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