Final answer:
To determine the astronaut's weight on the Moon, we use the gravitational force formula or the acceleration due to gravity on the Moon. With the mass of the Moon, the mass of the astronaut, and the acceleration due to gravity, we find that the astronaut weighs approximately 146.7 Newtons on the Moon.
Step-by-step explanation:
To calculate the weight of an astronaut on the Moon, we use the formula for gravitational force: F = G * (M*m) / r^2, where F is the force or weight, G is the gravitational constant (6.674 x 10^-11 N(m/kg)^2), M is the mass of the Moon (7.4 x 10^22 kg), m is the mass of the astronaut (90 kg), and r is the distance from the center of the Moon to the astronaut (1.738 x 10^6 m).
After substituting the given values into the formula, the calculation becomes: F = (6.674 x 10^-11) * (7.4 x 10^22 * 90) / (1.738 x 10^6)^2. Solving this expression will give us the astronaut's weight on the Moon.
However, we can also use the fact that the acceleration due to gravity on the Moon (g_moon) is about 1.63 m/s^2, which is much smaller than Earth's 9.81 m/s^2. Therefore, we can directly compute the weight as: weight_on_moon = mass * g_moon.
Weight_on_moon = 90 kg * 1.63 m/s^2 = 146.7 N (rounded to one decimal place). Hence, the astronaut's weight on the Moon is approximately 146.7 Newtons.