Weight and Mass

What we call weight is the effect of gravity on mass. On the surface of earth, weight = mass x g (gravitational acceleration). That’s simplified from Newton’s Law of Universal Gravitation: F = G * M₁ * M₂ / r², which describes the attraction between any two masses. You can use it to find out how much gravity attracts you and the Eiffel tower together, if you want (the answer will be very very small). But the earth is big enough that the force becomes significant, G * M_earth * M_you / (radius of earth)² = g * M_you. Note that this force always goes both ways. You attract the earth as much as it does you (Newton’s third law).

And if you fall to earth, it falls up to you. It’s just that it’s acceleration toward you is extremely small due to it’s large mass (Newton’s second law).

People like to think that in space you are weightless. If by space we mean in orbit around the earth, than not really. Or rather you are only weightless in the way you are in free fall. In fact, we can think of being in orbit as constantly falling to earth, but missing. Think of it this way: if you threw a ball straight ahead, it would fall to the ground. If you threw it hard enough, it would still fall to the ground, but the ground would have curved down a bit first, since the earth is round. 

Now if you threw it even harder, at some point the ground will be falling away as fast as the ball is falling and it will never hit the ground, but remain in orbit. That’s exactly what astronauts do: they use rockets to throw themselves hard enough that they miss the ground.