About planetary gravity

[gturner]

^ People have trouble thinking about motions in space, since they're used to having a nice stretch of terra firma as their absolute reference.

They know that when they roll their car, the bystanders, sidewalks, and trees aren't really aren't spinning around in crazy circular paths, their head is.

People can think of their airplane flight as the Earth falling away, tipping up at an angle, moving way down, spinning slowly around as they line up on the runway, then coming back up to kiss the plane's wheels as they land, but they know that's not a good way to describe things. But in an aircraft centered coordinate system, that's actually a pretty good way to think about it, where the pilot can work to keep the planet level, not the plane, and it's equally valid.

I wonder if we should tell him about shooting a monkey with a blowgun, and how changing a reference frame can turn mathematically difficult problems into trivial ones?

 

[sojourner]

Well, the easiest way to point out that it's wrong is the fact that all the planets orbiting our sun are on the same elliptic plane as the galaxy. Not perpendicular as the video shows it. That's the point where you can stop the video and dismiss it entirely.

Sorry, but that's not right. The ecliptic plane (the plane in which the Earth orbits the Sun) is tilted at 60.2 degrees relative to the galactic plane. It's closer to perpendicular than parallel.

Well, that's one on me.

 

[gturner]

^ When you view the night sky, the Milky Way is all cockeyed to the ecliptic where the planets and moon travel.

 

[Christopher]

Technically, only the Earth travels in the ecliptic plane. It's called that because it's the plane where eclipses happen, where the Moon passes directly between the Earth and the Sun -- which, naturally, would correspond to the plane of the Earth's motion around the Sun. Naturally the Moon doesn't orbit exactly in the ecliptic (it's off by about 5 degrees), or there'd be a solar eclipse every four weeks and a lunar eclipse midway between each one. And all the other planets' orbital planes range from about 3/4 of a degree (Uranus) to over 7 degrees (Mercury) off of the ecliptic.

 

[FPAlpha]

Reading this thread i'm actually frightened to see how other school systems educate their kids

I know that teachers are still humans and you get good ones and bad ones ( i once had a teaches in French who was unanimously voted as the worst teacher in school but he still was very good at French.. he just sucked as a person) but i never encountered a stupid teacher.

Honest to god.. if this was the standard i could sit myself in these classes and teach from the get go and i'm almost 20 years out of school and have forgotten much about the details of science (especially the math).
Would probably need a few weeks to brush up again.

 

[Maurice]

My first real sense of what it would be like to visit and alien planet was in my first trip to the southern hemisphere. I remember looking up at an utterly unfamiliar night sky, and as a stargazing buff, that ranked as one of the coolest moments in my memory. Second was watching a full Moon rise in Auckland, and noting that the Moon appeared to be laying on it's side compared to how I was used to seeing it, as I was standing at about 90 degrees to how I stand back home.

 

[gturner]

My first real sense of what it would be like to visit and alien planet was in my first trip to the southern hemisphere. I remember looking up at an utterly unfamiliar night sky, and as a stargazing buff, that ranked as one of the coolest moments in my memory. Second was watching a full Moon rise in Auckland, and noting that the Moon appeared to be laying on it's side compared to how I was used to seeing it, as I was standing at about 90 degrees to how I stand back home.

I also had my first sense of an alien planet when I went to to the Soutern Hemisphere on a trip to Australia. The plane landed, and after some time debating with the natives, I was perterbued, more than perturbed, irate, that a day of my life had been lost in transit. Just gone. Never happened. I didn't exist for an entire day of Earth's history, ad couldn't have affected events in any way. That was extremely disempowering and humbling.

Then I noticed that people were walking on the ceiling because we were underneath the planet, and things went downhill from there...

 

[Maurice]

Actually a more subtle thing that threw me is that in the southern hemisphere the sun transits he sky to the north, not the south, so that confounded my sense of direction.

 

[The Borgified Corpse]

Since we're sharing incompetant high school teacher horror stories, I thought I'd share a few of my own. (Then I'll ask a question about planetary gravity that's been kinda bugging me. I promise.)

