Structure of Earth, pressure and density model

In summary, the Earth has a layered structure consisting of the crust, mantle, outer core, and inner core. As you go deeper into the Earth, the pressure and density increase due to the weight of the overlying layers. Factors such as depth and composition affect the pressure and density within the Earth. Scientists use methods such as seismic waves, gravity measurements, and laboratory experiments to measure these properties. Understanding the Earth's structure, pressure, and density is important for understanding the planet, predicting natural disasters, and gaining insight into other celestial bodies.
  • #1
Jenab2
85
22
I created interpolative curvefits to the graph of Earth's density as a function of radius, shown here:

RadialDensityPREM.jpg

(Image from Wikipedia)

Earth is assumed to be a sphere of radius 6371 kilometers. The independent variable r is the geocentric distance as a fraction of the Earth's radius; i.e. the range of r is [0,1]. The dependent variable p is Earth's density in kilograms per cubic meter.

If 0 ≤ r < 0.1915,
ρ = −8088.796304 r² − 330.8910692 r + 13100.0

If 0.1915 ≤ r < 0.5469,
ρ = −10693.43214 r² + 1635.478802 r + 12203.95803

If 0.5469 ≤ r < 0.8947,
ρ = −3450.258769 r + 7486.946521

If 0.8947 ≤ r < 0.9953,
ρ = −6212.723658 r + 9558.523857

If 0.9953 ≤ r < 0.9992,
ρ = −102564.1026 r + 105082.0513

If 0.9992 ≤ r ≤ 1,
ρ = −125000.0 r + 126000.0

From these curvefits, the integrated mass of Earth is 5.9953e+24 kilograms, which is in excess of the experimentally measured value by 0.36%. The calculated surface gravity is 9.8579 m/sec², and the calculated average density is 5534.8 kg/m³. The relative errors are less than 1% in each case, so the equations appear to be returning a very good fit to the PREM density profile, ρ(r), of Earth's interior.

The absolute maximum for gravitational acceleration inside Earth, g(r), occurs at r=0.5470 Re (at the core-mantle boundary), enclosing 0.3259 Me, resulting in g=10.699 m/sec². There is also a local maximum for g(r) at r=0.8950 Re, enclosing 0.8179 Me, resulting in g=10.029 m/sec².

To follow is the model showing:

1. Radius fraction, r/Re
2. Enclosed mass fraction, M(r)/Me
3. Local density in kilograms per cubic meter, ρ(r)
4. Local gravitational acceleration in meters per second squared, g(r)
5. Local pressure in gigaPascals, P(r)

