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Uncertainty Parameter U and Orbit Quality Codes

Uncertainty Parameter U

The Minor Planet Center quantifies uncertainty in perturbed orbital solutions using the uncertainty parameter U, an integer in the range 0--9. A value of 0 indicates a very small uncertainty and 9 an extremely large uncertainty. In practice, U is rarely larger than 6.

Calculation Method

The U value is derived from the in-orbit longitude runoff, RUNOFF, in seconds of arc per decade:

RUNOFF = (dT * e + 10 / P * dP) * ko / P * 3600 * 3

where:

  • dT = uncertainty in perihelion time (days)
  • e = eccentricity
  • P = orbital period (years)
  • dP = uncertainty in orbital period (days)
  • ko = Gaussian constant in degrees = 180 / pi * 0.01720209895
  • 3600 = conversion factor to seconds of arc
  • 3 = empirical factor for realistic error modeling

The conversion from RUNOFF to U is:

CONS = ln(648000) / 9           (CONS ~ 1.49)
U    = INT(ln(RUNOFF) / CONS) + 1    (0 <= U <= 9)

where ln is the natural logarithm and INT returns the largest integer smaller than the argument.

U Value Reference Table

U RUNOFF (arcsec/decade) U RUNOFF (arcsec/decade)
0 < 1.0 5 < 1692
1 < 4.4 6 < 7488
2 < 19.6 7 < 33121
3 < 86.5 8 < 146502
4 < 382 9 > 146502

The U value should not be used as a predictor for the uncertainty in the future motion of NEAs.


Orbit Quality Codes

For long-period comets, orbit quality codes replace the U value. These are based on the integer orbit code Q from Marsden et al. (1978).

Q Quality Code
9, 8 1A
7 1B
6 2A
5 2B
4 3A
3 3B
2, 1, 0 4

Codes 1A and 1B are the highest quality, used for orbits with long observed arcs and full consideration of perturbations. The codes 3A, 3B, and 4 represent logical extensions beyond the original scheme.