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 decade
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
