Dimitrijevich, V.; Harmograv A Spherical Harmonic Function to Represent the Earth's Gravitational Potential; Defense Mapping Agency, Aerospace Center, Technical Report TR74007, St. Louis/Missouri, 1975 The coefficients are reproduced from the original publication by scanning and ocr. The coefficients C20 and C40 are not explicitely given in the report but their corrections dC20 and dC40 w.r.t the GRS67 values. (April, 2008, F. Barthelmes, GFZ) C20 = C20(grs67) + dC20(Harmograv) = -4.841981598630907E-04 + 7.1920E-09 = -4.841909678-04 C40 = C40(grs67) + dC40(Harmograv) = 7.904214682686718E-07 + 1.6526E-09 = 7.920740682-07 product_type gravity_field modelname HARMOGRAV radius 0.6378160E+07 earth_gravity_constant 0.398603E+15 max_degree 36 errors no key L M C S end_of_head ======================== gfc 0 0 1.0000e+00 gfc 2 0 -4.841909678e-04 gfc 2 1 3.8714e-10 -1.6143e-08 gfc 2 2 4.1636e-06 -1.4744e-06 gfc 3 0 2.8415e-07 gfc 3 1 1.5287e-06 -3.7002e-07 gfc 3 2 9.2610e-07 -3.9012e-07 gfc 3 3 9.0414e-07 1.7579e-06 gfc 4 0 7.920740682e-07 gfc 4 1 -1.5023e-07 -2.6514e-07 gfc 4 2 3.6068e-07 4.4729e-07 gfc 4 3 9.9917e-07 -1.9502e-07 gfc 4 4 -1.4010e-07 2.8979e-07 gfc 5 0 2.0596e-08 gfc 5 1 -3.4556e-07 -2.3069e-07 gfc 5 2 6.3123e-07 -2.1000e-07 gfc 5 3 -3.9246e-07 -2.8620e-08 gfc 5 4 -1.4847e-07 1.5858e-07 gfc 5 5 2.0088e-07 -5.3066e-07 gfc 6 0 -7.1803e-08 gfc 6 1 1.9946e-07 -4.6910e-09 gfc 6 2 3.4999e-07 -1.2167e-07 gfc 6 3 -1.2607e-07 -8.1337e-08 gfc 6 4 -1.3582e-07 -4.5262e-07 gfc 6 5 -4.3390e-07 -6.3805e-07 gfc 6 6 7.9459e-08 -2.1712e-07 gfc 7 0 1.8260e-07 gfc 7 1 2.6126e-07 1.1136e-07 gfc 7 2 3.0426e-07 2.5159e-07 gfc 7 3 1.3427e-07 -2.3552e-07 gfc 7 4 -2.7472e-07 -1.6816e-07 gfc 7 5 4.9288e-08 8.5824e-08 gfc 7 6 -3.7947e-07 1.5606e-07 gfc 7 7 6.3297e-08 -6.5358e-08 gfc 8 0 3.4016e-08 gfc 8 1 -1.3414e-07 1.3866e-07 gfc 8 2 2.3061e-08 1.1521e-07 gfc 8 3 2.4980e-08 1.0133e-08 gfc 8 4 -5.3437e-08 1.5605e-08 gfc 8 5 -9.2533e-08 1.4492e-07 gfc 8 6 4.9123e-09 1.2694e-07 gfc 8 7 -1.7269e-08 1.2205e-07 gfc 8 8 -2.4501e-07 1.2567e-07 gfc 9 0 1.1429e-07 gfc 9 1 5.1022e-08 -1.0490e-08 gfc 9 2 4.3309e-08 -6.4226e-09 gfc 9 3 -1.9064e-07 -6.6314e-08 gfc 9 4 -2.0907e-08 -8.2533e-08 gfc 9 5 -1.3660e-07 1.8452e-08 gfc 9 6 5.2235e-08 1.4852e-07 gfc 9 7 -5.1761e-08 4.3997e-08 