Question

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 4730 N. They plan to accomplish this by placing a mini black hole 6.05×10⁶ 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.

mini black hole mass in kg:

Answer 1

Given,

The force, F = 4730 N

The mass of the Moon, M = 7.36 * 10²² Kg

The distance, r = 6.05 * 10⁶ m

We know,

F = GMm / r²

The mass of a mini black hole, m = F r² / GM

m = 4730 * (6.05 * 10⁶)² / (6.67 * 10^-11) * (7.36 * 10²²)

m = 1.731 * 10¹⁷ / 4.91 * 10¹²

m = 35254.6 Kg