Final answer:
The gravitational force between the moon and an 85 kg astronaut is approximately 1.78 * 10^2 N.
Step-by-step explanation:
To calculate the gravitational force between the moon and an 85 kg astronaut, we can use Newton's Law of Universal Gravitation. The formula for gravitational force is F = G * ((m1 * m2) / r^2), where G represents the gravitational constant, m1 and m2 represent the masses of the objects, and r represents the distance between them.
Given m1 = mass of the moon = 7.35 * 10^22 kg, m2 = mass of the astronaut = 85 kg, r = radius of the moon = 1.74 * 10^6 m, and G = gravitational constant = 6.673 * 10^-11 N·m^2/kg^2, we can substitute these values into the formula to find the gravitational force.
F = (6.673 * 10^-11 N·m^2/kg^2) * ((7.35 * 10^22 kg * 85 kg) / (1.74 * 10^6 m)^2) = 1.78 * 10^2 N
Therefore, the gravitational force between the moon and the astronaut is approximately 1.78 * 10^2 N, which corresponds to option (a).