User:JohnOwens/Sedna orbit

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

$$M_{Sun} = 1.989\times10^{30} \mbox{kg}$$ $$\mu \equiv M_{Sun}G = 1.327178\times10^{20} {\mbox{m}^3 \over \mbox{s}^2}$$ $$590,000 \mbox{m} \le r_{Sedna} \le 1,180,000 \mbox{m}$$ $$1,180,000 \mbox{m} \le d_{Sedna} \le 2,360,000 \mbox{m}$$ Assuming density equal to Pluto, $$1.76\times10^{21} \mbox{kg} \le M_{Sedna} \le 1.41\times10^{22} \mbox{kg}$$ $$a = 463 \mbox{AU} = 6.93\times10^{13} \mbox{m}$$ $$T = 10,500 \mbox{yr} = 3.31\times10^{11} \mbox{s}$$ $$\left|\mathbf{h}\right| = 5.263\times10^{16} {\mbox{m}^2 \over \mbox{s}}$$ $$\mathcal{E}_{orbital} = -958,000 {\mbox{m}^2 \over \mbox{s}^2}$$

$$R_{peri} = 76\pm7 \mbox{AU} = 1.137\times10^{13}\pm0.105\times10^{13} \mbox{m}$$ $$v_{peri} \equiv {\left|\mathbf{h}\right| \over R_{peri}} = 4629 {\mbox{m} \over \mbox{s}}$$ $$\mathcal{E}_{grav,peri} = 11,700,000 {\mbox{m}^2 \over \mbox{s}^2}$$ $$\mathcal{E}_{kinetic,peri} = 10,700,000 {\mbox{m}^2 \over \mbox{s}^2}$$

$$R_{ap} = 850 \mbox{AU} = 1.27\times10^{14} \mbox{m}$$ $$v_{ap} \equiv {\left|\mathbf{h}\right| \over R_{ap}} = 414 {\mbox{m} \over \mbox{s}}$$ $$\mathcal{E}_{grav,ap} = 1,040,000 {\mbox{m}^2 \over \mbox{s}^2}$$ $$\mathcal{E}_{kinetic,ap} = 85,700 {\mbox{m}^2 \over \mbox{s}^2}$$

$$R_{now} = 90 \mbox{AU} = 1.35\times10^{13} \mbox{m}$$ $$v_{now} = 4,219 {\mbox{m} \over \mbox{s}}$$ $$\mathcal{E}_{grav,now} = 9,857,000 {\mbox{m}^2 \over \mbox{s}^2}$$ $$\mathcal{E}_{kinetic,now} = 8,899,000 {\mbox{m}^2 \over \mbox{s}^2}$$

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 $$(c\,dT)^2 = \left( 1-2{G\,M \over c^2\,r}\right)(c\,dt)^2 - \left( 1-2{G\,M \over c^2\,r}\right)^{-1}dr^2 - r^2\,d\theta^2 - r^2\,\sin^2\theta\,d\phi^2$$