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FREQUENTLY ASKED QUESTIONS__

- What are the elements of an asteroid's orbit?
- What are the criteria for an asteroid to become numbered?
- What is an astronomical unit (au)?
- What are the other quantities that appear in the tables?
- What are the proper elements?
- Which proper elements are shown in the tables?
- Where can I learn more on the proper elements?
- What is
*chi*? Why is it equal zero in the list of the observational data for the object I am interested in? - How good are your absolute magnitude estimates?
- Why are there too few (or too many) digits in the orbital elements?
- I don't have an observatory code. What should I enter in the services forms?
- Your home page says that it was last updated a long time ago, but I thought your site was updated daily. What's up?
- My question isn't here. Whom can I ask?

**What are the elements of an asteroid's orbit?**- These are six quantities that fully desribe an elliptical orbit; along with time, they specify the position of an orbiting body along its path. A typical set of orbital elements include:
*semimajor axis*- a half of the longer axis of an elliptical orbit;*eccentricity*- the amount by which an orbit deviates from circularity;*inclination*- an angle measured at ascending node between the orbital plane and the reference plane (e.g. ecliptical plane J2000).*longitude of the ascending node*- angle in the reference plane between the vectors from the origin of coordinates (heliocenter) to the ascending node and to the vernal equinox (gamma-point); ascending node is the point at which body crosses the reference plane passing from the southern to the northern celestial hemisphere;*argument of perihelion*- angle in the orbital plane between the vectors to the ascending node and to the periapse (perihelion) of the orbit;*mean anomaly*- angle in the orbital plane between the vectors to the "mean" position of the body at some epoch T and to the periapse. The mean position corresponds to the position the body would occupy at T, if it were moving along circular orbit with a constant angular velocity (mean motion).

**What are the criteria for an asteroid to become numbered?**- A well known orbit, which must be accurate enough to provide reliable
predicition of its motion over a long time span.

**What is an astronomical unit (au)?**- The mean distance of the
Earth from the Sun, about 93 million miles or 150 million
kilometers. The lunar distance is 0.0026 au and the radius of the
Earth is 0.000043 au.

**What are the other quantities that appear in the tables?**- There are several useful quantities whose values we report in our tables. Here are their definitions given in order of their appearance in the tables:
*Absolute Magnitude (H)*- an intrinsic measure of brightness. It is defined as the V-band magnitude of an object when it is 1 au from both the Sun and the observer, at mean brightness and at zero phase angle (see below);*Slope parameter (G)*- this parameter models the so-called opposition effect, that is a surge in brightness observed when the object is near the opposition. It is known for small number of objects, hence for most asteroids the rule of thumb value of 0.15 is used;*Perihelion distance*- the smallest distance to the Sun along the osculating orbit;*Aphelion distance*- the largest distance to the Sun along the osculating orbit;*Asc. nodal distance*- the distance along the nodal line from the ascending node of the asteroid to the orbit of the Earth; nodal line joins the two nodes - ascending and descending;*Desc. nodal distance*- the distance along the nodal line from the descending node of the asteroid to the orbit of the Earth;*Earth MOID*- the Minimum Orbital Intersection Distance. This is the minimum separation between the instantaneous ellipses of the Earth and the asteroid;*Orbital period*- the time interval to complete one revolution;*Date of orbit computation*- self-explanatory;*RMS of the residuals*- an estimate of the error of the observational data used to calculate the orbit. The value is computed using the error statistics of the astrometric observations; we are presently working on the improvements of the algorithm. For the details on the computation of this value you should soon be able to consult Carpino, Milani and Chesley: 'Error Statistics of Asteroid Astrometric Observations' (paper in preparation). See also here.*Date of the first observation*- date of the first observation taken into account in the orbit calculation;*Date of the last observation*- date of the last observation taken into account in the orbit calculation;*Number of observations*- total number of observations of a given object in the database;*Number discarded*- number of observations discarded in the course of the orbit computation;*Arc length*- orbital arc covered by observations taken into account in the orbit computation;*Right ascension and declination*- the two angular coordinates in a spherical, geocentric, equatorial coordinate system; RA is measured in time units, and DEC in the units of the arc.*V magnitude*- an apparent magnitude of the body at a given instant of time;*Solar elongation*- the angle asteroid-Earth-Sun. Elongation of 0 deg is called conjunction, that of 180 deg opposition, and the one of 90 deg quadrature.*Phase angle*- the angle Sun-asteroid-observer.*Galactic latitude*- one of the angular coordinates (the other is galactic longitude) in the galactocentric spherical coordinate system;*Distance from the Earth*- self-explanatory; Delta*Distance from the Sun*- self-explanatory; R*Apparent motion rate*- arc that asteroid describes in the unit of time;*Apparent motion direction*- direction of apparent motion measured from the North Celestial Pole.*Elements of the uncertainty ellipse*- self-explanatory (see What are the elements of an asteroid's orbit? and above).

