You often hear the phrase, "What is your weight?" Let's analyze what’s wrong with it and why it’s quite strange. There’s nothing inherently odd about the question itself, unless, of course, it’s being asked by a physics teacher. However, it’s more commonly heard from ordinary people, who actually mean something different by it. Of course, everyone is referring to mass. But it’s essential to understand that mass and weight are distinct terms. The mass of an object is a scalar quantity measured in kilograms. This parameter (mass) depends on the amount of substance contained in the object. Weight, on the other hand, is a vector quantity measured in newtons (N), which depends on the acceleration due to gravity (g). Objects can have the same mass but different weights.
These concepts are interrelated, as the weight of an object is determined by its mass. The mass of an object remains constant on any surface of our Earth, in its atmosphere, and even on the surfaces of other planets. However, weight, which is calculated using the formula P = m × g, depends on the variable g (acceleration due to gravity), which changes not only from planet to planet but even within different locations on Earth. The acceleration due to gravity at the surface of the Earth, g, varies from 9.780 m/s² at the equator to 9.82 m/s² at the poles. As I mentioned earlier, g can be expressed not only in meters per second squared (m/s²) but also in newtons per kilogram. In such cases, g under Earth conditions can be rounded to approximately 10 N/kg for simplification in calculations. With increasing height of an object above the Earth's surface, the acceleration due to gravity decreases. This is because the distance between the Earth's core and the object increases, resulting in a decrease in gravitational force. This means that even in an airplane, your weight will be slightly less than it is on the ground, while your mass will remain the same. Take a look at how the acceleration due to gravity changes at different altitudes.
| Altitude (km) | g (m/s²) |
|---|---|
| 0 | 9.8066 |
| 1 | 9.8036 |
| 10 | 9.7759 |
| 100 | 9.505 |
| 500 | 8.45 |
| 5000 | 3.08 |
| 10 000 | 1.50 |
| 50 000 | 0.13 |
| 400 000 | 0.0025 |
If the changes within the Earth and its atmosphere seem very minor, let's take a look at how much your weight would be on other objects in the solar system:
- Earth – 1 g – 9.80665 m/s²
- Moon – 0.165 g – 1.62 m/s²
- Mercury – 0.38 g – 3.7 m/s²
- Venus – 0.906 g – 8.87 m/s²
- Mars – 0.378 g – 3.711 m/s²
- Saturn – 1.065 g – 10.44 m/s²
- Jupiter – 2.442 g – 24.79 m/s²
- Neptune – 1.131 g – 11.15 m/s²
- Uranus – 0.903 g – 8.87 m/s²
- Pluto – 0.063 g – 0.617 m/s²
- Io – 0.183 g – 1.796 m/s²
- Europa – 0.134 g – 1.315 m/s²
- Ganymede – 0.146 g – 1.428 m/s²
- Callisto – 0.126 g – 1.235 m/s²
- Sun – 27.85 g – 274.0 m/s²
With this data, let's calculate the weight of a person with a mass of 70 kg.
On Mars, they would "weigh" 70 × 0.378 ≈ 26.46 kg
On Venus, they would weigh 70 × 0.906 ≈ 63.42 kg
On Jupiter, they would weigh 70 × 2.442 ≈ 170.94 kg
On the Moon, they would weigh 70 × 0.165 ≈ 11.55 kg
I hope this post has been at least somewhat useful to you, and you’ve understood that when people use the word "weight," they often want to know not the force with which a person presses down on a surface at a given point, but rather what their mass is. Otherwise, don’t be surprised if you receive an answer not in kilograms, but in newtons, and far from the numbers you expect.
