Gravity and Weight vs Mass

Pick up your school bag and step onto the bathroom scales: both give a number. Now imagine stepping off a spaceship onto the Moon, the scales read one-sixth as much, yet the bag feels exactly as hard to swing. Your mass is 50 kg whether you're in Sydney, on the Moon, or in deep space, and matter doesn't disappear just because gravity changes.

Mass is the amount of matter in an object, and it is measured in kilograms (kg). A greater mass means there is literally more stuff there, more atoms making the object up, which is why mass has nothing to do with where the object happens to be sitting. Move a 10 kg bag of dog food from Sydney to Mars and you have not removed a single atom from it, so its mass is still 10 kg.

The instrument that measures mass is a balance scale, and the reason it gives the same answer anywhere in the universe is worth pausing on, because it is the whole argument for why mass is constant. A balance does not measure a pull. It puts your object on one side and known masses on the other, and gravity pulls on both sides at once. Take the balance to the Moon and gravity gets six times weaker on both pans together, so they still tip level at the same point. Whatever changed, cancelled. That is why a balance reading is a measurement of matter rather than of gravity.

Common mistake, and it is worth being precise about: someone who says "I've lost mass on a diet" has actually lost both. They have fewer atoms in their body, so their mass fell, and because weight is what gravity does to that mass, their weight fell with it. On one planet, mass and weight always rise and fall together, which is exactly why the two words get muddled in everyday speech. What separates them is what happens when the planet changes instead of the person.

Weight is the force of gravity pulling an object toward the centre of a planet. It is a force, so it is measured in Newtons (N), not kilograms.

The equation is W = m × g, weight equals mass times gravitational field strength, and it is worth seeing why it has to be a multiplication rather than trying to remember it. Read the unit of g out loud: newtons per kilogram. On Earth, g is 9.8 N/kg, which is a rate, and it means gravity pulls with 9.8 N on every single kilogram of matter. So if an object contains 3 kg of matter, gravity pulls on the first kilogram with 9.8 N, on the second with another 9.8 N, and on the third with another 9.8 N. Adding those up is the same as multiplying, and 3 × 9.8 = 29.4 N. Any time you meet a quantity written as "something per something", multiplying by the number of the second thing is how you get the total.

The same reading also tells you what the answer's units must be. Kilograms multiplied by newtons per kilogram leaves newtons behind, because the kilograms cancel. If you ever finish a weight calculation and the answer is in kilograms, you have found a mistake without needing to recheck the arithmetic.

On the Moon, a 50 kg person weighs only 80 N, about one-sixth of their Earth weight. They'd feel incredibly light and could jump huge distances. But their mass is still 50 kg.

Bathroom scales actually measure weight force (how hard gravity pushes you onto the scale). They are calibrated to display mass in kg, but on the Moon, that scale would show about 8 kg even though you're still a 50 kg person. This is why scientists always distinguish mass from weight.

A common myth: "There's no gravity in space." This is completely wrong. Gravity acts everywhere in the universe, it just gets weaker as you move further from a massive object.

The ISS (International Space Station) orbits Earth at about 400 km altitude. At that height, gravity is still about 90% as strong as on Earth's surface. So why do astronauts float?

The answer: They are in continuous free fall. The ISS and everything inside it is falling toward Earth, but it's also moving sideways so fast that it keeps "missing" the planet. That sideways motion creates an orbit. Both the astronauts and the ISS are falling at exactly the same rate, so relative to each other, they float.

Think of it this way: if you jumped out of an aeroplane holding a bag and let go of it, you and the bag would fall at the same rate, so the bag would appear to hang motionless beside you even though both of you are plummeting. That is what an orbit is, an endless falling-and-missing.

Once you see an orbit as falling, every orbit in the Solar System works the same way and needs no extra idea. Gravity reaches out into deep space and simply gets weaker with distance, so it never switches off. The Moon is falling toward Earth constantly, and it moves sideways fast enough to keep missing, which is why it circles rather than lands. Earth does the identical thing around the Sun, and so does every other planet. The pattern to take away is that an object in orbit is not being held up by anything and is not free of gravity. It is being pulled by exactly one force, and that force is what bends its straight-line path into a circle.

Using W = m × g, calculate the weight of a 60 kg student on each planet/moon. Gravitational field strengths: Earth 9.8, Moon 1.6, Mars 3.7, Venus 8.9, Jupiter 24.8 N/kg.

Classify each item or instrument below as measuring/relating to Mass (M), Weight (W), or Both (B). Give a one-line reason.