According to Newton's Law of Universal Gravitation, the gravitational force (F) between two objects with masses M₁ and M₂ is directly proportional to the product of their masses and inversely proportional to the square of the distance (r) between their centers: F = G (M₁ M₂) / r². In this case, M₁ is the mass of the Earth (M_earth) and M₂ is the mass of the Moon (M_moon). Let the original distance be r. The original gravitational force is F = G (M_earth M_moon) / r². If the distance is halved, the new distance is r' = r/2. The new gravitational force F' will be: F' = G (M_earth M_moon) / (r')² F' = G (M_earth M_moon) / (r/2)² F' = G (M_earth M_moon) / (r²/4) F' = 4 [G (M_earth M_moon) / r²] So, F' = 4 F. The gravitational force increases to four times its original value.
If the Moon is brought closer to the Earth such that its distance from the Earth becomes half of the original distance, then the gravitational force of attraction between the Earth and the Moon would :
Asked in UPSC CDS 2 2023 · Topic: Mechanics (Gravitation and Central Force Motion (Kepler's Laws))
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