# 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

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

${\displaystyle R_{peri}=76\pm 7{\mbox{AU}}=1.137\times 10^{13}\pm 0.105\times 10^{13}{\mbox{m}}}$
${\displaystyle v_{peri}\equiv {\left|\mathbf {h} \right| \over R_{peri}}=4629{{\mbox{m}} \over {\mbox{s}}}}$
${\displaystyle {\mathcal {E}}_{grav,peri}=11,700,000{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$
${\displaystyle {\mathcal {E}}_{kinetic,peri}=10,700,000{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$

${\displaystyle R_{ap}=850{\mbox{AU}}=1.27\times 10^{14}{\mbox{m}}}$
${\displaystyle v_{ap}\equiv {\left|\mathbf {h} \right| \over R_{ap}}=414{{\mbox{m}} \over {\mbox{s}}}}$
${\displaystyle {\mathcal {E}}_{grav,ap}=1,040,000{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$
${\displaystyle {\mathcal {E}}_{kinetic,ap}=85,700{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$

${\displaystyle R_{now}=90{\mbox{AU}}=1.35\times 10^{13}{\mbox{m}}}$
${\displaystyle v_{now}=4,219{{\mbox{m}} \over {\mbox{s}}}}$
${\displaystyle {\mathcal {E}}_{grav,now}=9,857,000{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$
${\displaystyle {\mathcal {E}}_{kinetic,now}=8,899,000{{\mbox{m}}^{2} \over {\mbox{s}}^{2}}}$

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