*MPCs*(Info)

# 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 arc per decadeRUNOFF 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

## 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 4The 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]