0.00 , 0.000000 , 13100.00 , 0.00000 , 364.8373
0.01 , 0.000002 , 13095.88 , 0.23327 , 364.7400
0.02 , 0.000019 , 13090.15 , 0.46640 , 364.4482
0.03 , 0.000064 , 13082.79 , 0.69933 , 363.9622
0.04 , 0.000152 , 13073.82 , 0.93203 , 363.2826
0.05 , 0.000296 , 13063.23 , 1.16442 , 362.4098
0.06 , 0.000512 , 13051.03 , 1.39647 , 361.3446
0.07 , 0.000812 , 13037.20 , 1.62812 , 360.0878
0.08 , 0.001211 , 13021.76 , 1.85932 , 358.6403
0.09 , 0.001723 , 13004.70 , 2.09001 , 357.0031
0.10 , 0.002362 , 12986.02 , 2.32015 , 355.1774
0.11 , 0.003141 , 12965.73 , 2.54968 , 353.1645
0.12 , 0.004073 , 12943.81 , 2.77856 , 350.9656
0.13 , 0.005173 , 12920.28 , 3.00672 , 348.5823
0.14 , 0.006453 , 12895.13 , 3.23412 , 346.0162
0.15 , 0.007927 , 12868.37 , 3.46071 , 343.2689
0.16 , 0.009607 , 12839.98 , 3.68642 , 340.3423
0.17 , 0.011507 , 12809.98 , 3.91123 , 337.2383
0.18 , 0.013639 , 12778.36 , 4.13506 , 333.9589
0.19 , 0.016016 , 12745.13 , 4.35786 , 330.5063
0.20 , 0.018541 , 12103.32 , 4.55302 , 327.0398
0.21 , 0.021305 , 12075.83 , 4.74542 , 323.4590
0.22 , 0.024338 , 12046.20 , 4.93942 , 319.7381
0.23 , 0.027651 , 12014.44 , 5.13451 , 315.8775
0.24 , 0.031256 , 11980.53 , 5.33026 , 311.8781
0.25 , 0.035162 , 11944.49 , 5.52632 , 307.7410
0.26 , 0.039381 , 11906.31 , 5.72240 , 303.4678
0.27 , 0.043922 , 11865.99 , 5.91824 , 299.0602
0.28 , 0.048795 , 11823.53 , 6.11361 , 294.5203
0.29 , 0.054010 , 11778.93 , 6.30832 , 289.8505
0.30 , 0.059575 , 11732.19 , 6.50220 , 285.0532
0.31 , 0.065500 , 11683.32 , 6.69507 , 280.1312
0.32 , 0.071793 , 11632.30 , 6.88681 , 275.0874
0.33 , 0.078461 , 11579.15 , 7.07726 , 269.9247
0.34 , 0.085514 , 11523.86 , 7.26632 , 264.6466
0.35 , 0.092957 , 11466.43 , 7.45386 , 259.2562
0.36 , 0.100797 , 11406.86 , 7.63977 , 253.7573
0.37 , 0.109042 , 11345.15 , 7.82396 , 248.1534
0.38 , 0.117696 , 11281.31 , 8.00631 , 242.4483
0.39 , 0.126766 , 11215.32 , 8.18673 , 236.6459
0.40 , 0.136256 , 11147.20 , 8.36514 , 230.7503
0.41 , 0.146171 , 11076.94 , 8.54143 , 224.7657
0.42 , 0.156515 , 11004.54 , 8.71553 , 218.6962
0.43 , 0.167291 , 10930.00 , 8.88735 , 212.5462
0.44 , 0.178502 , 10853.32 , 9.05681 , 206.3203
0.45 , 0.190151 , 10774.50 , 9.22382 , 200.0228
0.46 , 0.202239 , 10693.55 , 9.38830 , 193.6586
0.47 , 0.214768 , 10610.45 , 9.55018 , 187.2322
0.48 , 0.227738 , 10525.22 , 9.70938 , 180.7485
0.49 , 0.241150 , 10437.85 , 9.86582 , 174.2123
0.50 , 0.255003 , 10348.34 , 10.01942 , 167.6287
0.51 , 0.269295 , 10256.69 , 10.17011 , 161.0025
0.52 , 0.284025 , 10162.90 , 10.31782 , 154.3390
0.53 , 0.299191 , 10066.98 , 10.46247 , 147.6431
0.54 , 0.314789 , 9968.91 , 10.60398 , 140.9202
0.55 , 0.328639 , 5589.30 , 10.67163 , 135.0875
0.56 , 0.337975 , 5554.80 , 10.58635 , 131.3145
0.57 , 0.347591 , 5520.30 , 10.50887 , 127.5935
0.58 , 0.357488 , 5485.80 , 10.43862 , 123.9216
0.59 , 0.367668 , 5451.29 , 10.37503 , 120.2961
0.60 , 0.378133 , 5416.79 , 10.31762 , 116.7143
0.61 , 0.388884 , 5382.29 , 10.26591 , 113.1740
0.62 , 0.399922 , 5347.79 , 10.21948 , 109.6732
0.63 , 0.411248 , 5313.28 , 10.17795 , 106.2097
0.64 , 0.422864 , 5278.78 , 10.14095 , 102.7819
0.65 , 0.434771 , 5244.28 , 10.10815 , 99.3882
0.66 , 0.446970 , 5209.78 , 10.07924 , 96.0269
0.67 , 0.459461 , 5175.27 , 10.05394 , 92.6968
0.68 , 0.472244 , 5140.77 , 10.03198 , 89.3966
0.69 , 0.485322 , 5106.27 , 10.01311 , 86.1251
0.70 , 0.498693 , 5071.77 , 9.99711 , 82.8813
0.71 , 0.512358 , 5037.26 , 9.98377 , 79.6643
0.72 , 0.526318 , 5002.76 , 9.97289 , 76.4730
0.73 , 0.540573 , 4968.26 , 9.96428 , 73.3068
0.74 , 0.555122 , 4933.76 , 9.95778 , 70.1648
0.75 , 0.569966 , 4899.25 , 9.95322 , 67.0465
0.76 , 0.585103 , 4864.75 , 9.95045 , 63.9512
0.77 , 0.600535 , 4830.25 , 9.94934 , 60.8784
0.78 , 0.616259 , 4795.74 , 9.94974 , 57.8275
0.79 , 0.632277 , 4761.24 , 9.95155 , 54.7982
0.80 , 0.648587 , 4726.74 , 9.95464 , 51.7900
0.81 , 0.665188 , 4692.24 , 9.95891 , 48.8026
0.82 , 0.682079 , 4657.73 , 9.96425 , 45.8356
0.83 , 0.699259 , 4623.23 , 9.97056 , 42.8888
0.84 , 0.716728 , 4588.73 , 9.97777 , 39.9620
0.85 , 0.734484 , 4554.23 , 9.98578 , 37.0548
0.86 , 0.752525 , 4519.72 , 9.99451 , 34.1672
0.87 , 0.770850 , 4485.22 , 10.00389 , 31.2989
0.88 , 0.789458 , 4450.72 , 10.01385 , 28.4498
0.89 , 0.808346 , 4416.22 , 10.02432 , 25.6199
0.90 , 0.826568 , 3967.07 , 10.02377 , 22.9477
0.91 , 0.844103 , 3904.95 , 10.01268 , 20.4355
0.92 , 0.861745 , 3842.82 , 10.00094 , 17.9658
0.93 , 0.879486 , 3780.69 , 9.98850 , 15.5386
0.94 , 0.897317 , 3718.56 , 9.97534 , 13.1540
0.95 , 0.915229 , 3656.44 , 9.96139 , 10.8121
0.96 , 0.933214 , 3594.31 , 9.94664 , 8.5130
0.97 , 0.951264 , 3532.18 , 9.93104 , 6.2567
0.98 , 0.969368 , 3470.05 , 9.91457 , 4.0433
0.99 , 0.987517 , 3407.93 , 9.89718 , 1.8729
1.00 , 1.003515 , 1000.00 , 9.85737 , 0.0001
 