gfc 9 8 2.4294e-07 5.0860e-08 gfc 9 9 2.1597e-08 6.1243e-08 gfc 10 0 2.6942e-08 gfc 10 1 4.7869e-08 -3.7387e-08 gfc 10 2 -1.1029e-07 -1.0227e-07 gfc 10 3 -9.0147e-08 -1.9897e-07 gfc 10 4 -5.6412e-08 -7.4054e-08 gfc 10 5 4.2268e-08 -8.7467e-09 gfc 10 6 -6.1336e-08 -1.1662e-07 gfc 10 7 1.2574e-07 -3.3921e-09 gfc 10 8 -7.5927e-09 -1.2414e-07 gfc 10 9 7.4967e-08 -7.9619e-08 gfc 10 10 8.5392e-08 -1.3874e-08 gfc 11 0 -5.5152e-08 gfc 11 1 -7.5166e-09 9.0523e-09 gfc 11 2 -7.2434e-08 -1.5291e-07 gfc 11 3 9.5592e-08 -1.3298e-07 gfc 11 4 -7.8768e-08 -1.3506e-07 gfc 11 5 1.0825e-08 -1.9851e-09 gfc 11 6 -7.7134e-08 -1.8640e-08 gfc 11 7 1.0356e-07 -9.3204e-08 gfc 11 8 3.0171e-09 6.8575e-08 gfc 11 9 -3.3828e-08 4.8479e-08 gfc 11 10 -1.4914e-08 -4.4214e-08 gfc 11 11 1.4070e-07 8.1357e-09 gfc 12 0 -4.4590e-08 gfc 12 1 -1.0897e-07 -5.7388e-08 gfc 12 2 2.1290e-08 1.2000e-08 gfc 12 3 6.8139e-08 2.6953e-08 gfc 12 4 -7.5692e-08 7.2521e-09 gfc 12 5 9.1987e-08 -3.8863e-10 gfc 12 6 3.4284e-08 -5.6109e-09 gfc 12 7 -8.6973e-08 4.6603e-08 gfc 12 8 -8.2156e-09 4.9523e-08 gfc 12 9 1.0670e-08 -2.6522e-08 gfc 12 10 3.0414e-08 -3.7557e-08 gfc 12 11 -2.7730e-08 -1.6193e-08 gfc 12 12 3.0637e-08 9.7006e-09 gfc 13 0 -4.5883e-10 gfc 13 1 8.5961e-09 1.2455e-08 gfc 13 2 3.0577e-08 -5.5277e-08 gfc 13 3 9.2792e-09 3.4575e-08 gfc 13 4 1.9891e-08 1.6174e-08 gfc 13 5 6.4885e-08 2.3887e-08 gfc 13 6 -8.5563e-08 2.5221e-08 gfc 13 7 -2.5202e-08 1.1764e-08 gfc 13 8 -3.3410e-08 -2.7398e-08 gfc 13 9 1.9269e-08 8.8352e-09 gfc 13 10 1.1538e-08 1.1958e-08 gfc 13 11 -3.1525e-08 3.9713e-08 gfc 13 12 4.9529e-09 9.4494e-08 gfc 13 13 -1.2771e-08 7.3414e-08 gfc 14 0 -2.1068e-09 gfc 14 1 -4.2580e-08 5.0677e-09 gfc 14 2 -6.8550e-08 4.1682e-09 gfc 14 3 2.1343e-08 1.8188e-08 gfc 14 4 4.6323e-08 -9.9765e-09 gfc 14 5 3.7946e-08 -3.8937e-08 gfc 14 6 8.2526e-09 5.0343e-08 gfc 14 7 2.4649e-08 -3.1304e-08 gfc 14 8 -1.9824e-08 -2.4645e-08 gfc 14 9 1.5850e-08 7.3420e-08 gfc 14 10 9.9278e-08 -3.4855e-08 gfc 14 11 1.8193e-08 -3.9388e-08 gfc 14 12 2.5729e-08 -7.7754e-08 gfc 14 13 7.7814e-09 4.7394e-08 gfc 14 14 -5.9701e-08 3.5530e-08 gfc 15 0 -4.5103e-08 gfc 15 1 2.4732e-08 3.0998e-08 gfc 15 2 -1.1782e-08 -4.9191e-08 gfc 15 3 3.3258e-08 5.0235e-08 gfc 15 4 -2.1177e-08 9.9942e-09 gfc 15 5 -7.8042e-09 1.5587e-08 gfc 