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Next: Summary Up: Heliospheric Coordinate Systems Previous: Jovian Systems

Spacecraft Elements


Table 7: Heliocentric mean orbital elements of major interplanetary spacecraft in $HAE_{J2000}$ fitted to data provided by NSSDC. The elements are semi-major axis $a$, eccentricity $e$, mean longitude $\lambda $, longitude of periapsis $\varpi $, inclination $i$, and ascending node $\Omega $. The time parameter $y_0$ is scaled in Julian years of 365.25 days from J2000.0, periods are given in decimal Julian years from J2000.0+2000.0. The last three columns contain the precision of positions determined from the elements relative to NSSDC position data: Maximal difference in HAE distance, longitude and latitude over the period given.

Mission Period $a$[AU] $e$ $\lambda[^\circ]$ $\varpi[^\circ]$ $i[^\circ]$ $\Omega[^\circ]$ $\Delta r$[AU] $\Delta\phi[^\circ]$ $\Delta\theta[^\circ]$
Galileo 1990.4-1990.9 0.982 0.298 195.36 + 366.670$y_0$ 182.17 3.39 76.51 0.014 1.2 0.10
Galileo 1991.2-1992.8 1.572 0.439 304.32 + 181.146$y_0$ -240.47 4.57 -103.37 0.036 0.7 0.09
Galileo 1993.8-1996.0 3.113 0.700 180.16 + 64.938$y_0$ -277.61 1.68 -105.39 0.014 0.8 0.09
Helios1 1977.0-1986.0 0.6472 0.5216 126.77 + 691.475$y_0$ -101.84 0.004 70.18 0.001 0.39 0.016
Helios2 1977.0-1981.0 0.6374 0.5436 147.76 + 707.453$y_0$ 294.58 0.024 121.85 0.002 0.89 0.004
Pioneer10 1972.4-1973.9 3.438 0.715 291.99 + 56.479$y_0$ 160.02 2.08 -17.06 0.019 0.18 0.07
Pioneer10 1974.3-2005.0 -6.942 1.727 111.81 + 19.700$y_0$ -42.02 3.14 -28.57 0.019 0.02 0.007
Pioneer11 1973.5-1974.8 3.508 0.7166 220.69 + 54.797$y_0$ 195.46 3.05 16.64 0.013 0.10 0.06
Pioneer11 1975.0-1979.6 16.729 0.7767 180.91 + 5.264$y_0$ 55.05 15.29 -5.24 0.012 0.25 0.20
Pioneer11 1979.7-2000.0 -8.059 2.161 127.99 + 15.668$y_0$ 173.21 16.63 160.40 0.06 0.23 0.12
Ulysses 1991.1-1992.1 9.035 0.8905 143.48 + 13.272$y_0$ 21.13 1.99 13.57 0.014 0.07 0.06
Ulysses 1992.2-2005.0 3.375 0.6032 256.31 + 58.073$y_0$ -22.93 79.15 -21.85 0.007 0.92 0.50
Voyager1 1978.0-1979.1 5.020 0.8009 332.66 + 31.820$y_0$ -17.71 0.93 -11.4 0.010 0.44 0.12
Voyager1 1979.2-1980.8 -4.109 2.258 302.05 + 43.088$y_0$ 112.12 2.46 113.23 0.010 0.23 0.06
Voyager1 1980.9-2005.0 -3.203 3.742 332.47 + 62.642$y_0$ 157.35 35.71 178.95 0.034 0.10 0.11
Voyager2 1977.9-1979.4 3.624 0.7244 65.98 + 52.225$y_0$ -20.65 0.84 -33.03 0.013 0.13 0.06
Voyager2 1979.6-1981.6 -17.345 1.2905 216.12 + 5.000$y_0$ 110.80 2.58 120.05 0.017 0.10 0.06
Voyager2 1981.7-1986.0 -3.913 3.4537 324.52 + 46.379$y_0$ 189.87 2.66 77.65 0.017 0.12 0.05
Voyager2 1986.1-1989.3 -2.902 6.0618 7.18 + 72.400$y_0$ -144.23 2.81 -98.07 0.034 0.12 0.12
Voyager2 1990.7-2000.0 -4.021 6.2853 256.56 + 44.661$y_0$ 231.66 78.92 101.65 0.045 0.13 0.10


To determine approximate positions of spacecraft relative to each other or to planets without using positional data files it is useful to have orbital elements of spacecraft in Keplerian orbits. This excludes most near Earth missions since their orbits are not Keplerian. In Tab.7 we list orbital elements for most major interplanetary missions. We have fitted these elements to trajectory data provided by NSSDC20. Not much accuracy is claimed by NSSDC for the propagated trajectories of any heliospheric spacecraft. But random cross-comparison with published papers had revealed mismatches of $< 0^\circ.1$ in angles or $< 1\%$ in radial distanceHEE (R.Parthasarathy, personal communication). We used the vector method given in ch.2 of Bate et al. (1971) to calculate initial values for the elements which we then fitted to achieve the smallest maximal deviation from the position data. The deviations are listed in the last three columns of Tab.7. The spatial resolution of the NSSDC position data is only $0.1^\circ$ and the temporal resolution 1 day. This results in a poor precision of the orbital elements at perihelion specifically for the Helios mission where the spacecraft moves $8^\circ$/day. For this reason we re-calculated the Helios orbits by integration from cartesian state vectors provided by JPL and then fitted elements to the re-calculated orbits. See also the JPL Voyager home page21for more Voyager orbital elements, and the ESA Ulysses home page22for a discussion of Ulysses orbital elements.


next up previous
Next: Summary Up: Heliospheric Coordinate Systems Previous: Jovian Systems
Markus Fraenz 2002-03-12