pi = 3.1415927 *2 = 6.2831853

mean radius of Earth = 6 378.1 kilometers R^2 40680160 kilometers^2

surface area of half the Earth = 2pi* R^2 = 2.556009e+08 kilometers^2

Earth Surface Area: 510,065,600 km2 http://en.wikipedia.org/wiki/Earth

The Surface Area of the Earth above any degree of latitude Snl is equal to. (1 -sin(Latitude) ) * 2pi* R^2

The Surface Area of the Earth between any two points of North or South latitude is their difference.

Sine and Cosine Tables

Area in square Kilometers of 10 degree bands of Latitude
90 degress of Latitude from the Pole to the Equator.
Latitude 1 -Sine(a) Surface Area above lat to pole. Surface Area 10 degrees Latitude ---
90 0 0 3883153.27 Pole
80 0.015192 3883153.27 11531472.17
70 0.060307 15414625.44 18829413.12
60 0.133975 34244038.57 25555231.88
50 0.233956 59799270.45 31504567.86
40 0.357212 91303838.32 36496653.48
30 0.5 127800491.80 40379806.75
20 0.65798 168180298.55 43036040.03
10 0.826352 211216338.59 44384645.01
0 1 255600983.60 Equator


Sine and Cosine and 1-sine(a) 0 to 90 degrees Table 1a.

Angle Degree a Sine(a) Cosine(a) 1-Sine(a) comment
0 0 1 1 As one looks at the values of 1 -sin(a), if latitude 0 degrees is the equator and 90 degrees is the pole, then
(1 -sin(a)) * 100 is the percentage of the hemisphere surface area from that latitude to the pole. For example above latitude 64 is only 10% of the Earths surface.

The hemisphere surface area is half the Earth's surface area.

1 0.017452 0.99985 0.982548
2 0.034899 0.99939 0.965101
3 0.052336 0.99863 0.947664
4 0.069756 0.99756 0.930244
5 0.087156 0.99619 0.912844
6 0.10453 0.99452 0.895472
7 0.12187 0.99255 0.878131
8 0.13917 0.99027 0.860827
9 0.15643 0.98769 0.843566
10 0.17365 0.98481 0.826352
11 0.19081 0.98163 0.809191
12 0.20791 0.97815 0.792088
13 0.22495 0.97437 0.775049
14 0.24192 0.97030 0.758078
15 0.25882 0.96593 0.741181
16 0.27564 0.96126 0.724363
17 0.29237 0.95630 0.707628
18 0.30902 0.95106 0.690983
19 0.32557 0.94552 0.674432
20 0.34202 0.93969 0.65798
21 0.35837 0.93358 0.641632
22 0.37461 0.92718 0.625393
23 0.39073 0.92050 0.609269
24 0.40674 0.91355 0.593263
25 0.42262 0.90631 0.577382
26 0.43837 0.89879 0.561629
27 0.45399 0.89101 0.54601
28 0.46947 0.88295 0.530528
29 0.48481 0.87462 0.51519
30 0.50000 0.86603 0.5
31 0.51504 0.85717 0.484962
32 0.52992 0.84805 0.470081
33 0.54464 0.83867 0.455361
34 0.55919 0.82904 0.440807
35 0.57358 0.81915 0.426424
36 0.58779 0.80902 0.412215
37 0.60182 0.79864 0.398185
38 0.61566 0.78801 0.384339
39 0.62932 0.77715 0.37068
40 0.64279 0.76604 0.357212
41 0.65606 0.75471 0.343941
42 0.66913 0.74314 0.330869
43 0.68200 0.73135 0.318002
44 0.69466 0.71934 0.305342
45 0.70711 0.70711 0.292893
46 0.71934 0.69466 0.28066
47 0.73135 0.68200 0.268646
48 0.74314 0.66913 0.256855
49 0.75471 0.65606 0.24529
50 0.76604 0.64279 0.233956
51 0.77715 0.62932 0.222854
52 0.78801 0.61566 0.211989
53 0.79864 0.60182 0.201364
54 0.80902 0.58779 0.190983
55 0.81915 0.57358 0.180848
56 0.82904 0.55919 0.170962
57 0.83867 0.54464 0.161329
58 0.84805 0.52992 0.151952
59 0.85717 0.51504 0.142833
60 0.86603 0.50000 0.133975
61 0.87462 0.48481 0.12538
62 0.88295 0.46947 0.117052
63 0.89101 0.45399 0.108993
64 0.89879 0.43837 0.101206
65 0.90631 0.42262 0.093692
66 0.91355 0.40674 0.086455
67 0.92050 0.39073 0.079495
68 0.92718 0.37461 0.072816
69 0.93358 0.35837 0.06642
70 0.93969 0.34202 0.060307
71 0.94552 0.32557 0.054481
72 0.95106 0.30902 0.048943
73 0.95630 0.29237 0.043695
74 0.96126 0.27564 0.038738
75 0.96593 0.25882 0.034074
76 0.97030 0.24192 0.029704
77 0.97437 0.22495 0.02563
78 0.97815 0.20791 0.021852
79 0.98163 0.19081 0.018373
80 0.98481 0.17365 0.015192
81 0.98769 0.15643 0.012312
82 0.99027 0.13917 0.009732
83 0.99255 0.12187 0.007454
84 0.99452 0.10453 0.005478
85 0.99619 0.087156 0.003805
86 0.99756 0.069756 0.002436
87 0.99863 0.052336 0.00137
88 0.99939 0.034899 0.000609
89 0.99985 0.017452 0.000152
90 1 0 0

