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Here’s a thorny problem that no doubt every physics teacher has grappled with. In a space-station, orbiting the earth, are you weightless?  

There are at least two ways of answering this:

1. Yes, you are. Let’s face it, you float around inside the space-station, water forms large blobs, some plants don’t know which way up is, pendulums don’t swing, and you need frightening machines to help you go to the toilet.

2. No, you still have weight, because you still feel the gravitational force of the earth. If you didn’t, there would be nothing keeping you in orbit.  You ‘feel’ weightless, because you and the space-station are accelerating at the same rate towards the centre of the earth (centripetal acceleration).

There is confusion here because we are often very loose with what we mean when we say ‘weight’. We often think of weight as being the force gravity exerts on us, and so we run into problems because when we are in the space-station, the earth’s gravitation field is still there, and so we are forced to conclude that we must still have weight. To alleviate this conundrum, often we talk about ‘apparent’ weight. Since the space-station is accelerating towards the centre of the earth at the same rate as its occupants, the occupants feel as if they are weightless – so they have no ‘apparent’ weight.

 In the article  "Apparent Weight: A Concept that Is Confusing and Unnecessary" in "The Physics Teacher", Albert Bartlett argues that us physicists should get our act together when it comes to talking about weight. If we abandon the concept of apparent weight and the equally confusing "acceleration due to gravity", and stick to a decent definition of weight and use "free-fall acceleration", the confusion should be alleviated.  I’m inclined to agree with him, and also stick my hand up as being guitly of  sometimes doing just what he wants stopped.

If you’re physics-educated, have a read and see what you think (the article is downloadable for free).

If we stick with the definition that an object’s weight (a force) is what a spring-balance would read when the object is placed on it, we should have no problems. In this case the weight might result from gravity, but it could also result from being in a rotating frame (e.g. a rotating spacestation in deep space), or a combination of the two (e.g. being at the equator on the earth), or, bringing in general relativity, in an accelerating lift.  Take your bathroom scales into work and go up and down in the lifts, and note that your weight really does change when the lift accelerates and decelerates.

Thanks to Steve Chrystall for sending this article to me.

Bartlett, A. A. "Apparent Weight": a concept that is confusing and unnecessary. (2010). The Physics Teacher, 48(8), 552.