User:JohnOwens/Sedna orbit
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With reference to Orbital variables. I may tack on a few more significant digits in places than are really warranted.
To consider also: 4179 Toutatis
<math>M_{Sun} = 1.989\times10^{30} \mbox{kg}<math>
<math>\mu \equiv M_{Sun}G = 1.327178\times10^{20} {\mbox{m}^3 \over \mbox{s}^2}<math>
<math>590,000 \mbox{m} \le r_{Sedna} \le 1,180,000 \mbox{m}<math>
<math>1,180,000 \mbox{m} \le d_{Sedna} \le 2,360,000 \mbox{m}<math>
Assuming density equal to Pluto,
<math>1.76\times10^{21} \mbox{kg} \le M_{Sedna} \le 1.41\times10^{22} \mbox{kg}<math>
<math>a = 463 \mbox{AU} = 6.93\times10^{13} \mbox{m}<math>
<math>T = 10,500 \mbox{yr} = 3.31\times10^{11} \mbox{s}<math>
<math>\left|\mathbf{h}\right| = 5.263\times10^{16} {\mbox{m}^2 \over \mbox{s}}<math>
<math>\mathcal{E}_{orbital} = -958,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>R_{peri} = 76\pm7 \mbox{AU} = 1.137\times10^{13}\pm0.105\times10^{13} \mbox{m}<math>
<math>v_{peri} \equiv {\left|\mathbf{h}\right| \over R_{peri}} = 4629 {\mbox{m} \over \mbox{s}}<math>
<math>\mathcal{E}_{grav,peri} = 11,700,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>\mathcal{E}_{kinetic,peri} = 10,700,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>R_{ap} = 850 \mbox{AU} = 1.27\times10^{14} \mbox{m}<math>
<math>v_{ap} \equiv {\left|\mathbf{h}\right| \over R_{ap}} = 414 {\mbox{m} \over \mbox{s}}<math>
<math>\mathcal{E}_{grav,ap} = 1,040,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>\mathcal{E}_{kinetic,ap} = 85,700 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>R_{now} = 90 \mbox{AU} = 1.35\times10^{13} \mbox{m}<math>
<math>v_{now} = 4,219 {\mbox{m} \over \mbox{s}}<math>
<math>\mathcal{E}_{grav,now} = 9,857,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
<math>\mathcal{E}_{kinetic,now} = 8,899,000 {\mbox{m}^2 \over \mbox{s}^2}<math>
Unrelated, I just need a place to stick it:
(c*dT)^2 = (1-2*G*M/c^2/r)*(c*dt)^2 - (1-2*G*M/c^2/r)^-1*dr^2 - r^2*dtheta^2 - r^2*sin^2(theta)*dphi^2
<math>(c\,dT)^2 = \left( 1-2{G\,M \over c^2\,r}\right)(c\,dt)^2 - \left( 1-2{G\,M \over c^2\,r}\right)^{-1}dr^2 - r^2\,d\theta^2 - r^2\,\sin^2\theta\,d\phi^2<math>