1976 Standard Atmosphere 0 to 86Km in 1Km increments.

The following data tables were calculated at http://www.digitaldutch.com/atmoscalc/
Altitude [km] Temperature [Fahrenheit] Pressure [mb] Density [kg/m3]
0 59 1013.25 1.225
1 47.3 898.745705 1.111643
2 35.6 794.952155 1.00649
3 23.9 701.085447 0.909122
4 12.2 616.402353 0.819129
5 0.5 540.199121 0.736116
6 -11.2 471.810276 0.659697
7 -22.9 410.607432 0.589501
8 -34.6 355.998114 0.525168
9 -46.3 307.424584 0.466348
10 -58 264.362676 0.412707
11 -69.7 226.32064 0.363918
12 -69.7 193.30405 0.310828
13 -69.7 165.104058 0.265483
14 -69.7 141.017996 0.226753
15 -69.7 120.445709 0.193674
16 -69.7 102.874591 0.16542
17 -69.7 87.866821 0.141288
18 -69.7 75.048447 0.120676
19 -69.7 64.100069 0.103071
20 -69.7 54.748887 0.088035
21 -67.9 46.778862 0.074874
22 -66.1 39.997902 0.063727
23 -64.3 34.224343 0.05428
24 -62.5 29.304922 0.046267
25 -60.7 25.110234 0.039466
26 -58.9 21.530938 0.033688
27 -57.1 18.474574 0.028777
28 -55.3 15.862898 0.024599
29 -53.5 13.629648 0.021042
30 -51.7 11.718665 0.018012
31 -49.9 10.08232 0.015429
32 -48.1 8.680187 0.013225
33 -43.06 7.482282 0.011262
34 -38.02 6.461222 0.009609
35 -32.98 5.589235 0.008214
36 -27.94 4.843167 0.007034
37 -22.9 4.203671 0.006035
38 -17.86 3.654547 0.005187
39 -12.82 3.182205 0.004466
40 -7.78 2.775216 0.003851
41 -2.74 2.423955 0.003326
42 2.3 2.120299 0.002878
43 7.34 1.857378 0.002494
44 12.38 1.629374 0.002164
45 17.42 1.431348 0.001881
46 22.46 1.259103 0.001638
47 27.5 1.109063 0.001428
48 27.5 0.977545 0.001258
49 27.5 0.861623 0.001109
50 27.5 0.759448 0.000978
51 27.5 0.669389 0.000862
52 22.46 0.589622 0.000767
53 17.42 0.518668 0.000682
54 12.38 0.455632 0.000605
55 7.34 0.3997 0.000537
56 2.3 0.350137 0.000475
57 -2.74 0.306274 0.00042
58 -7.78 0.267509 0.000371
59 -12.82 0.233296 0.000327
60 -17.86 0.203143 0.000288
61 -22.9 0.176606 0.000254
62 -27.94 0.153287 0.000223
63 -32.98 0.132826 0.000195
64 -38.02 0.1149 0.000171
65 -43.06 0.09922 0.000149
66 -48.1 0.085527 0.00013
67 -53.14 0.07359 0.000114
68 -58.18 0.063199 0.000099
69 -63.22 0.054172 0.000086
70 -68.26 0.046342 0.000074
71 -73.3 0.039564 0.000064
72 -76.9 0.033718 0.000055
73 -80.5 0.028692 0.000047
74 -84.1 0.024377 0.000041
75 -87.7 0.020679 0.000035
76 -91.3 0.017514 0.00003
77 -94.9 0.014809 0.000025
78 -98.5 0.012501 0.000022
79 -102.1 0.010535 0.000018
80 -105.7 0.008863 0.000016
81 -109.3 0.007443 0.000013
82 -112.9 0.006239 0.000011
83 -116.5 0.00522 0.00001
84 -120.1 0.00436 0.000008
85 -123.1672 0.003634 0.000007
86 -123.1672 0.003027 0.000006

