Final answer:
The center of mass of the Earth-Moon system would move if 1% of Earth's mass were transferred to the Moon, but exact calculations are required to determine by how much it moves. It involves applying the formula for the center of mass in a two-body system.
Step-by-step explanation:
To find out how far the center of mass of the Earth-Moon system would move if 1% of the Earth's mass were transferred to the Moon, we can use the concept of the center of mass in a two-body system like the Earth and the Moon.
The formula for finding the center of mass (CoM) R for two objects, such as Earth and the Moon, where m1 is Earth's mass, m2 is the Moon's mass, and d is the distance between the two objects, is given by:
R = (m1 * r1 + m2 * r2) / (m1 + m2)
where r1 and r2 are the distances of Earth and the Moon from the CoM, respectively.
If 1% of Earth's mass is transferred to the Moon, the new masses become m1' = 0.99m1 and m2' = m2 + 0.01m1. The new center of mass R' can then be calculated. The difference ΔR between R and R' will indicate how far the center of mass has moved. However, without the detailed calculations, we cannot assign an exact value.
Given the specific numbers provided, precise calculations are required to find the exact amount by which the center of mass would shift. That would involve a deeper understanding and application of the formula, which is not outlined here in full.