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## Sagot :

__[tex] F_{g} = \frac{G. m_{1} . m_{2}}{ r^{2} } [/tex].__

For note : r is a distance from center of the earth to the object.

Then, if [tex] r_{1} [/tex] is 6.400 km, and if [tex] r_{2} [/tex] is 12.800 km,

we can say that [tex] r_{2} [/tex] is [tex]2r_{1}[/tex]

In first equation we can say that :

[tex]F_{g} = \frac{G.m_{1} m_{2} }{ r_{1}^{2} } = 100.000 N[/tex]

then in second equation we can say that :

[tex]F_{g} = \frac{G.m_{1} m_{2} }{ r_{2}^{2} } [/tex],

[tex]F_{g} = \frac{G.m_{1} m_{2} }{ (2r_{1})^{2} }[/tex] (because [tex] r_{2} [/tex] is [tex]2r_{1}[/tex] )

[tex]F_{g} = \frac{G.m_{1} m_{2} }{ 4r_{1}^{2} }[/tex],

we can say that : [tex]F_{g} = \frac{1}{4} \frac{G.m_{1} m_{2} }{ r_{1}^{2} }[/tex]

so, by plugging first equation into second equation, we can get

[tex]F_{g} = \frac{1}{4} \frac{G.m_{1} m_{2} }{ r_{1}^{2} } = \frac{1}{4} . 100.000 N = 25.000 N[/tex]