Final answer:
If the distance between you and Earth's center decreased by a factor of 5, your new weight would increase significantly, specifically becoming 25 times your original weight due to the inverse square law of gravitation.
Step-by-step explanation:
If the distance between you and Earth's center decreased by a factor of 5, your weight would change significantly because weight is directly related to the gravitational force exerted on you by Earth. This relationship is governed by Newton's Law of Universal Gravitation, which states that the force of gravity (F) between two 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, where G is the gravitational constant.
Since your mass and the Earth's mass would remain constant, but the distance is reduced by a factor of 5, the equation becomes: New Force (F') = G(m1*m2)/(r/5)² = G(m1*m2)*25/r². Comparing the new force to the old force, F'/F = 25. Hence, your new weight would be 25 times your old weight because weight is the measure of gravitational force.