Final answer:
To determine the force of gravity between two asteroids, we can use Newton's law of gravitation. The force can be calculated using the formula F = G * (m1 * m2)/(r^2), where F is the force, G is the gravitational constant, m1 and m2 are the masses of the asteroids, and r is the distance between them. When the distance between the asteroids is doubled, the force of gravity decreases.
Step-by-step explanation:
To determine the force of gravity between two asteroids, we can use Newton's law of gravitation. The formula for gravitational force is F = G * (m1 * m2)/(r^2), where F is the force, G is the gravitational constant (6.674 × 10^(-11) m^3 kg^(-1) s^(-2)), m1 and m2 are the masses of the asteroids, and r is the distance between them.
Using the given values, we can calculate the force of gravity:
F = (6.674 × 10^(-11) m^3 kg^(-1) s^(-2)) * ((8.958 × 10^20 kg)^2)/(3.51 × 10^4 m)^2
F = 4.830 × 10^(-5) N
When the distance between the asteroids is doubled, the new distance is 2 * 3.51 × 10^4 m = 7.02 × 10^4 m. Using the same formula, we can calculate the new force of gravity:
F_new = (6.674 × 10^(-11) m^3 kg^(-1) s^(-2)) * ((8.958 × 10^20 kg)^2)/(7.02 × 10^4 m)^2
F_new = 1.207 × 10^(-5) N
Comparing the two forces, the force when the asteroids are 3.51 × 10^4 m apart is greater than the force when they are 7.02 × 10^4 m apart.