1976 Standard Atmosphere 0 to 12Km in 100 meter increments.

Altitude [m] Temperature [Fahrenheit] Pressure [mb] Density [kg/m3]
0 59 1013.25 1.225
100 57.83 1001.294386 1.213283
200 56.66 989.453256 1.201651
300 55.49 977.725771 1.190106
400 54.32 966.111094 1.178645
500 53.15 954.608393 1.167269
600 51.98 943.216841 1.155977
700 50.81 931.935613 1.144769
800 49.64 920.76389 1.133644
900 48.47 909.700858 1.122602
1000 47.3 898.745705 1.111643
1100 46.13 887.897625 1.100765
1200 44.96 877.155816 1.089969
1300 43.79 866.519479 1.079255
1400 42.62 855.987819 1.068621
1500 41.45 845.560048 1.058067
1600 40.28 835.23538 1.047594
1700 39.11 825.013031 1.0372
1800 37.94 814.892226 1.026885
1900 36.77 804.872191 1.016648
2000 35.6 794.952155 1.00649
2100 34.43 785.131354 0.99641
2200 33.26 775.409027 0.986407
2300 32.09 765.784417 0.976481
2400 30.92 756.25677 0.966632
2500 29.75 746.825337 0.956859
2600 28.58 737.489373 0.947162
2700 27.41 728.248137 0.93754
2800 26.24 719.100892 0.927993
2900 25.07 710.046905 0.91852
3000 23.9 701.085447 0.909122
3100 22.73 692.215792 0.899798
3200 21.56 683.43722 0.890546
3300 20.39 674.749012 0.881368
3400 19.22 666.150457 0.872262
3500 18.05 657.640844 0.863229
3600 16.88 649.219467 0.854267
3700 15.71 640.885626 0.845377
3800 14.54 632.638621 0.836557
3900 13.37 624.477761 0.827808
4000 12.2 616.402353 0.819129
4100 11.03 608.411712 0.81052
4200 9.86 600.505157 0.801981
4300 8.69 592.682007 0.79351
4400 7.52 584.941588 0.785108
4500 6.35 577.28323 0.776775
4600 5.18 569.706264 0.768509
4700 4.01 562.210029 0.76031
4800 2.84 554.793863 0.752179
4900 1.67 547.457111 0.744114
5000 0.5 540.199121 0.736116
5100 -0.67 533.019244 0.728183
5200 -1.84 525.916836 0.720317
5300 -3.01 518.891255 0.712515
5400 -4.18 511.941864 0.704778
5500 -5.35 505.06803 0.697106
5600 -6.52 498.269121 0.689497
5700 -7.69 491.544512 0.681953
5800 -8.86 484.893581 0.674471
5900 -10.03 478.315707 0.667053
6000 -11.2 471.810276 0.659697
6100 -12.37 465.376675 0.652404
6200 -13.54 459.014296 0.645172
6300 -14.71 452.722534 0.638002
6400 -15.88 446.500788 0.630892
6500 -17.05 440.348461 0.623844
6600 -18.22 434.264958 0.616856
6700 -19.39 428.249689 0.609928
6800 -20.56 422.302067 0.60306
6900 -21.73 416.421508 0.596251
7000 -22.9 410.607432 0.589501
7100 -24.07 404.859263 0.58281
7200 -25.24 399.176427 0.576177
7300 -26.41 393.558355 0.569602
7400 -27.58 388.004481 0.563084
7500 -28.75 382.514241 0.556624
7600 -29.92 377.087078 0.55022
7700 -31.09 371.722434 0.543873
7800 -32.26 366.419758 0.537582
7900 -33.43 361.1785 0.531347
8000 -34.6 355.998114 0.525168
8100 -35.77 350.878059 0.519043
8200 -36.94 345.817795 0.512973
8300 -38.11 340.816786 0.506958
8400 -39.28 335.874501 0.500997
8500 -40.45 330.990409 0.49509
8600 -41.62 326.163987 0.489236
8700 -42.79 321.39471 0.483435
8800 -43.96 316.682061 0.477687
8900 -45.13 312.025523 0.471992
9000 -46.3 307.424584 0.466348
9100 -47.47 302.878735 0.460756
9200 -48.64 298.387468 0.455216
9300 -49.81 293.950283 0.449727
9400 -50.98 289.566678 0.444289
9500 -52.15 285.236158 0.438901
9600 -53.32 280.958229 0.433563
9700 -54.49 276.732402 0.428275
9800 -55.66 272.558189 0.423036
9900 -56.83 268.435107 0.417847
10000 -58 264.362676 0.412707
10100 -59.17 260.340417 0.407615
10200 -60.34 256.367857 0.402571
10300 -61.51 252.444525 0.397575
10400 -62.68 248.569952 0.392627
10500 -63.85 244.743673 0.387725
10600 -65.02 240.965227 0.382871
10700 -66.19 237.234155 0.378064
10800 -67.36 233.550001 0.373303
10900 -68.53 229.912313 0.368588
11000 -69.7 226.32064 0.363918
11100 -69.7 222.779816 0.358224
11200 -69.7 219.294389 0.35262
11300 -69.7 215.863493 0.347103
11400 -69.7 212.486273 0.341673
11500 -69.7 209.16189 0.336327
11600 -69.7 205.889518 0.331065
11700 -69.7 202.668343 0.325886
11800 -69.7 199.497563 0.320787
11900 -69.7 196.376391 0.315768
12000 -69.7 193.30405 0.310828

