What is weight?

There then occurred to me the “glückischste Gedanke meins Lebens,” the happiest thought of my life, in the following form. The gravitational field has only a relative existence . . . . Because for an observer falling freely from the roof of a house there exists — at least in his immediate surroundings — no gravitational field.
– Albert Einstein, as quoted by Abraham Pais

Canadian astronaut Chris Hadfield aboard the International Space Station (ISS), demonstrating weightlessness with tomatoes. [Credit: International Business Times]
Canadian astronaut Chris Hadfield aboard the International Space Station (ISS), demonstrating weightlessness with tomatoes. [Credit: International Business Times]
Weight is not the same thing as the gravitational force. You don’t need a formal study of physics to know that: all you have to do is ride a swing at a playground, or drive over the lip of a hill a little too fast, or ride an elevator on a tall building. In all of these cases, you experience fluctuations in your weight: heavier at the bottom of the swing’s arc, lighter at the top, maybe even momentarily weightless. The elevator is the best example of these, since you could take a scale onto it and see how your weight changes during the various stages of acceleration. (Try it at the Sears Tower or Empire State sometime. Tell them I sent you.)

Gravity’s pull is roughly the same on you in all of these instances, since your distance from the center of Earth (which determines the strength of gravity) doesn’t change that much. Yet your weight — your own personal sensation of heaviness, as well as what a bathroom scale measures — increases and decreases according to your motion, specifically your acceleration. To phrase it another way, we feel acceleration, but we don’t feel gravity. As the Einstein quote above indicates, if you’re falling freely, as out of an airplane in a skydive, you won’t feel the pull of gravity as you fall. Air resistance, yes, but not gravity.

The strength of gravity as a function of altitude above Earth's surface. The ISS orbits at 370 km altitude, where the gravitational strength is about 90% of its value at the surface - hardly zero gravity!
The strength of gravity as a function of altitude above Earth’s surface. The ISS orbits at 370 km altitude, where the gravitational strength is about 90% of its value at the surface – hardly zero gravity!

The effect is most prominent for those fortunate enough to go into space: they are continuously weightless while in orbit. According to Mary Roach in Packing for Mars, some astronauts never get over the nausea and disorientation that often produces. (That nausea is also the source of the astronaut training airplane’s nickname: the Vomit Comet.) Normal scales are useless: if they want to measure their body mass, astronauts must use a calibrated spring mechanism, a fun subject I’m writing about for a Super Seekrit Project. Gravity isn’t zero, though, or else the spacecraft wouldn’t stay in orbit. In fact, as you can see from the plot above, the gravitational strength at the altitude of the ISS isn’t much less than it is at the surface.

Of course, that means the common phrase “zero gravity” is false. It does contain a kernel of truth, though: if you are moving under the influence of nothing except gravity, you won’t feel anything, the same as you’d feel if you were out in deep space far from any galaxy. (The term “microgravity” is widely used now for that reason.) Nevertheless, the paths you would follow in those environments would be different, the result of gravity’s shaping of the geometry of space. Einstein’s “happiest thought” led him to a new theory of gravitation, the general theory of relativity.

So what is weight?

Dem bones gotta walk around

The answer is simple: weight is what you measure with a scale. That’s it. It’s not an absolute quantity, independent of state of motion. The reason you feel weight while standing is that the ground pushes back, thanks to molecular forces (derived from electric interactions), and your body naturally distributes that force throughout your frame. The same applies for sitting or lying down. You’re weightless in orbit or in other free-fall circumstances because your spaceship is falling at exactly the same rate you are: there’s no way for it to push back against you, meaning the true forces responsible for weight aren’t active.

Of course, we could say that weight is the same as the force of gravity, meaning that you aren’t weightless in orbit. Some introductory physics textbooks conflate the two concepts, and I even had an argument with my former department chair about it. Their take: it’s too complicated to separate weight from gravity. My take: you have to jettison intuition and experience, as well as general relativity to do so.

However, weight as the distribution of forces through the body has several physiological effects. For example, if you linger in a weightless environment, your bones will begin losing density at an alarming rate, akin to an advanced case of osteoporosis. International Space Station astronauts lose between 1 and 2% of bone mass per month in orbit, so extended stays aboard the ISS lead to extended recuperation periods upon return to Earth. Even sedentary, bedridden people experience some bone loss on Earth because the distribution of weight is different than for upright postures.

In fact, it was an article about such bone loss that triggered this piece. (Tip o’ the pendulum to Peter Newbury for sending the article my way.) I assume the physiology in that post is fine, given the source, but it’s incorrect on a crucial point: it’s not lack of gravity that causes the problems. Human bodies evolved to deal with the consequences of weight: everything from skeletal structure to the circulatory system is well adapted to life on the ground, with the distribution of forces that implies.

