What Is Weightlessness?

The term "weightless" is usually thought to mean that someone is in a "zero-gravity" zone, aka space or freefall, and therefore has no weight. This can be seen in many space-related movies, like Apollo 13. However, if you actually look at the physics of it, this is false. Weightlessness is actually the absence of a normal force. Most people don't know what this is so let's contextualize. To do this, we'll have to take a look at Newton's three laws. Or at least two of them.

According to Newton's second law, for there to be a net force acting on an object, there has to be some sort of mass and acceleration. But as commonly misconstrued, mass does not equal weight. So where does weight come in? Well, Newton's third law states that for every action, there is an equal an opposite reaction. So when your body is pushing on the Earth due to gravity pulling you down, the Earth is pushing right back with the same amount of force perpendicular to the surface you are on. That force is called the normal force, and its effect on the body is the feeling of weight. So another way to calculate net force is by adding up the normal force and force due to gravity.
Because there is 80N acting on the surface, 80N are also applied back to the object. 
In the context of Apollo 13, it is seen that the astronauts are just floating around which makes them appear weightless. This is correct because in space, while there is still an acceleration due to gravity, it is so so so small that it can't really be felt. Therefore, if there is basically no gravity pushing them down, there is no normal force acting back on them. So this is what makes them feel weightless. Another way this effect can be applied is through free fall, which is actually how this movie was filmed. During freefall, gravity is being applied to the object in motion, but there is no surface below it to apply a force back. No normal force, no feeling of weight. So to film the actors experiencing weightlessness, they had them in an aircraft in freefall. The closest many of us can get to this feeling is the Tower of Terror at Disney World, the Frogger rides in any kiddy park, or any other freefall ride. The producers weren't just going to send three untrained actors into space, so this was their next best decision. It was a great decision on their part because it made it very realistic and accurate, rather than imitating weightlessness using cables which is very noticeable and sad. Apollo 13 gets a GP rating for this level of dedication and knowledge and appreciation of physics.

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