I had a couple of really bad teachers that just never taught the subject at all. I'm not sure if they were always that bad or if I just caught them at a bad time because I usually seemed to have the worst teachers during the very last period of the day. So maybe the kids in the earlier periods got good education but by the end the teachers just stopped caring. Or maybe they just sucked because they were a bit out of their field.

My regular freshman year chem-physics teacher went on maternity leave for most of the 2nd semester, which was the chemistry portion. Her long-term substitute was a biology major. He tried to teach the class for the first couple days, then he just gave up. He spent the next several months playing around with the geiger counter he found in the lab and showing us his vast collection of cheesy old sci-fi movies (Fiend Without a Face, It!, Them!, Creature from the Black Lagoon, etc.).

My senior year, I took government/economics with "Coach" Hoffmeyer, which probably tells you all he knew about government or economics. (He was a really nice guy, though.) Mostly, we watched movies. To his credit, many of them did have something to do with government, like All the President's Men or The Candidate. But when we got to Remember the Titans, I felt like he was reaching. He was still better than one of his substitutes though, who kept insisting that Animal Farm was about Nazi Germany, not Soviet Russia.

Then there was Mr. Draper, who I had for a one-semester elective called "Criminal Justice." In reality, the whole class was just a bunch of his paranoid rants about how high school was not really meant to educate us but to socialize us into doing the same boring jobs that our parents did.

Although, oddly, the weirdest teacher I had was when I went to ASU and took a lower level economics course. The class was taught by a racist Welshman, who went on leave for some surgery, and left his class in the hands of his TA, who was a younger, even more racist Welshman. And the crazy thing was the way he was able to smoothly integrate his racism into his class examples. Like, when he would explain the principle of specialization: Canadians are big, so they can make a lot of lumber, but they're dumb, so they can't make computers. The Chinese are smart, so they can make computers, but they're short, so they can't chop down trees. So the Canadians sell lumber to China and the Chinese sell computers to Canada.

He really couldn't understand why everyone was so shocked by this example, especially the Chinese girl sitting in the front row. I tried to help him dig himself out of this hole (or at least get everyone else to jump down in it with him) by suggesting, "Say something bad about Wales." And, without missing a beat, he just shrugged and said, "Well, there's nothing bad to say."

Over short ranges at least, gravity is subject to the inverse square law. That means the farther you get from the center, the less its gravity affects you. From the nebula/ball example above, this means that the force of gravity half a light year away from the center is considerably less than it would be half a mile from the center. Just as important to understand, however, is that you can only be pulled in by the gravity of something BELOW you, so if you are INSIDE the gas cloud, you will not be affected by any mass that is farther away from the center than you are.

This brings me to a question I have. I just came back from seeing the remake of Total Recall. Now, I know I'm not supposed to take any of its science seriously, but it did make me think. In the movie, there's this transportation device called "The Fall" which literally takes you through the center of the Earth to ferry commuters from Australia to London. Now, when they reach the middle of the planet, they briefly become weightless while the entire apparatus shifts to point the other way. My question is, would the effect of gravity in the exact center of the planet be like weightlessness? Or, being so close to the Earth's gravitational center, would the force of gravity be so strong that it would cause harm (or at least be noticibly uncomfortable)?

 

[Tobin_Dax]

At the center of the Earth, there is nothing "below" you to pull you down. All of the mass of the Earth surrounds you in a (pretty much) symmetric distribution, so the gravitational pull from that cancels out. So you would be weightless.

 

[Christopher]

This brings me to a question I have. I just came back from seeing the remake of Total Recall. Now, I know I'm not supposed to take any of its science seriously, but it did make me think. In the movie, there's this transportation device called "The Fall" which literally takes you through the center of the Earth to ferry commuters from Australia to London. Now, when they reach the middle of the planet, they briefly become weightless while the entire apparatus shifts to point the other way. My question is, would the effect of gravity in the exact center of the planet be like weightlessness? Or, being so close to the Earth's gravitational center, would the force of gravity be so strong that it would cause harm (or at least be noticibly uncomfortable)?

