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:
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:
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.