Mass

Le Grande Kilo – Stored in a vault near Paris

The next SI Unit is that of temperature, i.e. the kelvin (K) . One of the more interesting aspects of temperature is that we can cool something down to a certain point, and then the laws of nature stop us from cooling it down any further. Other SI units are available from the menus at the top of the page.

How much would you weigh on the Moon? In order to answer that question we need to understand the SI quantity of mass , which has the unit kilograms and the symbol kg . We will see that when standing on the Moon our mass stays the same, but our weight will be different.

Humans have been concerned about how much things weigh for a very long time . It's such an important subject that there are depictions of weighing scales going back to antiquity, including examples found in ancient Egyptian artwork. Much of this concern is due to commerce – how much something weighs is often a measure of how much it costs, whether it's rice or gold. As civilizations grew they each adopted standards for measuring weight, or as we will shortly see, mass. Today we use the kilogram (1000 grams) as the standard measure of mass. This was originally defined as one litre of pure water at a temperature of four degrees Celsius and at standard atmospheric pressure. This was followed by, firstly a platium cylinder in 1799 and then the international prototype of the kilogram, often called Le Grande Kilo or Le Grande K, and stored at the Bureau International des Poids et Mesures on the outskirts of Paris. This is shown in the picture above - it is a 39 x 39 mm platinum-iridium cylinder, made in 1889. From time to time copies were taken and distributed to other countries, and from them further copies were made. These were then used directly by industry and commerce or for calibrating weighing scales. However, the prototype and the copies have varied in mass over time. Being metal they can decay, and so become lighter, as well as attract other particles and so become a little heavier. In the case of Le Grande Kilo this is by a very tiny amount - less than the weight of an eyelash since it was manufactured - but still sufficient to have a significant effect on the mass measurements involved in new medical drug developments and precision engineering. For this reason the definition of the kilogram was changed in 2019, and is now based on the relationship between weight and electrical current. The full definition is rather technical, but you can see it here . However, it means that instead of using a lump of metal on a balance, a measurement of electrical force used by an electromagnet is used instead. This is actually an old idea and is commonly seen in scrap yards:

Your weight on the Moon So why would our weight change, but not our mass, if we stood on the Moon? The answer is that weight is a function of gravity, but mass isn't. In short we can think of weight as something affected by how much gravitational (or accelerating) force we are under and mass as being "an amount of stuff". This isn't strictly true, but will do for our purposes here. The Earth has greater mass than the Moon, and so it pulls down harder on objects surrounding it or on its surface, i.e. it exerts more gravitational force. Objects may weigh more on the Earth than they do on the Moon, but the amount of stuff they contain doesn't change and so the mass remains the same – mass remains “invariant”. So how much weight difference would there be?

Earth and Moon – Weights change but mass stays the same

The Earth's mass is about 5.97 x 10 24 kg and the Moon's mass is about 7.35 x 10 22 kg, so the Moon's gravitational pull is less than the Earth's. We also need to take into account the distance from the centre of the body to its surface, together with its density, and when we do we find that objects only weigh about 16.5% (about 1/6th) on the Moon as compared to the Earth. Adults are usually said to have an average "weight" of about 75 kg (165 pounds), so on the Moon an average adult would "weigh":

75 kg x 0.165 = 12.4 kg

That's about 27 pounds . Remember though, that although the measured weight is different the mass stays the same, hence the use of quote marks for "weight". Strictly speaking its wrong to say something has a weight of a certain amount of kilograms or pounds – we have seen that the kilogram is a measure of mass and not weight. Instead, scientists define weight as the force of acceleration acting on a body. On the Earth that force is about 9.81 metres per second squared and has the derived SI unit of newtons, with the symbol N. To calculate a weight on the surface of the Earth we simply multiply its mass by 9.81 m/s 2 . So a person with a mass of 75kg on the Earth will have a weight of:

75 kg x 9.81 m/s 2 = 735 N

On the Moon the same person would weigh:

735 N x 0.165 = 121 N

When we are asked for our weight we should really give the answer in newtons rather than kilograms or pounds, but that's very likely to just confuse people. Finally, what would you weigh on other bodies? Here are a few examples for a person with a mass of 75 kg (it's probably best not to stand on the surface of a neutron star!):


An electromagnetic crane - a balance of electrical force and mass

Although the idea has been around for a long time it’s only recently become possible to use this method of defining the kilogram due to improvements in the measurement precision of an electrical current going through an electromagnet. This method allows anyone with the right equipment to very precisely measure mass, independently of Le Grande Kilo or its copies.