**What are the proper elements?**- The proper elements are quasi integrals of motion, or, in other
words, integrals of a simplified system of equations of motion. Since
freed from the most important short and long periodic perurbations,
they represent a sort of "averaged" parameters of motion over very
long time spans. Proper elements can be defined and computed in
different ways, depending on the dynamics involved, but for majority
of the main belt asteroids they are computed either by means of an
analytic theory, or by means of a purely numerical procedure
(synthetic theory).

The*analytic theory*involves the computation of the mean elements from their instantaneous osculating counterparts by means of a canonical transformation to remove the short periodic perturbing effects, and the subsequent computation of the proper elements from the mean ones, by means of another canonical transformation to account for the long periodic effects.

The*synthetic theory*, on the other hand, consists of a simultaneous integration of asteroid and planetary orbits and an online filtering of the short-periodic perturbations; the output of the integration is next spectrally resolved, and the principal harmonics (proper values) are extracted from the time series. For each asteroid we also estimate the accuracy and stability in time of the proper elements, and compute the maximum*Lyapounov Characteristic Exponent*to monitor the chaotic behaviours.

Note that analytic proper elements are less time consuming to compute and that therefore they are updated monthly for all the numbered and multiopposition asteroids in the database. On the other hand, they are typically less accurate than the synthetic ones, and the exact estimates of their instability are known for a small number of representative cases. The synthetic proper elements take a significantly longer time to be determined, and therefore they are provided in AstDyS on a regular basis only for the numbered asteroids. Each month the synthetic proper elements are computed for all the newly numbered objects, and simply appended to the existing catalogs. The synthetic proper elements are available for a number of multiopposition asteroids as well, but the completeness of these catalogs depends strongly on the influx of new identifications and on the available computing power. On the other hand, not only that synthetic proper elements are typically more accurate than the analytic ones, but they are also all given with their individual accuracy estimates, which makes them more reliable and useful in the applications,

**Which proper elements are shown in the table?**- There are three principal proper elements that are reported
in both tables:
*proper semimajor axis, proper eccentricity, sine of proper inclination*, along with:*frequency of perihelion*- the presession rate of the perihelion of the asteroid's orbit, expressed in arc seconds per year; positive if in counterclockwise direction and positive for most asteroids.*frequency of node*- the presession rate of the ascending node of the asteroid's orbit, expressed in arc seconds per year; positive if in counterclockwise direction, but negative for most asteroids.*resonance code*- number that indicates whether an asteroid is located close to some secular resonance (zero means no secular resonance in the vicinity); number different from zero is a coded label of the nearby resonance that affects the asteroid's motion, and consequently also the determination of its analytic proper elements. Codes are available here.

*quality code mean elements*- the QCM quality code provides an estimate of the uncertainty of the mean elements as computed by means of the analytic theory. It is given in a decibel scale and calibrated in such a way that QCM=0 corresponds to an unremoved short periodic perturbation in the mean semimajor axis of an amplitude 0.003 au. QCM=10 then corresponds to 0.03 au, etc. QCM>10 indicates presence of the mean motion resonance.

*mean motion*- mean rate of progression along the osculating orbit; related to osculating semimajor axis by Kepler's equation.

*Lyapunov Exponent*- indicator of chaos that measures exponential divergence of the initially nearby orbits (formaly defined as limes when time tends to infinity). Nearly zero value indicates stable motion; the more it differs from zero, the motion is more chaotic. The inverse of the exponent is the so-called Lyapunov time.