The former. It's called shell theory -- the gravity inside a uniform spherical shell of mass is zero everywhere within it, because the pull in every direction is cancelled out by the stuff on the other side. So if you're deep beneath the Earth's surface, you'll only feel gravity from the percentage of the Earth that's closer to the core than you are. (Newtype_alpha alluded to this, but it doesn't quite work with a nebula, unless it's a spherical one.) So if it were somehow possible for there to be an open, habitable space in the center of the Earth -- which it isn't because of the pressure and temperature and so forth -- then yes, you'd be in microgravity.

The thing is, though, that the simplest way to operate something like the Fall would simply be to drop it straight through the Earth and let gravity power it. It would work pretty much like a pendulum -- aside from loss to friction, it would rise back up on momentum almost exactly as far as it fell down. (Martin Gardner covered this in one of his mathematical puzzle tales from Asimov's magazine decades ago, reprinted in a book called Mathematical Puzzle Tales.) So really you'd be in free fall, and thus feel weightless, for the entire trip. Which would be 42 minutes long for any chord directly through the Earth, not just through the center. (The longer the chord, the longer you fall for, so the faster you get, and it balances out.)

Now, if for some reason the Fall wasted time and energy by braking on the way down and using thrust to climb all the way back up (which would be really, really hard to do), then passengers would still feel their weight gradually diminishing as they neared the center. It wouldn't be full weight all the way until the exact center.

So it sounds to me that this version of Total Recall bungled the science of the Fall as badly as the previous film of that name bungled the science of, well, practically everything about Mars. (They got the color right. That's about it.)

I'm reminded of the mistake Jules Verne made in From the Earth to the Moon. He assumed the passengers would only feel weightless when they reached the point where terrestrial and lunar gravity cancelled -- failing to realize that the whole trip would be in free fall except when they were under thrust. The problem is mistaking gravity for weight. Weight is what you feel when you're pressed by gravity against something that isn't moving, or when something under thrust presses against you. If you and the vehicle you occupy are both being pulled by gravity the same way, then you'll feel weightless, no matter how strong the gravity is.

 

[RB_Kandy]

Is it possible that the cause of gravity (not just planetary) is the force of the universe expanding outward?

Like, if you blow up a balloon it creates pressure from the surface to the center.

 

[Crazy Eddie]

^ There's a someone well known interpretation called "Shade theory" that goes exactly like this. The idea being that the expansion of the universe -- or other form of omnidirectional pressure -- is somehow reduced in the space between two massive bodies where a "Shade" region appears between them; both bodies are pulled towards each other because there is slightly less energy in the shade region than there is around them.

 

[Tiberius]

Is it possible that the cause of gravity (not just planetary) is the force of the universe expanding outward?

Like, if you blow up a balloon it creates pressure from the surface to the center.

That would suggest that on one side of the Earth gravity would push you down (if the earth is between you and the center of the universe) and on the other side, gravity would fling you out into space.

 

[Christopher]

Is it possible that the cause of gravity (not just planetary) is the force of the universe expanding outward?

Like, if you blow up a balloon it creates pressure from the surface to the center.

No. Vacuum isn't air.

Although there is an interesting theory that it could actually be the cumulative pressure of vacuum energy, the virtual particles constantly forming and disappearing within the quantum foam. The idea is that when it seems like two masses are attracted to each other, it's really that they're shielding each other from a bit of that uniform energy pressure on all sides, and so that creates an imbalance that causes them to be pushed toward each other.

I've also heard another interesting offbeat theory... not sure I remember the details, but it's something to do with the way every particle exists in multiple overlapping quantum states. And the idea is that particles tend toward the most probable state, and statistically, the most probable location for any given particle in an ensemble is toward the center. So that creates a sort of probability pressure that causes masses to try to reach the center of whatever system they belong to.