15 6 2.5526e-08 -8.7010e-08 gfc 15 7 3.1437e-08 3.3045e-08 gfc 15 8 -4.7953e-08 4.3200e-08 gfc 15 9 -5.9582e-08 3.1683e-08 gfc 15 10 7.0998e-10 -3.6743e-08 gfc 15 11 9.2789e-09 -1.0833e-08 gfc 15 12 -2.0387e-08 1.1796e-08 gfc 15 13 -3.1750e-08 1.9672e-08 gfc 15 14 2.1013e-09 -2.0339e-08 gfc 15 15 -2.7551e-08 3.7285e-08 gfc 16 0 1.5517e-08 gfc 16 1 -3.7467e-09 2.9770e-09 gfc 16 2 -5.0537e-08 2.3940e-08 gfc 16 3 7.7898e-09 3.7891e-08 gfc 16 4 4.0122e-08 5.2490e-08 gfc 16 5 -2.2212e-09 3.6898e-08 gfc 16 6 -2.1438e-09 1.5548e-09 gfc 16 7 -1.7891e-08 -3.7178e-10 gfc 16 8 -1.8468e-08 -2.1812e-08 gfc 16 9 -7.6852e-09 -1.5968e-08 gfc 16 10 -9.3597e-09 -4.3785e-08 gfc 16 11 -1.4145e-08 2.0365e-08 gfc 16 12 1.6132e-08 -2.1089e-08 gfc 16 13 4.1841e-08 -1.4123e-08 gfc 16 14 -1.4074e-08 -4.8666e-08 gfc 16 15 -2.4810e-08 -4.4174e-08 gfc 16 16 -8.8636e-09 3.2076e-09 gfc 17 0 -1.1146e-08 gfc 17 1 -3.6277e-08 -2.2977e-08 gfc 17 2 -7.0630e-08 -8.8487e-08 gfc 17 3 -3.0925e-08 -1.7463e-08 gfc 17 4 -3.8571e-08 4.1554e-08 gfc 17 5 -1.9796e-08 1.8879e-08 gfc 17 6 -1.9995e-08 -3.3210e-08 gfc 17 7 1.5727e-08 -3.0862e-08 gfc 17 8 3.3068e-08 7.0116e-09 gfc 17 9 2.1772e-09 -2.5621e-08 gfc 17 10 -1.4676e-08 2.9771e-08 gfc 17 11 2.6064e-08 6.3507e-09 gfc 17 12 -1.3485e-09 5.1759e-09 gfc 17 13 2.4318e-08 2.8780e-08 gfc 17 14 -6.3836e-09 4.4531e-08 gfc 17 15 2.1080e-08 3.7928e-08 gfc 17 16 -2.1023e-08 -1.3963e-08 gfc 17 17 -3.5797e-08 -1.8771e-08 gfc 18 0 2.9864e-08 gfc 18 1 -8.8654e-09 -5.9994e-08 gfc 18 2 -9.0484e-09 -2.6031e-08 gfc 18 3 -2.9580e-08 -2.3713e-08 gfc 18 4 2.8303e-08 -1.3323e-08 gfc 18 5 -1.1868e-08 2.3511e-08 gfc 18 6 -1.5466e-08 -6.8291e-08 gfc 18 7 -1.9762e-08 1.3016e-08 gfc 18 8 4.2446e-08 -3.3737e-08 gfc 18 9 1.1654e-08 4.2173e-08 gfc 18 10 2.6615e-08 -3.6699e-08 gfc 18 11 1.4887e-08 2.1456e-08 gfc 18 12 -1.4743e-08 -1.4890e-08 gfc 18 13 -1.5862e-08 -2.0117e-08 gfc 18 14 1.6259e-08 -3.0639e-08 gfc 18 15 -6.2292e-08 -2.4294e-08 gfc 18 16 2.2427e-08 -1.0817e-08 gfc 18 17 1.7065e-09 -2.1401e-08 gfc 18 18 3.0055e-09 -1.0035e-08 gfc 19 0 1.3429e-09 gfc 19 1 -2.0096e-08 1.7013e-08 gfc 19 2 2.9497e-08 1.5705e-08 gfc 19 3 -2.8344e-08 8.5305e-09 gfc 19 4 -4.3207e-09 -1.4070e-08 gfc 19 5 -4.1578e-08 2.8434e-08 gfc 19 6 -1.0485e-08 9.3369e-09 gfc 19 7 -1.8059e-09 -3.2187e-08 gfc 19 8 3.7160e-09 -1.0161e-08 gfc 19 9 9.9400e-09 -7.6231e-09 gfc 19 10 -2.2156e-09 -5.1994e-09 gfc 19 11 6.6759e-09 2.3676e-08 gfc 19 12 1.1355e-08 1.8224e-08 gfc 19 13 1.5365e-09 -2.6816e-08 gfc 19 14 -4.9908e-09 -1.7178e-08 gfc 19 15 -6.1032e-09 -1.5788e-08 gfc 19 16 -9.5493e-09 1.8083e-08 gfc 19 17 9.4525e-09 -2.8147e-08 gfc 19 18 6.0033e-08 -1.2114e-08 gfc 19 19 -5.4124e-09 2.9867e-08 gfc 20 0 -1.0316e-08 gfc 20 1 -1.7418e-08 -2.0955e-08 gfc 20 2 9.4963e-09 -8.0889e-09 gfc 20 3 -5.7805e-09 -1.6359e-08 gfc 20 4 -1.5665e-08 -2.0888e-08 gfc 20 5 -1.2548e-08 1.7643e-08 gfc 20 6 -1.0068e-08 6.4008e-09 gfc 20 7 -2.9473e-08 -1.2293e-08 gfc 20 8 6.1451e-09 2.3091e-08 gfc 20 9 3.1911e-08 6.6984e-09 gfc 20 10 -2.8362e-08 9.6299e-09 gfc 20 11 3.3081e-08 -1.0844e-08 gfc 20 12 -2.8854e-08 -4.7186e-09 gfc 20 13 6.0616e-09 1.1598e-08 gfc 20 14 6.8355e-09 -3.3044e-09 gfc 20 15 -2.9058e-08 6.1067e-09 gfc 20 16 -2.1390e-08 -1.6274e-08 gfc 20 17 2.7052e-08 -3.0852e-08 gfc 20 18 -7.6519e-09 1.2186e-09 gfc 20 19 2.2730e-08 1.6787e-08 gfc 20 20 3.8663e-08 -1.2543e-08 gfc 21 0 2.9242e-08 gfc 21 1 5.2445e-09 2.2325e-08 gfc 21 2 1.1801e-08 1.1687e-08 gfc 21 3 -1.1478e-08 3.3065e-08 gfc 21 4 -1.0583e-08 -1.1850e-08 gfc 21 5 1.8662e-08 -3.0827e-08 gfc 21 6 -5.2659e-09 -2.2001e-08 gfc 21 7 8.7323e-09 2.4199e-08 gfc 21 8 -1.3928e-09 1.6743e-08 gfc 21 9 -5.2922e-09 4.8252e-08 gfc 21 10 2.8442e-09 -9.8021e-09 gfc 21 11 7.8057e-09 -1.4645e-08 gfc 21 12 1.0835e-08 8.5969e-09 gfc 21 13 -1.4503e-08 4.4932e-08 gfc 21 14 2.1044e-08 -1.3555e-09 gfc 21 15 5.8021e-09 7.9981e-09 gfc 21 16 -8.3771e-09 -2.6134e-09 gfc 21 17 -3.5038e-08 2.2762e-08 gfc 21 18 3.2934e-08 1.8206e-09 gfc 21 19 -2.7453e-08 1.7474e-08 gfc 21 20 -2.7283e-08 9.1455e-09 gfc 21 21 -8.7230e-11 -6.2872e-09 gfc 22 0 -1.5974e-09 gfc 22 1 1.1848e-08 1.2336e-08 gfc 22 2 -2.4683e-08 -3.5287e-08 gfc 22 3 -3.2967e-09 2.8121e-08 gfc 22 4 -5.5473e-09 -1.3751e-08 gfc 22 5 7.4990e-09 -6.1978e-09 gfc 22 6 8.3672e-09 -1.4775e-08 gfc 22 7 2.5807e-08 -8.6492e-09 gfc 22 8 -4.4149e-08 -1.7498e-08 gfc 22 9 -6.0025e-09 1.6457e-08 gfc 22 10 1.9279e-08 1.4854e-08 gfc 22 11 5.2243e-09 1.6772e-09 gfc 22 12 -9.7359e-09 1.6071e-09 gfc 22 13 -2.1144e-08 1.1081e-08 gfc 22 14 5.0141e-09 4.9940e-09 gfc 22 15 1.5570e-08 -1.6196e-09 