# 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...
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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...
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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

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...
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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)

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...
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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

u = 1.5284920 radians

True anomaly.

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

Q = 2.0115809 radians

Heliocentric distance.

r = a (1 - e cosh u)

r = 13.468621 AU

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

u = 1.5284920 radians

True anomaly.

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

Q = 2.0115809 radians

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'...
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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

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

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