Sine and Cosine 0 to 90 degrees Table1.

Angle Degrees Sine Cosine Angle Degrees Sine Cosine
0 0 1
1 0.017452 0.99985 46 0.71934 0.69466
2 0.034899 0.99939 47 0.73135 0.68200
3 0.052336 0.99863 48 0.74314 0.66913
4 0.069756 0.99756 49 0.75471 0.65606
5 0.087156 0.99619 50 0.76604 0.64279
6 0.10453 0.99452 51 0.77715 0.62932
7 0.12187 0.99255 52 0.78801 0.61566
8 0.13917 0.99027 53 0.79864 0.60182
9 0.15643 0.98769 54 0.80902 0.58779
10 0.17365 0.98481 55 0.81915 0.57358
11 0.19081 0.98163 56 0.82904 0.55919
12 0.20791 0.97815 57 0.83867 0.54464
13 0.22495 0.97437 58 0.84805 0.52992
14 0.24192 0.97030 59 0.85717 0.51504
15 0.25882 0.96593 60 0.86603 0.50000
16 0.27564 0.96126 61 0.87462 0.48481
17 0.29237 0.95630 62 0.88295 0.46947
18 0.30902 0.95106 63 0.89101 0.45399
19 0.32557 0.94552 64 0.89879 0.43837
20 0.34202 0.93969 65 0.90631 0.42262
21 0.35837 0.93358 66 0.91355 0.40674
22 0.37461 0.92718 67 0.92050 0.39073
23 0.39073 0.92050 68 0.92718 0.37461
24 0.40674 0.91355 69 0.93358 0.35837
25 0.42262 0.90631 70 0.93969 0.34202
26 0.43837 0.89879 71 0.94552 0.32557
27 0.45399 0.89101 72 0.95106 0.30902
28 0.46947 0.88295 73 0.95630 0.29237
29 0.48481 0.87462 74 0.96126 0.27564
30 0.50000 0.86603 75 0.96593 0.25882
31 0.51504 0.85717 76 0.97030 0.24192
32 0.52992 0.84805 77 0.97437 0.22495
33 0.54464 0.83867 78 0.97815 0.20791
34 0.55919 0.82904 79 0.98163 0.19081
35 0.57358 0.81915 80 0.98481 0.17365
36 0.58779 0.80902 81 0.98769 0.15643
37 0.60182 0.79864 82 0.99027 0.13917
38 0.61566 0.78801 83 0.99255 0.12187
39 0.62932 0.77715 84 0.99452 0.10453
40 0.64279 0.76604 85 0.99619 0.087156
41 0.65606 0.75471 86 0.99756 0.069756
42 0.66913 0.74314 87 0.99863 0.052336
43 0.68200 0.73135 88 0.99939 0.034899
44 0.69466 0.71934 89 0.99985 0.017452
45 0.70711 0.70711 90 1 0

