# What are New Horizons' Keplerian elements?

I can't find New Horizons orbital elements on the web. I found a graphic showing distance from the sun and speed relative to the sun, and used the Vis Viva equation to get a semimajor axis of -5.652 AU. It's a hyperbolic escape orbit, so the semimajor axis is negative. But I'd like to have the whole set... show more I can't find New Horizons orbital elements on the web. I found a graphic showing distance from the sun and speed relative to the sun, and used the Vis Viva equation to get a semimajor axis of -5.652 AU. It's a hyperbolic escape orbit, so the semimajor axis is negative. But I'd like to have the whole set of post-Jupiter keps: a,e,i,Ω,ω,T.
Update: I found the elements through Dana M's link. Here are two sets of elements, computed 100 days apart. New Horizons, Keplerian elements for 1 March 2009 (JD 2454891.5), relative to the solar system barycenter. a = -5.663523 AU e = 1.399370 i = 2.346257 degrees Ω = 229.544976 degrees ω = 287.928129... show more I found the elements through Dana M's link. Here are two sets of elements, computed 100 days apart.

New Horizons, Keplerian elements for 1 March 2009 (JD 2454891.5), relative to the solar system barycenter.
a = -5.663523 AU
e = 1.399370
i = 2.346257 degrees
Ω = 229.544976 degrees
ω = 287.928129 degrees
T = JD 2453772.547955

New Horizons, Keplerian elements for 9 June 2009 (JD 2454991.5), relative to the solar system barycenter.
a = -5.663407 AU
e = 1.399390
i = 2.346188 degrees
Ω = 229.543416 degrees
ω = 287.930748 degrees
T = JD 2453772.550417
Update 2: http://ssd.jpl.nasa.gov/horizons.cgi#top Ephemeris Type [change] : ELEMENTS Target Body [change] : New Horizons Spacecraft [NH New_Horizons (Spacecraft)] [-98] Center [change] : Solar System Barycenter (SSB) [500@0] Time Span [change] : Start=2009-3-1, Stop=2010-3-31, Step=100 d Table Settings... show more http://ssd.jpl.nasa.gov/horizons.cgi#top

Ephemeris Type [change] : ELEMENTS
Target Body [change] : New Horizons Spacecraft [NH New_Horizons (Spacecraft)] [-98]
Center [change] : Solar System Barycenter (SSB) [500@0]
Time Span [change] : Start=2009-3-1, Stop=2010-3-31, Step=100 d
Table Settings [change] : defaults
Display/Output [change] : default (formatted HTML)
Update 3: Calculating New Horizons position at 12h UT on 1 June 2009. Time since perihelion. dt = t - T dt = (2454984 - 2453772.55) = 1211.45 days Hyperbolic mean motion. b = 0.01720209895 sqrt[1/(-a)^3] b = 0.00127633530 radians per day Hyperbolic mean anomaly. M = b dt = 1.5462164 radians Hyperbolic... show more Calculating New Horizons position at 12h UT on 1 June 2009.

Time since perihelion.
dt = t - T
dt = (2454984 - 2453772.55) = 1211.45 days

Hyperbolic mean motion.
b = 0.01720209895 sqrt[1/(-a)^3]
b = 0.00127633530 radians per day

Hyperbolic mean anomaly.
M = b dt = 1.5462164 radians

Hyperbolic eccentric anomaly.
u1 = 0
Repeat
u0 = u1
f0 = e sinh u0 - u0 - M
f1 = e cosh u0 - 1
f2 = e sinh u0
f3 = e cosh u0
d1 = -f0 / f1
d2 = -f0 / [ f1 + (d1)(f2)/2 ]
d3 = -f0 / [ f1 + (d1)(f2)/2 + d2^2 (f3)/6 ]
u1 = u0 + d3
Until |u1-u0| < 1E-14
u = u1

True anomaly.
Q = arccos { (e - cosh u) / (e cosh u - 1) }

Heliocentric distance.
r = a (1 - e cosh u)
r = 13.468621 AU
Update 4: Canonical position vector. x''' = -r cos Q = -5.746376 AU y''' = -r sin Q = +12.181253 AU Rotate by argument of the perihelion. x'' = x''' cos ω - y''' sin ω y'' = x''' sin ω + y''' cos ω Rotate by inclination. x'... show more Canonical position vector.
x''' = -r cos Q = -5.746376 AU
y''' = -r sin Q = +12.181253 AU

Rotate by argument of the perihelion.
x'' = x''' cos ω - y''' sin ω
y'' = x''' sin ω + y''' cos ω

Rotate by inclination.
x' = x''
y' = y'' cos i
z' = y'' sin i

Rotate by longitude of ascending node.
x = x' cos Ω - y' sin Ω
y = x' sin Ω + y' cos Ω
z = z'

Heliocentric position for New Horizons in ecliptic coordinates on 1 June 2009.
x = +0.6354501 AU
y = -13.4483298 AU
z = +0.3773384 AU