The gravitational force would be [tex]8\cdot 10^{20} N[/tex]
Explanation:
The magnitude of the gravitational force between two objects is given by
[tex]F=G\frac{m_1 m_2}{r^2}[/tex]
where
[tex]G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}[/tex] is the gravitational constant
m1, m2 are the masses of the two objects
r is the separation between them
In this case, we can write the gravitational force between the Moon and the Earth as:
[tex]F=G\frac{M m}{r^2}[/tex]
where M is the Earth's mass and m is the Moon's mass.
We know that:
[tex]r=3.84\cdot 10^8 m[/tex] is their separation
[tex]F=2.0 \cdot 10^{20}N[/tex] is the force between them
So we can find:
[tex]GMm = Fr^2 = (2.0\cdot 10^{20})(3.84\cdot 10^8)^2=2.95\cdot 10^{37} Nm^2[/tex]
Now, we are asked to find the gravitational force when the Earth and the Moon are separated by
[tex]r'=1.92\cdot 10^8 m[/tex]
In this case the new force would be
[tex]F'=G\frac{M m}{r'^2}[/tex]
And substituting the values of (GMm) found previously and r', we find
[tex]F'=\frac{2.95\cdot 10^{37}}{(1.92\cdot 10^8)^2}=8\cdot 10^{20} N[/tex]
Learn more about gravitational force:
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