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. Now it's defined as being equal to 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. As shown in the picture
above it is a 39 x 39 mm platinum-iridium cylinder, made in 1889. From time to time copies
are taken and distributed to other countries, and from them further copies are made. These
are then used directly by industry and commerce or for calibrating electronic weighing
scales.

All of the other SI units are rationally defined in terms of universal constants, such as the
speed of light for length, but the kilogram is unique in being based on a lump of metal stored
in a vault. It's such an important artefact that one hopes the security surrounding it is as
strong as it can possibly be.
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% on the Moon as compared to the Earth. Adults
are usually said to have an average "weight" of about 75kg (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 75kg (it's probably best not to stand on the surface of a neutron star!):

Click for kilograms to pounds, kg to tons, kg to stones and newtons to weight.

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. Now it's defined as being equal to 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. As shown in the
picture above it is a 39 x 39 mm platinum-iridium cylinder, made
in 1889. From time to time copies are taken and distributed to
other countries, and from them further copies are made. These
are then used directly by industry and commerce or for
calibrating electronic weighing scales.

All of the other SI units are rationally defined in terms of
universal constants, such as the speed of light for length, but the
kilogram is unique in being based on a lump of metal stored in a
vault. It's such an important artefact that one hopes the security
surrounding it is as strong as it can possibly be.
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% on the
Moon as compared to the Earth. Adults are usually said to have
an average "weight" of about 75kg (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 75kg (it's probably best not
to stand on the surface of a neutron star!):

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