Of course, these are fringe ideas -- not to the point of being crackpot theories, but alternate scientific proposals that don't have real evidentiary support. The leading view is the general-relativistic one that the presence of energy -- including the energy contained in mass -- alters the geometry of spacetime, so that the paths of objects or light beams in the vicinity of masses are redirected toward them. Or there's the alternate quantum view that masses emit fields of gravitons that create attraction between them, similarly to the way the electromagnetic fields emitted by charged particles create attraction or repulsion between them.

That would suggest that on one side of the Earth gravity would push you down (if the earth is between you and the center of the universe) and on the other side, gravity would fling you out into space.

No, because there's no center of the universe. The universe is effectively infinite and its expansion is uniform.

 

[gturner]

I hate to shoot down the shielding theory, but the force woule be like a gas around BB's, acting uniformly. It can't come from outside without being here too because we've not just had seconds, minutes, or hours to reach equilibrium with it, but billions of years. If it came from elsewhere we'd have noticed that distant objects act differently elsewhere, and we haven't.

Expansion pressure sounds like light pressure, one of the ideas Newton rejected, and he wore tube socks and funny pants. It's a notion that always get rejected but a notion that alway occurs, even to people in tube socks.

 

[Christopher]

I hate to shoot down the shielding theory, but the force woule be like a gas around BB's, acting uniformly. It can't come from outside without being here too because we've not just had seconds, minutes, or hours to reach equilibrium with it, but billions of years. If it came from elsewhere we'd have noticed that distant objects act differently elsewhere, and we haven't.

I think I must not have explained it clearly enough. I'm talking about the vacuum energy that pervades the entire universe. It's not from outside, it's from inside, everywhere.

 

[The Borgified Corpse]

No, because there's no center of the universe. The universe is effectively infinite and its expansion is uniform.

How does that reconcile with the Big Bang Theory? Isn't all matter in the universe thought to have expanded outward from a single pinpoint? Wouldn't the original site of that pinpoint be the ostensible center of the universe (even if we're currently incapable of observing where that would be)?

This brings me to a question I have. I just came back from seeing the remake of Total Recall. Now, I know I'm not supposed to take any of its science seriously, but it did make me think. In the movie, there's this transportation device called "The Fall" which literally takes you through the center of the Earth to ferry commuters from Australia to London. Now, when they reach the middle of the planet, they briefly become weightless while the entire apparatus shifts to point the other way. My question is, would the effect of gravity in the exact center of the planet be like weightlessness? Or, being so close to the Earth's gravitational center, would the force of gravity be so strong that it would cause harm (or at least be noticibly uncomfortable)?

The former. It's called shell theory -- the gravity inside a uniform spherical shell of mass is zero everywhere within it, because the pull in every direction is cancelled out by the stuff on the other side. So if you're deep beneath the Earth's surface, you'll only feel gravity from the percentage of the Earth that's closer to the core than you are. (Newtype_alpha alluded to this, but it doesn't quite work with a nebula, unless it's a spherical one.) So if it were somehow possible for there to be an open, habitable space in the center of the Earth -- which it isn't because of the pressure and temperature and so forth -- then yes, you'd be in microgravity.

The thing is, though, that the simplest way to operate something like the Fall would simply be to drop it straight through the Earth and let gravity power it. It would work pretty much like a pendulum -- aside from loss to friction, it would rise back up on momentum almost exactly as far as it fell down. (Martin Gardner covered this in one of his mathematical puzzle tales from Asimov's magazine decades ago, reprinted in a book called Mathematical Puzzle Tales.) So really you'd be in free fall, and thus feel weightless, for the entire trip. Which would be 42 minutes long for any chord directly through the Earth, not just through the center. (The longer the chord, the longer you fall for, so the faster you get, and it balances out.)

Now, if for some reason the Fall wasted time and energy by braking on the way down and using thrust to climb all the way back up (which would be really, really hard to do), then passengers would still feel their weight gradually diminishing as they neared the center. It wouldn't be full weight all the way until the exact center.

So it sounds to me that this version of Total Recall bungled the science of the Fall as badly as the previous film of that name bungled the science of, well, practically everything about Mars. (They got the color right. That's about it.)

