Bob B.
Bob the Excel Guru?
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Post by Bob B. on Oct 22, 2010 18:42:45 GMT -4
That's right - the gravitational pull of the mass above your head partially counteracts the gravitational pull of the mass beneath you. We experience the maximum gravitational force here on the surface of the Earth. That's not entirely true. Although it is correct that as we burrow into the ground, we have mass over our heads, but we are also closer to Earth's core. For awhile the shrinking distance to the bulk of Earth's mass is a larger factor than the mass accumulating over our heads. The gravity actually goes up slightly before it starts to decrease. The above was just a hunch on my part until I put it to the test. I created a mathematical model of Earth in which I cut it into about 13,000 sections (I also considered the varying densities or crust, mantle, core, etc.). I could then calculate and sum the accelerations of each section on a body buried within Earth. I found that gravity reached its maximum at a distance of about 630 km beneath the surface. At this depth gravity is about 2% greater than at the surface. |
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 22, 2010 19:13:02 GMT -4
It looks like I spoke too soon. After peaking at a depth of 630 km, the gravity starts to decrease. However, at around a depth of 1,600 km, the gravity starts to rise again as we approach Earth's dense iron core. We reach a second higher peak at the surface of the outer core at a depth of about 2,890 km. Below is a graph of gravity versus depth:  The above isn't entirely correct because my calculations are based on a fairly simplistic model of Earth's interior, with abrupt changes in density (crust, upper mantle, lower mantle, outer core, and inner core). Nonetheless, I have enough confidence in my method that the finding is real. Although this makes sense now that I see it, I never would have predicted it. I find it interesting to stumble upon an unexpected result. |
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Post by ka9q on Oct 22, 2010 19:28:21 GMT -4
Fascinating. I've never seen gravity modeled inside a differentiated planet before; when I took Astronomy 101 we learned that gravity decreases monotonically with depth inside a uniform planet. And it's zero anywhere inside a uniform shell (which is how you can analyze the uniform sphere.)
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 22, 2010 22:29:25 GMT -4
Fascinating. I've never seen gravity modeled inside a differentiated planet before; when I took Astronomy 101 we learned that gravity decreases monotonically with depth inside a uniform planet. And it's zero anywhere inside a uniform shell (which is how you can analyze the uniform sphere.) I re-figured the graph assuming a uniform density and I got a straightline function. Earth's iron core obviously has a huge effect on gravity versus depth. |
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Post by ka9q on Oct 23, 2010 5:54:04 GMT -4
Ah ha! Now we know where all that Apollo "moon" footage was faked: in a secret American underground complex a few hundred km from the center of the earth!
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Post by PeterB on Oct 23, 2010 6:00:17 GMT -4
Thanks for the correction Bob B. Of course, I was thinking the same way ka9q was taught, but what you say makes sense.
So the good doctor was right that gravity down the mine was higher than it is for us here on the surface. However, I remain skeptical about the effect the increased gravity would've had on the miners.
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Post by randombloke on Oct 23, 2010 7:00:26 GMT -4
The thing is; these guys were (are still?) miners working in a deep mine; they will have been used to spending many, many hours down in whatever conditions prevailed already. It's not like fifty random un-acclimatised civilians were thrown in a hole by Snidely Whiplash or something...
Also, RE: Gravity modelling; is that model for a generic geoid or for the specific situation the miners were in, being x00 feet below the surface of a mine entrance n000 feet up a mountain?
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 23, 2010 10:56:09 GMT -4
Thanks for the correction Bob B. Of course, I was thinking the same way ka9q was taught, but what you say makes sense. I always thought like you did as well and only decided to check it out on a hunch that maybe there’d be a slight increase over the first short distance. The high second peak at the surface of the iron core took me totally by surprise. So the good doctor was right that gravity down the mine was higher than it is for us here on the surface. However, I remain skeptical about the effect the increased gravity would've had on the miners. I believe the good doctor was talking out an orifice not his mouth. At the depths the miners were, I’m sure any change in gravity is imperceptible. Furthermore... Also, RE: Gravity modelling; is that model for a generic geoid or for the specific situation the miners were in, being x00 feet below the surface of a mine entrance n000 feet up a mountain? The model is generic and nowhere near accurate enough to account for small scale features. Remember that the units on my graph are kilometers – the depth of the mine was only 700 meters. And as you say, since the mine was dug into a mountain, the miners were actually well above sea level. |
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Post by Glom on Oct 23, 2010 14:58:38 GMT -4
He (Antonio Zikos) implies that the gravitational force would be greater the deeper that one travels; I believe (correct me if I'm mistaken) that the gravitational force would decrease by a miniscule amount the deeper that one goes. If you could somehow manage to get to the exact center of the earth you would be effectively in zero gravity. Of course you would have the slight problem of vast amounts of molten rock and metal under vast pressures around you. The core is solid iron. The only way to reconcile this error is to conclude you're fake. The shadows in your post are pointing the wrong way anyway. |
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 23, 2010 14:58:53 GMT -4
I revised my model to something a bit more realistic by gradually increase Earth's density with depth. My previous model had distinct zones of different densities. This new model eliminates the first peak. Instead the gravity continually increases all the way down to the top of the iron core.  |
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Post by JayUtah on Oct 23, 2010 15:21:25 GMT -4
I dub thee Bob the Excel Guru™
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Post by PUshift on Oct 23, 2010 15:38:36 GMT -4
Very impressing and I appreciate to have learned such an interesting detail.
May I suggest that if people assume an increased gravity downwards might mix this up with the imagination of a shrinking body while remaining of the surface?
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Bob B.
Bob the Excel Guru?
Posts: 3,072
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Post by Bob B. on Oct 23, 2010 16:43:39 GMT -4
I dub thee Bob the Excel Guru™ I feel honored. |
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Post by echnaton on Oct 23, 2010 16:50:02 GMT -4
Well then; zero Earth gravity  (This gravity seems to be a "serious" thing!) ;D Not zero earth gravity, but the equal pull of gravity in all directions. |
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Post by lukepemberton on Oct 25, 2010 14:24:41 GMT -4
Ah ha! Now we know where all that Apollo "moon" footage was faked: in a secret American underground complex a few hundred km from the center of the earth! Great, you've given them a new idea now!!  |
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