Final answer:
The initial distance between two bodies can be calculated using Newton's law of universal gravitation and the inverse square law. By establishing a ratio that correlates the percentage decrease in force with the percentage of remaining force and the increased distance, we can solve for the original distance.
Step-by-step explanation:
The question regards the calculation of the initial distance between two bodies based on a change in the gravitational force when the distance between them is increased. According to Newton's law of universal gravitation, the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. When the student states that the force is deceased by 36% when the distance is increased by 3m, we can set up a ratio using the inverse square law of gravity to find the initial distance.
Since a decrease of 36% in force corresponds to a 64% (100% - 36%) remaining force, we have the equation (d + 3)^2/d^2 = 1/0.64, where d is the initial distance. By solving the equation, we find that the initial distance d must satisfy the equation (d + 3)^2 = 1.5625 * d^2. When we solve this quadratic equation, we find the initial distance as an option from the given multiple-choice answers.