There's a lot of things about the Total Recall remake that don't make sense.

First, you're right. They got the gravity of the Fall totally wrong.

Second, it seems extremely implausible that this future Earth would posess the technology & resources necessary to make something like the Fall, particularly when considering all of the other problems facing future Earth.

Third, why have commuters from the Colony travel daily to & from their jobs in London via the Fall? If there's an overpopulation problem, why can't they employ the local people from the UFB to work in the factories? Or just build factories on the Colony itself?

Fourth, the movie establishes that hardly any of the Earth is habitable anymore thanks to chemical warfare. Only England & Australia remain.

Spoiler: Total Recall remake

But when Quaid visits the leader of the resistance, it's in an area of London that's been ruined by chemical warfare. (At least, I think it's supposed to be London. There's double-decker buses and I'm pretty sure I could see the Post Office Tower in the background.) How can there be such an uninhabitable area of London so close to the highly populated part of London? There doesn't seem to be any actual barrier between the two parts of the city. Shouldn't the poisonous gas be wafting over there pretty regularly?

Do you have an equation for that "any freefall trip through the Earth would take only 42 minutes" thing? My dad kept insisting that the Fall couldn't work by freefall because the fastest speed you could possibly reach would be 150 miles per hour, which would mean the trip would take about 53 hours.

 

[Christopher]

No, because there's no center of the universe. The universe is effectively infinite and its expansion is uniform.

How does that reconcile with the Big Bang Theory? Isn't all matter in the universe thought to have expanded outward from a single pinpoint? Wouldn't the original site of that pinpoint be the ostensible center of the universe (even if we're currently incapable of observing where that would be)?

That's not what it means at all. "Big Bang" is a misnomer, coined by Fred Hoyle in order to ridicule the theory, since he was a fan of the continuous-creation cosmological model which has since been definitively debunked. It shouldn't be interpreted as a literal explosion into space. After all, it was space itself that was being created. It didn't expand into anything, it just expanded -- it started out infinitely dense and then things within it got further apart, uniformly.

A useful analogy is to imagine a microbe living on the surface of a balloon. When you blow up a balloon, the whole surface expands, but the center of that expansion is nowhere on the surface itself; it's in the center of the balloon. The microbe will perceive the balloon expanding outward from itself in all directions, and imagine itself (it's an unusually thoughtful microbe) as being at the center of the ballooniverse. But another microbe on the other side of the balloon will see the same thing, and so will every other microbe no matter where it lives on the surface. None of them has any more claim to calling its location the center of their 2-dimensional universe than any other, because the surface is expanding outward from every point within it, not just one.

It used to be thought that our universe might be a 3-dimensional "surface" of a 4-dimensional closed shape, like the skin of a balloon with a dimension added, so that there'd be no center of expansion within the universe itself. We now think that the universe is "flat" but infinite -- and something that's infinite can't have a definable center, because it has no edges relative to which a center could be defined.

 

[The Borgified Corpse]

So, let me see if I've got this straight? In the beginning, the universe was infinitely dense in an infinite space. That infinite space then expanded, leading to the level of density that we are now familiar with in the universe. But since space is infinite and always has been (even though infinity seems to be getting bigger), it means that there can be no center to it. Am I grasping the concept so far?

I've certainly never been able to wrap my head around the idea that the universe is really a 2-dimensional or 4-dimensional object and that the 3-dimensional space that we interact with on a day-to-day basis is merely an illusion. It seems to me like Occam's Razor would slice that one to shreds. The fundamental existence of 3-dimensional space as the only space with any practical applications in the universe in which we live seems undeniable.

I suppose, if I'm to interpret the balloon analogy correctly, what you're saying is that, if there is a center to the universe, the center exists in a 4th dimension that cannot be measured and that is the thing that is actually expanding, causing the rest of the universe to become more spread out without changing the actual infinity of it all. Is that right? So that would mean that all matter in the universe, particularly galaxies, is spreading out and away from each other in all directions at equal rates, right?