Tuesday, November 22, 2011

Where can I get a dataset of the Voyager 1 probe positions?

I am wondering if there is any datasets out there that can provide me with a list of equatorial coordinate (ra/dec) postions of the Voyager 1 probe since it's launch?|||Dude, if this kind of question comes up a lot with you, then you seriously need to learn how to reduce Keplerian orbital elements to a state vector and then do the coordinate transformations to translate from heliocentric to geocentric coordinates, and rotate from ecliptic to celestial coordinates. It isn't hard to learn at all. Just a short little procedure. I've never been a professional astronomer and I can do it, which just proves how easy it is.



Here's how to do the calculation for Pioneer 10. You can look up Voyager 1's orbital elements for yourself.



Pioneer 10, orbital elements.

a = −6.93850 AU

e = 1.72923

i = 3.143 degrees

Ω = 331.996 degrees

ω = 346.732 degrees

T = JD 2442017.13



Hyperbolic mean anomaly.

M = 0.01720209895 (t − T) √[1/(−a)³]



Hyperbolic eccentric anomaly.

u = 0

Repeat...

. u₀ = u

. 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 + d₂² f₃/6 ]

. u = u₀ + d₃

Until |u − u₀| %26lt; 1E-14



True anomaly.

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



Heliocentric distance.

r = a (1 − e cosh u)



Canonical position vector.

x''' = r cos Q

y''' = r sin Q



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 to get...

The heliocentric position in ecliptic coordinates.

x = x' cos Ω − y' sin Ω

y = x' sin Ω + y' cos Ω

z = z'



Heliocentric longitude.

λ = (180/π) { arctan( y / x ) + Δ } degrees

if x%26gt;0 and y%26gt;0 then Δ=0

if x%26gt;0 and y%26lt;0 then Δ=2π

if x%26lt;0 then Δ=π



Heliocentric latitude.

β = (180/π) { arcsin( z / r ) } degrees



Some of the details are different for elliptical orbits, but the objects you're interested in are in hyperbolic trajectories, so that's the procedure I am showing.|||This is the ephemeris for the droid you are looking for.



http://vho.nasa.gov/mission/voyager/1/ep…



http://vho.nasa.gov/vxo/metadata.php?id=…



http://ipnpr.jpl.nasa.gov/progress_repor… (PDF)

http://en.wikipedia.org/wiki/Voyager_1

http://voyager.jpl.nasa.gov/



Voyager 1 is heading toward (2000): RA 17:28, Dec +12°

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