Planning for long trips to other worlds, such as Mars, would require understanding and compensating for bone loss and possibly other physiological changes. Mars’ gravity is only about 38% of Earth’s, so a person standing on Mars would only have 38% of the weight they have on Earth. The trip itself would be mostly weightless (at least as far as modern propulsion technology allows), since it doesn’t matter if you’re in orbit or en route between planets: the presence or lack of gravity isn’t the issue.

To close, here’s a song about a weight of a different sort, performed by a few of my favorite musicians.

12 responses to “What is weight?”

  1. Great article! Thank you for pointing out the distinction between weight and gravity. Changing gravity is still at the root of the issue of bone loss in space, it just depends on what component of the process you want to pinpoint. An environmental change in gravity in space results in weightlessness and impacts inner ear function and bone density decreases. Regardless of whether you’re traveling through space or living on Mars for extended periods of time, the vestibular system is going to sense the change in weight, due to the change in gravity, and function differently than on Earth. I realize that my article states that microgravity is the root of bone issues, but what I meant to convey was the change in gravity.

    1. But it’s still not gravity that’s the issue – it’s weight (or rather weightlessness). Since gravity is still 90% of what it is at Earth’s surface at the location of the ISS, that can’t really be what’s causing bone loss or inner ear problems. You can replicate the same disorientation on the Vomit Comet (which they do deliberately to see if people can take spaceflight), which experiences nearly 100% of Earth’s surface gravity, yet still simulates weightlessness.

      Think of it this way: if you could build a platform (somehow, never mind how) on a huge tower 340 km high, it would be at the same altitude as the ISS. If you weighed 100 pounds on Earth, you’d weigh roughly 90 pounds at the top of this tower – but you still wouldn’t experience the same rapidity of bone loss as if you were aboard the ISS because you wouldn’t be weightless. Does that argument make sense?

      1. Ya, that’s a great illustration and astronauts are weightless because of the effective gravity inside the ISS is very close to zero, because it is in free fall (aka microgravity) and is causing issues with the vestibular system.

      2. Perhaps the issue lies in the definition of “microgravity”.

      3. No, I think the problem is that you’re saying “gravity” (or “effective gravity”) when a physicist would say “weight”. My quibble with using gravity in lieu of weight is that it’s important to remember that gravity isn’t zero. Both the ISS and the astronauts inside are independently in orbit around Earth, held that way by gravity. If you took away the ISS (and put ’em in spacesuits), the astronauts would still be in orbit. They’d be as weightless in orbit as they would be out in deep space, but gravity would be zero (or close enough) out there.

        My concern is that fiddling with the definition of “gravity” changes its meaning in a way that’s a problem. Microgravity refers to the fact that there is a very tiny difference in the strength of gravity between the two sides of the spacecraft that you can measure with very sensitive instruments, but that can’t be the reason for bone loss.

      4. Then you should take that up with NASA because they’re the ones defining microgravity as “The condition of microgravity comes about whenever an object is in free fall.”

        Thanks for the insight on weightlessness!

    2. Sorry not defining gravity but rather using “the condition of microgravity” in place of weightlessness.

      1. OK, fair enough. The point is that it’s weightlessness, not lack of gravity, that’s causing the problems. You can have weightlessness with or without gravity, but it’s the lack of weight that produces health concerns for astronauts.

        Which is another interesting point in itself: you can create weight by spinning a spaceship (like in 2001), though it requires either a huge ship or a very fast spin. That’s sometimes called artificial gravity, but again the key is making weight.

  2. I think your graph could be clearer. The point marked ‘earths radius’ I take it is the point where you are twice as far from the earth’s core as on earth’s surface (With 0.25 the gravity due to earth.) but it could be mistaken for being at the earth’s surface.

    Also by complete coincidence Of Particular Significance just did an article on nearly the same thing on the same day: http://profmattstrassler.com/articles-and-posts/relativity-space-astronomy-and-cosmology/why-do-astronauts-float/

  3. I desperately want to go on the vomit comet…

  4. Great article – good read! Thanks!

    But there’s something wrong with Einstein’s quote. Written out, the German part is “glücklichste Gedanke meines Lebens”. I think this could be another funny example of a back-and-forth translation (German -> English -> German) which often happened to Einstein quotes. ;-)

    1. That might be a transcription error on my part; I don’t speak or read German, so I just typed in the quote from the book. I’ll check it later, when I have the book in front of me again!

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