Final answer:
The force of gravity between two objects can be calculated using the formula F = G * (m1 * m2) / r^2. Doubling the mass of an object doubles its weight, but doubling its distance from the center reduces its weight fourfold.
Step-by-step explanation:
The gravitational force between two objects is given by the formula F = G * (m1 * m2) / r^2, where F is the force, G is the gravitational constant (6.674 x 10^-11 N.m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
a) To calculate the force of gravity between the two 10,000-kg objects, we can plug in the numbers into the formula. F = (6.674 x 10^-11) * (10,000) * (10,000) / (1^2) = 6.674 x 10^-6 N
b) If we double one of the masses, the new force of gravity can be calculated as F = (6.674 x 10^-11) * (2 * 10,000) * (10,000) / (1^2) = 1.3348 x 10^-5 N
c) If we double both masses, the new force of gravity can be calculated as F = (6.674 x 10^-11) * (2 * 10,000) * (2 * 10,000) / (1^2) = 2.6696 x 10^-5 N
d) If we double both the masses and the distance between them, the new force of gravity can be calculated as F = (6.674 x 10^-11) * (2 * 10,000) * (2 * 10,000) / (2^2) = 6.674 x 10^-6 N