Volume (V) |  Weight / Mass | Density
2. Weight / Mass
In this section, we are going to study how our weight is different on different planets. First, we need to know the difference between weight and mass. We have learned that mass is a property - how much stuff something has. Weight is a measure of force on that same object.

Here on Earth, we often talk about how much we weigh. Talking about our weight is just a direct way of stating that we have mass and that the Earth is pulling on our mass. When we weigh ourselves we step on a scale that measures how much the Earth is pulling us down onto the scale. The more mass that we have, the more the Earth will pull us down onto the scale.
When we gain some mass the Earth pulls on us harder, so we weigh more. The force on us has increased and, because weight is a measure of force, our weight has increased.

Thus, the difference between weight and mass is that they measure different things. An object's mass depends only on how much stuff is in it. An object's weight depends on what is pulling on it. If something other than the Earth were pulling on us we would have a different weight.

Very few of us have had anything but the Earth pull us down onto a scale but remember that your mass would still be the same no matter where you went because you are still you (and don't you go changin'!).

Now, watch this video clip of an astronaut bouncing along on the Moon.
Being on the Moon would be fun because we would all weigh less - just 1/6 th of what we weigh on Earth. Do we weigh less because we lost mass? No. What changed? The gravitation pull must have changed. The moon does not pull on us as hard as the Earth. Because the force on us is less, we weigh less. Remember - weight is a measure of force.

Our mass is a property of our body and does not change when we travel to different places. The different gravity that our body feels depends on two things: the mass of the planet that pulls us and how far we are from its center.

Sir Isaac Newton was the first to express the strength of gravity in a mathematical equation. Here is how we write it:

Fg = GMm/r2

Fg is the force of gravity. G is what is known as the Gravitational Constant, a number that is always the same everywhere in the universe. M and m are masses (for example, the mass of the Earth and your mass), and r is the distance between the centers of the two masses (for your weight on Earth, this would be the distance to the center of the Earth).

Notice that the force of gravity decreases as the objects get further apart. That means that you weigh more in New Orleans than you do in Los Alamos, since Los Alamos is at a higher altitude (further from the center of the Earth). The difference is very small (only about one-tenth of a pound), but it is measurable with very precise scales. Gravity follows what is known as an inverse square law, which refers to the r 2 under the division sign.  This means that if you double the distance between two objects, the force of gravity between them becomes one quarter (1/22 = 1/4) of what it was originally.

Also notice that the the force of gravity is proportional to the masses of the objects. This means that if you double one of the masses and keep everything else the same, then the force of gravity doubles as well. For example, a planet the same size as Earth but with twice the Earth's mass would pull on us twice as hard.

In the SI or "metric" system, weight is measured in Newtons (N).  In the English system, it is measured in pounds (lb).

Scaling Saves Time!

Now let's see how we don't need to use the full-blown equation to calculate our weight on another planet if we know it on Earth. We can just do it by scaling. For instance, Mars has about one-tenth the mass of the Earth and about half the radius. So if we just considered the mass of Mars, the force of gravity on us would be one-tenth of Earth's force. But since the radius is about one-half Earth's, and radius appears squared in the denominator, then the above factor of one-tenth is offset by a factor of four. So taking into account the mass and radius of Mars, our weight would be 0.4 times as much or 2.5 times less than on Earth. We didn't even need to know what G is!
 

Click Here to calculate how much you weigh on other planets.