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The mass of the Earth is 5.972×1024 kg

Its radius is 6.371×106 m

Calculate the intensity of gravity on the Earth.

HINT: $$g=\frac{m \cdot G}{r^2}$$

g stands for gravity

m stands for mass

G is a constant and is equal to 6.67×10-11 N•m2•kg-2

r stands for the radius

EinsteinJr  Apr 30, 2015

Best Answer 

 #6
avatar+18715 
+5

P.S.

$$\small{\text{Newton's Law of Gravitation: }} F=\boxed{\,G*\frac{m_1*m_2}{r^2}=m_2*g\,} \Rightarrow \boxed{\,
g=\frac{m \cdot G}{r^2} \,}$$

heureka  May 4, 2015
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7+0 Answers

 #1
avatar+18715 
+5

$$\boxed{ g=\dfrac{m \cdot G}{r^2} }$$

 

$$\\\small{\text{$g_{earth}=G*\dfrac{m_{earth}}{r_{earth}^2}\qquad G= 6.673 * 10^{-11} * \frac { N*\ m^2 } { kg^2 } \qquad m_{earth}=5.972\cdot 10^{24}\ kg\qquad r_{earth}=6.371\cdot 10^6\ m$}}\\\\
\small{\text{$g_{earth}=6.673 \cdot 10^{-11}*\dfrac{ 5.972\cdot 10^{24} }{ ( 6.371\cdot 10^6 )^2}\cdot \frac{N\cdot \ m^2 \cdot\ kg}{ kg^2\cdot\ m^2 } = \dfrac{ 6.673\cdot 5.972\cdot 10^{-11+24-12}} { 6.371^2 } \cdot \frac { N } { kg } $}}\\\\
\small{\text{$g_{earth}= \dfrac{ 6.673\cdot 5.972\cdot 10^{1}} { 6.371^2 } \cdot \frac { \dfrac{kg\cdot \ m }{s^2} } { kg } $}}\\\\
\small{\text{$g_{earth}= 9.81806072145\cdot \dfrac{ m }{s^2}$}}$$

heureka  Apr 30, 2015
 #2
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Congratulations ! You earned a cookie:

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EinsteinJr  Apr 30, 2015
 #3
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Can Heureka have  smaller cookie next time please.  That one choked up my computer and it gave Heureka a belly ache   

Melody  Apr 30, 2015
 #4
avatar+91049 
+5

SO

 

The gravitational force between two objects is        $$F=\frac{Gm_1m_2}{r^2}$$

but 

If you want the intensity of gravity for the Earth it is just     $$g=\frac{Gm_E}{r^2}$$

 

That actually does make sense I think :/

Melody  Apr 30, 2015
 #5
avatar+886 
+5

Sorry, that was the smallest cookie I had under the hand I'll try to find a smaller one.

EinsteinJr  Apr 30, 2015
 #6
avatar+18715 
+5
Best Answer

P.S.

$$\small{\text{Newton's Law of Gravitation: }} F=\boxed{\,G*\frac{m_1*m_2}{r^2}=m_2*g\,} \Rightarrow \boxed{\,
g=\frac{m \cdot G}{r^2} \,}$$

heureka  May 4, 2015
 #7
avatar+91049 
0

Thanks Heureka   

Melody  May 4, 2015

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