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Gravitational field intensity at the center of the earth 
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#1
Dec1410, 08:49 AM

P: 91

1. The problem statement, all variables and given/known data
what is the gravitational field intensity at the center of the earth 2. Relevant equations 3. The attempt at a solution i was told that it was zero because you have the earth's mass surrounding it, and graivty moves to the center of its mass (center of radius) therefore the net force would be zero? is this correct? also if you sub in 0 in the gravitational field intensity formula for the radius, you get a value over zero, meaning it is undefined... so i can't really use that to support why it is zero at the center...... thanks 


#2
Dec1410, 09:52 AM

P: 474

In fact you should be thinking about 'r' as the distance to each bit of mass above you  and since the earth is all around you there is an equal force in every direction out from the centre  hence zero overall field 


#3
Dec1410, 09:55 AM

Mentor
P: 15,202

[tex]a(r) = \frac{GM_{\text{inner}}}{r^2}[/tex] where M_{inner} is the mass of that inner portion. If the density of the Earth is finite at every point inside the Earth, including at the center, then as r approaches zero, the inner mass will approach zero much faster than will r^{2}. That in turn means that a(r)→0 as r→0. 


#4
Dec1410, 12:46 PM

P: 91

Gravitational field intensity at the center of the earth
Thank you very much! You have both helped! I really appreciate it!



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