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Sagot :
Given:
Original distance between the planets, d1 = 5 x 10¹⁰ km
Distance after the planets moved, d2 = 2 x 10¹⁰ km.
Let's determine what would happpen to the gravitational force between the planets.
Apply the formula:
[tex]F=G\frac{m_1m_2}{d^2}[/tex]Let F1 be the gravitational force before the movement.
Let F2 be the gravitational force after the movement.
[tex]\begin{gathered} F_1=\frac{Gm_1m_2}{d^2_1} \\ \\ F_2=\frac{Gm_1m_2}{d^2_2} \end{gathered}[/tex]Equate both equations
Now, for the two gravitational forces, we have the equations:
[tex]\begin{gathered} F_1=\frac{Gm_1m_2}{(5\times10^{10})^2} \\ \\ F_2=\frac{Gm_1m_2}{2\times10^{10}} \end{gathered}[/tex]The relationship between the gravitational force between planets and the distance is:
[tex]F=\frac{1}{r^2}[/tex]The gravitational force is inversely proportional to the square of the distance between the planets.
Thus, we have:
[tex]\begin{gathered} F_1=\frac{1}{(5\times10^{10})}=4\times10^{-22}\text{ N} \\ \\ F_2=\frac{1}{(2\times10^{10})^2}=2.5\times10^{-21}N \end{gathered}[/tex]We can see the force after the movement F2 is greater than the force before the movement F1.
Therefore, the gravitational force will increase.
ANSWER:
Increase.
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