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The evil team of Ms. Moonstruck and Mr. Luny intend to deflect the Moon from its orbit around Earth by pulling it with a force of 8170 N . They plan to accomplish this by placing a mini black hole 7.47×106 m from the center of the Moon and letting gravitation do what gravitation does. What must the mass of the mini black hole be for the evil duo's evil scheme to succeed? The mass of the Moon is 7.36×1022 kg .

Respuesta :

Rau7star

Answer:

92867kg

Explanation:

DATA:

mass of the moon '[tex]m_1[/tex]'= 7.36 x [tex]10^2^2[/tex]kg

mass of the mini black hole '[tex]m_2[/tex]'=?

universal gravitational constant= 6.67x[tex]10^-^1^1[/tex] Nm²/kg²

distance 'r'= 7.47×[tex]10^6[/tex] m

force 'F'= 8170N

Newton's Law of Universal Gravitation is given by:

[tex]F=G\frac{m_1m_2}{r^2}[/tex]

[tex]m_2=[/tex][tex]\frac{(8170)(7.47*10^6)^2}{(6.67*10^-^1^1)(7.36*10^2^2)}[/tex]

[tex]m_2=[/tex]92867kg

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