Last edited:
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  • #3
Me = 5.974e24 kilograms
Re = 6371000 meters

The integration over density to find the enclosed mass, M(r), used layers of dr=6.371 centimeters thickness.
 

FAQ: Structure of Earth, pressure and density model

1. What is the structure of the Earth?

The Earth has a layered structure, consisting of the crust, mantle, outer core, and inner core. The crust is the outermost layer and is composed of solid rock. The mantle is the thickest layer and is mostly made of solid rock, but also contains some molten material. The outer core is liquid and primarily made of iron and nickel, while the inner core is solid and also made of iron and nickel.

2. How do the pressure and density change as you go deeper into the Earth?

As you go deeper into the Earth, the pressure and density increase. This is because the weight of the overlying layers of the Earth compresses the materials in the deeper layers, causing an increase in density. The increase in density also contributes to an increase in pressure, as the weight of the material above exerts more force on the deeper layers.

3. What factors affect the pressure and density within the Earth?

The pressure and density within the Earth are primarily affected by the depth and composition of the layers. As mentioned before, the weight of the overlying layers contributes to the pressure and density. Additionally, the composition of each layer plays a role, as different materials have different densities and can withstand different amounts of pressure.

4. How do scientists measure the pressure and density within the Earth?

Scientists use a variety of methods to measure the pressure and density within the Earth, including seismic waves, gravity measurements, and laboratory experiments. Seismic waves are produced by earthquakes and can reveal information about the density and composition of the layers they pass through. Gravity measurements can also give insight into the density of the Earth. Laboratory experiments, such as high-pressure experiments, can help scientists understand how materials behave under extreme pressure.

5. Why is understanding the Earth's structure, pressure, and density important?

Understanding the Earth's structure, pressure, and density is crucial for many reasons. It helps us understand the processes that have shaped our planet and continue to shape it. It also allows us to predict and prepare for natural disasters, such as earthquakes and volcanic eruptions. Additionally, studying the Earth's structure can provide insight into the formation and evolution of other planets and celestial bodies.

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