How to Calculate Weight and Mass of an Astronaut on the Moon and Earth

Question:

The weight of an astronaut plus their space suit on the Moon is only 250 N. How much do they weigh on Earth? What is the mass on the Moon? On Earth?

Answer:

Final answer: The astronaut plus their space suit weighs 250 N on the Moon, which equates to approximately 1500 N on Earth, closest to 1530 N. The mass, which is constant, is approximately 154 kg both on the Moon and Earth.

Understanding the Weight of an Astronaut on the Moon and Earth

The weight of an astronaut plus their space suit on the Moon is 250 N. To determine what this would translate to on Earth, we must consider the gravitational pull of the Earth compared to that of the Moon. The gravitational acceleration on the Moon is about 1/6th of that on Earth. Therefore, to find the astronaut's weight on Earth, we can multiply the moon weight by 6.

Weight on Earth = 250 N (moon weight) × 6 = 1500 N

Since weights provided in answers a) 250 N, b) 625 N, c) 981 N, and d) 1530 N do not match exactly, we take the closest value, which is d) 1530 N.

The mass of the astronaut and suit remains constant whether on the Moon or Earth, because mass is a measure of the amount of matter in an object and does not depend on gravitational field strength. To calculate this mass, we use the weight on the Moon as it is the given:

Mass = Weight / Gravitational Acceleration (Moon's gravity = 1.625 m/s²).

Mass on the Moon = Mass on Earth = 250 N / 1.625 m/s² approximately 154 kg