gfc 22 16 -2.4987e-08 -9.7202e-09 gfc 22 17 6.0414e-09 -2.5014e-08 gfc 22 18 -1.6601e-08 -2.7089e-08 gfc 22 19 1.2538e-08 -5.6105e-09 gfc 22 20 -2.9346e-08 1.1652e-08 gfc 22 21 -2.1960e-08 1.8172e-08 gfc 22 22 1.0311e-08 -1.3009e-08 gfc 23 0 -2.6431e-08 gfc 23 1 1.2477e-08 1.0743e-08 gfc 23 2 -1.5902e-08 -2.0174e-08 gfc 23 3 1.2396e-08 -4.5869e-10 gfc 23 4 -1.4778e-08 2.6743e-09 gfc 23 5 1.7239e-08 1.2174e-08 gfc 23 6 4.9269e-09 2.8973e-08 gfc 23 7 -1.2111e-08 -3.7799e-09 gfc 23 8 -1.8470e-08 -9.1053e-10 gfc 23 9 -8.5522e-09 -1.9795e-08 gfc 23 10 1.0512e-08 1.9866e-08 gfc 23 11 8.6822e-09 8.7605e-09 gfc 23 12 -3.9704e-09 -2.7002e-08 gfc 23 13 1.1326e-09 1.9625e-08 gfc 23 14 7.4903e-09 4.4099e-09 gfc 23 15 3.6550e-08 -4.9531e-09 gfc 23 16 1.9223e-08 1.7404e-08 gfc 23 17 2.0812e-09 -1.6898e-08 gfc 23 18 2.0495e-08 -2.0298e-08 gfc 23 19 1.1146e-08 9.9380e-09 gfc 23 20 -2.1546e-09 7.7723e-09 gfc 23 21 -5.2480e-09 1.8524e-08 gfc 23 22 -2.7238e-08 3.9817e-09 gfc 23 23 -7.3747e-09 3.2453e-09 gfc 24 0 -3.6683e-09 gfc 24 1 1.8342e-08 -2.7231e-08 gfc 24 2 -2.8784e-09 1.1513e-08 gfc 24 3 -2.7279e-09 -1.8000e-08 gfc 24 4 -2.2584e-08 4.2575e-08 gfc 24 5 -1.2203e-08 -1.3556e-08 gfc 24 6 -1.7521e-08 2.0031e-08 gfc 24 7 -4.3481e-09 -1.8424e-08 gfc 24 8 1.6015e-08 1.5331e-08 gfc 24 9 -2.7803e-08 -1.6291e-08 gfc 24 10 9.9306e-09 1.4979e-08 gfc 24 11 1.2295e-09 2.3273e-08 gfc 24 12 1.2214e-08 -1.0603e-08 gfc 24 13 -3.1888e-09 7.8907e-09 gfc 24 14 -3.6729e-08 -2.0895e-08 gfc 24 15 1.0632e-08 -4.0309e-09 gfc 24 16 8.2189e-09 -1.8299e-08 gfc 24 17 -2.4956e-08 -2.5183e-08 gfc 24 18 -5.1519e-09 -1.5672e-08 gfc 24 19 -2.0205e-08 -1.4866e-08 gfc 24 20 1.1200e-08 3.4819e-09 gfc 24 21 8.8613e-09 2.2553e-08 gfc 24 22 -9.4845e-09 -6.6897e-09 gfc 24 23 6.7092e-09 -1.7004e-08 gfc 24 24 1.0639e-08 1.1727e-08 gfc 25 0 3.2418e-09 gfc 25 1 -3.9652e-09 -1.2629e-08 gfc 25 2 1.7510e-08 1.6545e-08 gfc 25 3 -3.3126e-09 -8.6364e-09 gfc 25 4 8.9902e-09 -7.2478e-09 gfc 25 5 1.0812e-08 -1.4120e-08 gfc 25 6 1.8316e-08 5.8409e-09 gfc 25 7 5.5041e-09 -2.6680e-09 gfc 25 8 8.3533e-09 -1.1465e-08 gfc 25 9 -2.5607e-08 -1.1078e-08 gfc 25 10 1.6260e-08 7.3617e-09 gfc 25 11 1.5777e-08 1.5648e-08 gfc 25 12 -6.2836e-09 7.1854e-11 gfc 25 13 9.7422e-10 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