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Old September 27 2012, 10:33 PM   #58
The Borgified Corpse
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Re: About planetary gravity

Christopher wrote: View Post
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)?

Christopher wrote: View Post
The Borgified Corpse wrote: View Post
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.

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.
Kegg: "You're a Trekkie. The capacity to quibble over the minutiae of space opera films is your birthright."
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