Final answer:
The mass of the other asteroid is approximately 1.8 × 10^19 kg.
Step-by-step explanation:
The force of gravity between two objects can be calculated using Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant (approximately 6.67 × 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.
Given that the force of gravity is 1.14 N, one of the asteroids has a mass of 8 kg, and the distance between them is 75,000 m, we can rearrange the formula to solve for the mass of the other asteroid:
m2 = (F * r^2) / (G * m1)
Plugging in the values:
m2 = (1.14 N * (75,000 m)^2) / (6.67 × 10^-11 N*m^2/kg^2 * 8 kg)
Simplifying the calculation gives us:
m2 ≈ 1.8 × 10^19 kg
Therefore, the mass of the other asteroid is approximately 1.8 × 10^19 kg.