Final answer:
Using Newton's Universal Law of Gravitation, we find that none of the provided options for the gravitational force between two identical 50,000kg asteroids separated by 1000m is correct. The calculated force is approximately 1.6685 × 10^-1 N.
Step-by-step explanation:
To calculate the gravitational force between two identical 50,000kg asteroids whose centers of mass are separated by 1000m, you can use Newton's Universal Law of Gravitation. The formula is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (6.674 × 10^-11 N·m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass. Inputting the given values:
F = 6.674 × 10^-11 * (50,000 * 50,000) / 1000^2
F = 6.674 × 10^-11 * 2.5 × 10^9 / 10^6
F = 16.685 × 10^-2 N
F = 1.6685 × 10^-1 N
After calculating, the gravitational force between the two asteroids therefore falls between the provided options, and none of the options a) 6.67 x 10^-11 N, b) 3.335 x 10^11 N, c) 3.335 x 10^-11 N, or d) 6.67 x 10^11 N is correct.