Is "weightlessness" an artifact of a free-fall orbit?

December 12, 2004 11:28 AM

Science hour question: My niece asked me this and I didn't have a good answer. People in orbit around the earth are "weightless." But what would happen if an object in space were kept stationary at 150-200 miles up? Would an astronaut in such a stationary but very high station in fact feel significant gravity? Is "weightlessness" (in near-Earth space) an artifact of a free-fall orbit? C'mon rocket scientists, I know you're out there.
posted by socratic to science & nature (20 comments total)

Is "weightlessness" (in near-Earth space) an artifact of a free-fall orbit?

Yes. (although there is still some reduction in gravity due to the distance from the earth)
posted by reverendX at 11:37 AM on December 12, 2004

It seems like you know the answer already. The astronaut's weightlessnes only occurs because they are in orbit. Their acceleration "away" from the earth matches their gravitational attraction toward the earth so their forces are balanced.

Technically, they are always falling towards earth but missing it and so end up going in circles (this is what an orbit is)

An object held stationary above the earth would fall down.
posted by vacapinta at 11:40 AM on December 12, 2004

Yup, they would feel gravity, since they're not freely falling any more (the floor of their magical stationary space station is keeping them from doing that.) "Weightlessness" is a consequence of being in free-fall — this was Einstein's big realization that led him to invent General Relativity.

Now, of course, since your hypothetical astronauts are farther from the Earth, and gravity gets weaker as you go farther away from a source of matter, the gravity they would feel is less than the gravity we feel here on earth. If you do the math, it works out to being about 7% weaker at an altitude of 150 miles and 10% weaker at 200 miles.

On preview: damn, beaten to the punch. But my reply has numbers, so neener neener.
posted by Johnny Assay at 11:42 AM on December 12, 2004

If you were perfectly stationary, then yes, you would feel rather signifigant weight. Low earth orbit is still pretty low, and gravity would only be about 10-20% lower than normal.
posted by zsazsa at 11:44 AM on December 12, 2004

Heh, I didn't know the answer, but I thought I did. Actually, the niece is a pretty smart kid: her question was, "If astronauts are weightless, how does the Earth keep something as big as the Moon in orbit?"

So, a nuance on my question: When we see a movie like Apollo 13, and the astronauts experience weightlessness en route, is that because the trajectory is still technically free-fall into a gravity well? If you were to place a hypothetical magic stationary space station at some point between the earth and the moon (obviously not at the point where the two bodies' gravity cancels out), an astronaut there would still feel significant, if lessened, gravity?

I don't like to say "I don't know" to family... :) Though I'm a little worried that the next question is going to do with what "pefectly stationary" means.
posted by socratic at 11:55 AM on December 12, 2004

I don't want to confuse your niece, but by "stationary" we all assume you mean disregarding the fact that the earth is also rotating.

It is in fact possible to have satellites hover "above" the earth. In fact, they are still orbiting around the earth but at the exact same rate that the earth is also rotating (once every 24 hrs) This is called a geosynchronous orbit.
posted by vacapinta at 11:57 AM on December 12, 2004

vacapinta - already been there. :) I mean stationary without respect to any point on earth. But then we run into the problem that the earth itself is in free-fall around the sun, so, to remain "stationary," our hypothetical station would have to be as well. This is about the point where I start to get nosebleeds. :)
posted by socratic at 12:10 PM on December 12, 2004

The only time the astronauts feel "weight" is when the rockets are firing. At launch, they actually feel several g's (i.e., feel several times heavier than normal). Once the booster rockets shut off at launch, they are basically following a ballistic tragectory and feel weightless relative to their surroundings.

Actually, even military science geek Tom Clancy confuses stuff about orbital dynamics. I remember him describing a polar orbit satellite as floating motionless over the pole, which is impossible. A polar orbit is one in which the object crosses one pole, then the other, repeatedly, in a big circle that covers all latitudes. Satellites that "hover" motionless are in an equatorial, geosynchronous orbit 22,300 miles above the earth. They are not really motionless, but at that altitude the speed they need to travel to stay in orbit happens to be the same speed at which the earth spins.
posted by Doohickie at 12:14 PM on December 12, 2004

if you were on a flight that went in a straight line from earth to moon, at a constant speed (apart from some initial acceleration and final breaking) then you'd be weightless only at one point, "balanced" between earth and moon.

however, people on apollo 13 were weightless because the flight was not like that in two important ways:

first, rockets don't travel at constant speed. they have an initial push and then "freewheel". while freewheeling they're under the influence of gravity in the same way as the astronaut. so the astronaut appears "weightless" because they are stationary releative to the vehicle (on preview - what doohickie says).

second, and really a special case of the first, typical trajectories involve going into orbit, then changing course, etc. so a voyage to the moon may well include time in orbit. again, this appears weightless because you're "falling" at the same speed as the rocket. the difference compared with the first case is only that this is (relatively) stable - by design you happen to have the correct rotational speed to "miss the earth as you fall".
posted by andrew cooke at 12:25 PM on December 12, 2004

But then we run into the problem that the earth itself is in free-fall around the sun, so, to remain "stationary," our hypothetical station would have to be as well. This is about the point where I start to get nosebleeds. :)

Likewise, our Sun is orbiting the Galaxy etc. But thats all irrelevant. Those external forces are already balanced so they don't come into play.

