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I seem to remember learning the pecise reason why plants both respond to sunlight and to gravity during my Freshman year Biology class in high school. I remember that it is due to a single plant hormone that stunts the elongation of cells. I think it begins with an 'a'.

Aren't the mechanics of this well-known?

Auxin, I did a science project on this in 5th or 6th grade. My father helped me rig up a centrifuge-like apparatus that would spin seeds at what was supposed to simulate greater than earth gravity. I remember doing research (reading) about auxins and coming to the conclusion that higher gravity would stunt plant height.
And what happened to the seeds on your science project? :)
For the sunlight part: sunlight inhibits growth on the sun-facing side of the plant, and so the flower faces towards the sun.
Except this works for buried seeds and seeds germinated in the dark.
I think it's just a function of how the liquid in the plant's cells settled by gravity. The denser liquid is pulled to the bottom by gravity while thinner liquid floats to the top. The plant must grow toward the thinner liquid, away from gravity.
While this sounds plausible, it doesn't explain how roots grow downwards.
I'm surprised that the plant was robust in space. It could just as well have stopped growing at all. Makes you wonder if there are any low gravity growth places on earth. If not, where has the plant learned this skill?
I'm not sure if you're joking, but you should know that I had a good laugh at this comment. :) In case you are indeed wondering, gravity has no effect on cell growth, or indeed on any of the cell's vital functions. More than anything, cellular processes rely on chemical diffusion, which at that scale is more strongly affected by temperature than by gravity.

Also, gravity is almost constant everywhere on the earth's surface.

Wow. Complete cognitive dissonance between us :) I was reasoning about the plant as a biological device which has adapted to life according to Darwin's theory of evolution. Since gravity, as you point out, is quite constant on earth, one could expect that a plant has come to rely on it for its existence. Unless trained otherwise. So I was contemplating that the ability to survive without gravity would have had to be a skill learned off the surface of the planet. And if it has never experienced such an environment before in its evolutionary development, one could consider it extreme luck that it kept on living without the previously nearly constant gravity parameter. If the plant manages to survive in spite of fundamental environmental changes without previous training, it must have a very robust design. It's like a computer program which would keep on running if you removed main memory. Not impossible, but very unlikely that it wouldn't be dependent on main memory by now. If it still works, must it not be designed in a very robust manner?

Are plants this robust? One could be lead to believe that this is indeed a useful property in a evolutionary sense. But it must surely also have high costs. So it is nonetheless a very interesting question in my opinion.

Addendum: Regarding cells not being dependent on gravity for growth: In the article is was mentioned that plant in fact are dependent on gravity for their survival, in fact very much so. Without gravity the plant would not be able to physically locate its root system correctly or get its leaves above ground. It was, however, also mentioned that the plant survive in space just fine.

Plants did evolve in what is effectively low gravity 'environments' namely under water, which is why hydroponics can still work. We don't actually know much about how large plants like trees grow in space so while some plants are fine that does not mean they all are.
There's no reason to leap from the presence of an environmental factor to reliance on that factor for survival.

For instance, air is thick with nitrogen, something that most organisms need but are unable to extract from that air.

Do you have anything for your claim (like maybe NASA planting something on the space). Because, after reading this article, I'm having a hard-time figuring out the chance that the plant will actually find its way to the top.
With plants, the "default" is to grow a shoot in a straight line. When an adjustment needs to be made, the shoot's two sides grow at different rates, resulting in a bend. If there is no stimulus that makes the plant want to "turn", it will just combine growing in the same direction (probably with some random small variations thrown in).

By analogy to cars, if you disable the steering wheel, the car can still move, but it won't have a particular destination.

Some bacteria know up and down by knowing magnetic north and south. They take advantage of the fact that magnetic north usually points slightly down or up.

By knowing up and down the bacteria can move to the area with optimal parameters like temperature/oxygen saturation - these usually change with depth.

did not click cause of one obvious word: gravity
You would've been a bundle of excitement in school science when the teacher discussed humans knowing which way was up and which way down. Yelled "gravity" and then blocked your ears while the teacher explained the utricle and so on?
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There was a bit of a non sequitur at the end, where they mention that the statolith theory has support from plants growing in space. That's no confirmation for the theory, we already knew they sensed gravity, the question is how they sense it.
Right. The experiment does nothing to confirm the conjecture. A neat trick would be, say, to figure out how to line up the statholiths (sp?) in zero g and see what happens relative to a plant whose statholiths are randomly arranged.

Note that ultimately we would like to come up with ways to convince human bodies that they're in a gravitational field, so this is not entirely academic.

Learned about statoliths in university. Didn't realize the statolith theory was up for debate.
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"...where the pull of gravity is nearly zero": No it's not! This is sloppy science journalism physics where there's a gravity shield around Earth. The pull is there but objects are in free fall.
"would the plants respond to the centrifugal pull of gravity"

Sometimes I have to reread sentences like this to get what the author is trying to convey. I don't understand why the author didn't leave it at "centrifugal pull. " It's already an adequate layman's term. A sentence like this only serves to confuse and make physics sound harder than it is. If a good teacher can open kids eyes to the wonders of the world, a bad teacher can easily fog the world in obscurity and inconsistencies.