惑星名 | 軌道長半径a[m] | 平均軌道速度V[m/s] | 離心率e | (1-e^2) | 3.0/(1-e^2) | (v/c)^2 | 2πdφ | rs=a(1-e^2)2πdφ/3π) | rs=2a(V/c)^2 |
---|---|---|---|---|---|---|---|---|---|
水星 | 57909656770 | 47872.5 | 0.2056 | 0.95772864 | 3.1324112851 | 2.5499449799789e-8 | 5.018679455692e-7 | 2953.328771 | 2953.328771 |
金星 | 108208930000 | 35021.4 | 0.0068 | 0.99995376 | 3.0001387264147 | 1.36466357799887e-8 | 2.57244919280835553e-7 | 2953.3757117 | 2953.37571 |
地球 | 149597870700 | 29780 | 0.0167 | 0.99972111 | 3.0008369 | 9.86751921971e-9 | 1.86050242679988148e-7 | 2952.31972537 | 2952.31972872 |
火星 | 227936640000 | 24130.9 | 0.0934 | 0.99127644 | 3.02640099 | 6.4789650016638728e-9 | 1.232003588093984e-7 | 2953.5870257 | 2953.5870263 |
木星 | 778412010000 | 13069.7 | 0.0485 | 0.99764775 | 3.007073388 | 1.900596092587527e-9 | 3.5909861298224e-8 | 2958.893648887 | 2958.893649 |
土星 | 1426725400000 | 9672.4 | 0.0555 | 0.99691975 | 3.0092693 | 1.040943340003783e-9 | 1.9681944998115e-8 | 2970.28060454459 | 2970.2806 |
天王星 | 2870990000000 | 6800 | 0.0463 | 0.99785631 | 3.0064448858 | 5.14489385919193163e-10 | 9.7187303959641e-9 | 2954.1877641236 | 2954.18776416 |
海王星 | 4495060000000 | 5500 | 0.009 | 0.999919 | 3.00024301968 | 3.36576641956219576e-10 | 6.3448341659952e-9 | 3025.8644 | 3025.8644 |
以下の式を用いて、各種の物理量を算出しています。
Planet name | Orbital semi-major axis a [AU] | Orbital semi-major axis a [m] | Eccentricity e | Orbital period T [Earth years] | Orbital period T [sec] | Average orbital speed Vavg [m/sec] | Perihelion velocity Vp [m/sec] | Aphelion velocity Va [m/sec] | Specific angular momentum h | Specific orbital energy E | dφ | 2a(Vavg/c)^2(1+dφ) | a(1-e^2)dφ(2/3) | (8π^2a^3/c^2T^2)(1+dφ) | (2a(Vp/c)^2(1-e))(1+dφ)/(1+e) | (2a(Va/c)^2(1+e))(1+dφ)/(1-e) | (2h^2)(1+dφ)/(c^2a(1-e^2)) | (-4aE/c^2)(1+dφ) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Mercury | 0.3871 | 57909335747.97 | 0.2056 | 0.241 | 7605225.432 | 47360 | 58981.8245518867 | 38864.5997213162 | 2713351274428838 | -1146152501.02099 | 7.81737E-08 | 2890.41761017372 | 2890.41738421905 | 2949.64619982031 | 2953.99400232239 | 2953.99400232239 | 2953.99400232239 | 2953.99400232239 |
Venus | 0.7233 | 108204139877.31 | 0.0068 | 0.615 | 19407525.48 | 35020 | 35264.8306131018 | 34788.4681812999 | 3.78985E+015 | -613404718.85141 | 4.09385E-08 | 2953.00898396617 | 2953.00886307433 | 2954.87861991337 | 2953.99389232987 | 2953.99389232987 | 2953.99389232987 | 2953.99389232987 |
Earth | 1 | 149597870700 | 0.0167 | 1 | 31556952 | 29780 | 30290.1329043849 | 29295.0601798777 | 4455666017974531 | -443675633.145225 | 2.96108E-08 | 2952.31981614066 | 2952.31972872007 | 2953.48301086581 | 2953.99385886788 | 2953.99385886788 | 2953.99385886788 | 2953.99385886788 |
Mars | 1.5237 | 227942275585.59 | 0.0934 | 1.881 | 59358626.712 | 24080 | 26502.0659476983 | 21974.3671009542 | 5476717309904882 | -291183063.034209 | 1.95253E-08 | 2941.21277103664 | 2941.21271360854 | 2952.94449752574 | 2953.99382907537 | 2953.99382907537 | 2953.99382907537 | 2953.99382907537 |
Jupiter | 5.2028 | 778327801677.96 | 0.0485 | 11.86 | 374265450.72 | 13060 | 13709.103081907 | 12440.831266032 | 1.01526725255784E+016 | -85276319.1253219 | 5.70675E-09 | 2954.18364717428 | 2954.18363031549 | 2957.17130472142 | 2953.99378825542 | 2953.99378825542 | 2953.99378825542 | 2953.99378825542 |
Saturn | 9.5388 | 1426984169033.16 | 0.0555 | 29.46 | 929667805.92 | 9650 | 10195.9818305455 | 9123.73741255352 | 1.37420071513116E+016 | -46512730.4425321 | 3.11799E-09 | 2957.07522669051 | 2957.07521747039 | 2953.59000447722 | 2953.99378060823 | 2953.99378060823 | 2953.99378060823 | 2953.99378060823 |
Uranus | 19.1914 | 2870992575751.98 | 0.0463 | 84.01 | 2651099537.52 | 6810 | 7122.24123368717 | 6491.90620717524 | 1.95011638557061E+016 | -23118461.0369866 | 1.55134E-09 | 2962.88560330786 | 2962.88559871142 | 2957.96116322479 | 2953.99377598035 | 2953.99377598035 | 2953.99377598035 | 2953.99377598035 |
Neptune | 30.0611 | 4497076550899.77 | 0.009 | 164.79 | 5200270120.08 | 5440 | 5482.19031957957 | 5384.39108692106 | 2.44319450679472E+016 | -14759128.3467746 | 9.87900E-10 | 2961.53363889885 | 2961.53363597315 | 2954.52291069398 | 2953.99377431596 | 2953.99377431597 | 2953.99377431597 | 2953.99377431596 |
※2a(Vavg/c)^2(1+dφ)/√(1-e^2) および a(1-e^2)dφ(2/3)/√(1-e^2) の式について:
これらの修正により、太陽のシュワルツシルト半径の理論値に近づきましたが、その理論的な妥当性についてはさらなる検討が必要です。
Planet name | 2a(Vavg/c)^2(1+dφ)/√(1-e^2) | a(1-e^2)dφ(2/3)/√(1-e^2) |
---|---|---|
Mercury | 2953.51619901886 | 2953.51596813154 |
Venus | 2953.07725990169 | 2953.07713900707 |
Earth | 2952.73158850882 | 2952.73150107604 |
Mars | 2954.12624436109 | 2954.12618668085 |
Jupiter | 2957.66427810698 | 2957.66426122832 |
Saturn | 2961.64004046082 | 2961.64003122647 |
Uranus | 2966.06647243991 | 2966.06646783855 |
Neptune | 2961.6535882982 | 2961.65358537239 |