[Newton's second law of motion]] would yield:

<math>ma = \frac{GMm}{R^2}</math>

where <math>a</math> is the acceleration of the body in the direction of the center of the earth (i.e., downward). We thus get:

<math>a = \frac{GM}{R^2}</math>

Note that the quantity on the right side is independent of <math>m</math>, and this quantity is called the ''acceleration due to gravity'', and is denoted by the letter <math>g</math>. We thus get:

<math>g = \frac{GM}{R^2}</math>

Acceleration due to gravity - Revision history

Vipul: Created page with "==Definition== '''Acceleration due to gravity''' refers to the value of the acceleration on one body due to another that ''would'' arise as a result of the [[gravitational force..."