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• # Uncertainty Parameter U and Orbit Quality Codes

## Uncertainty Parameter U

In order to quantify the uncertainty in a perturbed orbital solution for a minor planet in a concise fashion, the Minor Planet Center has introduced the U parameter. This is an integer in the range 0 to 9, where 0 indicates a very small uncertainty and 9 an extremely large uncertainty. In practice, U is rarely larger than 6.

The U value is calculated in the following manner. First, calculate:

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

where dT is the uncertainty in the perihelion time (in days)
e is the eccentricity
P is the orbital period (in years)
dP is the uncertainty in the orbital period (in days)
ko is the Gaussian constant in degrees
= 180 / pi * 0.01720209895
3600 converts to seconds of arc
3 is a empirical factor to make the formal errors more
closely model reality
and   RUNOFF is the in-orbit longitude runoff in seconds of
```
RUNOFF is then converted to the "uncertainty parameter" (denoted by 'U') in the range 0 to 9:
```      CONS = ln(648000)/9            CONS ~ 1.49
U = INT(ln(RUNOFF)/CONS)+1  (0 <= U <= 9)

where ln is the natural logarithm
INT is a function that returns the largest integer
smaller than the argument (e.g., INT(3.5) = 3,
INT(0.99) = 0, INT(-0.45) = -1)
```
As a guide, the values of U correspond to the following values of RUNOFF (in seconds of arc per decade):
```   U      RUNOFF              U      RUNOFF

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, the orbit quality code is used instead of the U value. The orbit quality codes are based on the integer orbit code Q defined by Marsden et al. (1978), which should be consulted for how Q is determined.
```    Q      Quality code
9,8         1A
7          1B
6          2A
5          2B
4          3A
3          3B
2,1,0        4
```
The quality codes 3A, 3B and 4 were not defined in Marsden et al., but are a logical extension to the scheme. Codes 1A/1B are the highest quality, used for orbits with long observed arcs and full consideration of perturbations.

## References

Marsden et al., 1978 : B. G. Marsden, Z. Sekanina and E. Everhart, 1978, "New Osculating Orbits for 110 Comets and Analysis of Original Orbits for 200 Comets", Astron. J. 83, 64-71. [1978AJ.....83...64M]