Sine and Cosine 0 to 90 degrees Table2.

Angle Degrees Sine Cosine Angle Degrees Sine Cosine Angle Degrees Sine Cosine
0 0 1 30 0.50000 0.86603 60 0.86603
1 0.017452 0.99985 31 0.51504 0.85717 61 0.87462 0.48481
2 0.034899 0.99939 32 0.52992 0.84805 62 0.88295 0.46947
3 0.052336 0.99863 33 0.54464 0.83867 63 0.89101 0.45399
4 0.069756 0.99756 34 0.55919 0.82904 64 0.89879 0.43837
5 0.087156 0.99619 35 0.57358 0.81915 65 0.90631 0.42262
6 0.10453 0.99452 36 0.58779 0.80902 66 0.91355 0.40674
7 0.12187 0.99255 37 0.60182 0.79864 67 0.92050 0.39073
8 0.13917 0.99027 38 0.61566 0.78801 68 0.92718 0.37461
9 0.15643 0.98769 39 0.62932 0.77715 69 0.93358 0.35837
10 0.17365 0.98481 40 0.64279 0.76604 70 0.93969 0.34202
11 0.19081 0.98163 41 0.65606 0.75471 71 0.94552 0.32557
12 0.20791 0.97815 42 0.66913 0.74314 72 0.95106 0.30902
13 0.22495 0.97437 43 0.68200 0.73135 73 0.95630 0.29237
14 0.24192 0.97030 44 0.69466 0.71934 74 0.96126 0.27564
15 0.25882 0.96593 45 0.70711 0.70711 75 0.96593 0.25882
16 0.27564 0.96126 46 0.71934 0.69466 76 0.97030 0.24192
17 0.29237 0.95630 47 0.73135 0.68200 77 0.97437 0.22495
18 0.30902 0.95106 48 0.74314 0.66913 78 0.97815 0.20791
19 0.32557 0.94552 49 0.75471 0.65606 79 0.98163 0.19081
20 0.34202 0.93969 50 0.76604 0.64279 80 0.98481 0.17365
21 0.35837 0.93358 51 0.77715 0.62932 81 0.98769 0.15643
22 0.37461 0.92718 52 0.78801 0.61566 82 0.99027 0.13917
23 0.39073 0.92050 53 0.79864 0.60182 83 0.99255 0.12187
24 0.40674 0.91355 54 0.80902 0.58779 84 0.99452 0.10453
25 0.42262 0.90631 55 0.81915 0.57358 85 0.99619 0.087156
26 0.43837 0.89879 56 0.82904 0.55919 86 0.99756 0.069756
27 0.45399 0.89101 57 0.83867 0.54464 87 0.99863 0.052336
28 0.46947 0.88295 58 0.84805 0.52992 88 0.99939 0.034899
29 0.48481 0.87462 59 0.85717 0.51504 89 0.99985 0.017452
0.50000 90 1 0