Going back to the astronauts. They could take a pencil and put it in mid-air in front of them. That pencil will just stay there - it won't start falling towards Earth - it is already in orbit like they are, although it may still feel a tiny gravitational attraction toward the astronaut. Likewise, a satellite around Earth is the same as that pencil, just on a different scale.
posted by vacapinta at 12:28 PM on December 12, 2004

...and you can see that both direction and speed are important in these arguments, which is why your niece will one day learn about velocity, which includes both and makes the maths much easier.
posted by andrew cooke at 12:29 PM on December 12, 2004

I don't think understanding velocity is a problem. She didn't articulate an understanding of the difference between scalar and vector values, for example, but she did seem to understand that there's a difference between having a speed and having a direction. The difficulty was with conveying the fact that "weightlessness" is an artifact of the "weightless" thing actually having signficant weight (i.e., being in free-fall because it's getting tugged into the well). That's not exactly intuitive.

The other problem we were running into was the onion skin complexity of it all. I have some college physics and a reasonably active level of common sense, but orbital mechanics and problems involving multiple bodies are not my strong area.

I'm only going to tackle quantum theory (what little I know of it) when she's old enough to drink.
posted by socratic at 12:42 PM on December 12, 2004

I'm only going to tackle quantum theory (what little I know of it) when she's old enough to drink.

"I swear, I explained it all to you last night at the bar... what do you mean you don't remember?"
posted by Krrrlson at 12:58 PM on December 12, 2004

It might be better to think of it as an infinitely tall. infinitely strong, infinitely rigid tower made of massless unobtainium.

If you built that tower above a nonrotating object, then no matter how high you went up on that tower, you'd always feel some miniscule weight since gravity just keeps going and going and going (at least in simple models of gravity, for all I know there may be a distance limit in more realistic/advanced models so that two one-kilo masses separated by a trillion light years don't attract each other at all instead of only a teensy amount).

But if you built that tower on Earth, it and the Earth beneath it would rotate once per 24 hrs, creating centrifugal force as it goes. If you climbed up to geosynch at 36000km, you'd be going around the Earth once per day just like the satellite next to you. Presumably you'd be weightless, not just because of the distance from Earth but primarily because of your immense velocity. If you went out far enough, you'd start to feel a force pushing you into the "ceiling"; go out a light-year or two and it would almost certainly be strong enough to squish you into neutronium or get you to undergo spontaneous fusion, o the embarrassment.

This figures into Clarkes's The Fountains of Paradise, where the orbital tower has a halfway-station substantially farther out than halfway because it's actually at the lowest altitude whose velocity is above orbital velocity.
posted by ROU_Xenophobe at 1:02 PM on December 12, 2004

(i didn't mean to imply that she didn't understand velocity, rather that this would be a way to introduce it if it was new to her; on the weight thing, you may find it helps to be careful about when you use "mass" and when you use "weight").
posted by andrew cooke at 1:08 PM on December 12, 2004

Hey, a 12-year-old who understands the difference between velocity and speed is ahead of the curve in my book. She's not even a "math person" (to perpetuate a stereotype). Anyway, you're right. My conversation with her on this topic has been a magnificent exercise in teaching about precision in expression, not just "weightlessness".
posted by socratic at 1:20 PM on December 12, 2004

Insert smiley in above after "book." and before "She's not" please. (On rereading, my comment sounds a little snarky, and that's NOT how it's meant.) :)
posted by socratic at 1:22 PM on December 12, 2004

The difference between velocity and speed is easy. The difference between velocity and acceleration is a bit tricky...
posted by neckro23 at 1:41 PM on December 12, 2004

(no snark noticed - i haven't a clue about children, ages etc).
posted by andrew cooke at 1:44 PM on December 12, 2004

I'm only going to tackle quantum theory (what little I know of it) when she's old enough to drink.

"How I need a drink, alcoholic of course, after the tough lectures involving quantum mechanics!"
posted by Johnny Assay at 2:10 PM on December 12, 2004