*Integration time span*- the time span over which the above estimate of Lyapunov Exponent is computed.

**Where can I learn more on the proper elements?**-
*The analytic theory to compute proper elements is described in a series of published papers of which we quote here just the most important ones:**Milani A. and Knezevic Z.*1990. Secular perturbation theory and computation of asteroid proper elements. Celestial Mechanics, Vol. 49, 347-411.*Milani A. and Knezevic Z.*1992. Asteroid proper elements and secular resonances. Icarus, Vol. 98, 211-232.*Milani A. and Knezevic Z.*1994. Asteroid proper elements and the dynamical structure of the asteroid main belt. Icarus, Vol. 107, 219-254. -
*The synthetic theory to compute asteroid proper elements is described in the papers:**Knezevic Z. and Milani A.*2000. Synthetic proper elements for outer main belt asteroids. Celestial Mechanics and Dynamical Astronomy, Vol. 78, 17-46.*Knezevic Z., Lemaitre A. and Milani A.*2002. The determination of asteroid proper elements . In: Asteroids III (W. Bottke et al. Eds.), University of Arizona Press and LPI, Tucson, pp. 603-612.*Knezevic Z. and Milani A.*2003. Proper element catalogs and asteroid families. Astronomy and Astrophysics, Vol. 402, 1165-1173.

*Interested reader can find appropriate to consult also the papers describing the specially adapted asteroid proper element theories - the semianalytic theory by Lemaitre and Morbidelli for the highly inclined asteroidal orbits, and the theories by Milani and by Beauge and Roig for Trojan asteroids:*

*Lemaitre A. and Morbidelli A.*1994. Proper elements for highly inclined asteroidal orbits. Cel. Mech. Dyn. Astron., Vol. 60, 29-56.

*Milani A.*1993. The Trojan asteroid belt: proper elements, stability, chaos and families. Celestial Mechanics, Vol. 57, 59-94.

*Beauge C. and Roig F.*2001. A semianalytical model for the motion of the Trojan asteroids: proper elements and families. Icarus, Vol. 153, 391-415.

Available for download (PostScript, gzipped) are the following papers describing the analytic theory to compute asteroid mean elemens, the synthetic theory of asteroid proper elements, the semianalytic theory for Trojans and a special theory for the Earth crossing asteroids:

Milani A. and Knezevic Z. Asteroid mean elements: higher order and iterative theories.

Knezevic Z. and Milani A. Synthetic proper elements for outer main belt asteroids.

This paper is also available here. for the on line browsing.

Knezevic Z. and Milani A. Proper element catalogs and asteroid families.

Beauge C. and Roig. F. A semianalytical model for the motion of the Trojan asteroids: proper elements and families.

Gronchi G. and Milani A. Proper elements for Earth-crossing asteroids.

The following is a review paper on asteroid proper elements:

Knezevic Z., Lemaitre A. and Milani A. Determination of asteroid proper elements

**What is***chi*? Why is it equal zero in the observational data for the object I am interested in?- This refers to the chi-square statistical quantity that is used to
determine our cutoff for observational outlier rejection and
recovery. We currently reject observations if
*chi***2 > 8 and we recover previously rejected observations if*chi***2 < 7.5. The*chi*column in the observational data describes the quality of the observation, essentially the weighted circular error in arc-sec.

There are a very few unusual objects for which our automated routine for rejecting outliers in the observational data fails. In such cases the*chi***2 test is not applied and outlier rejection is done on a manual basis. Presently (February 1999) there are no objects in this category. Of course, objects without uncertainty information are not subjected to automatic outlier rejection, so they fall into this category also. See the next question below.

**How good are your absolute magnitude estimates?**- Our computed
absolute magnitudes are in excellent agreement with the computations
of others in the field, but it is important to note that the source of
our data is solely the photometry published by the Minor Planet Center
with their astrometric observations. For the numbered asteroids
(esp. those below 100), our computation can be quite different from
the "official" IAU value because we have not included any photometric
data not reported to the MPC with astrometry. The link to additional
physical information will typically provide a more better value in
these cases. However, for unnumbered asteroids our result typically
represents the best estimate that can be obtained with the available
data.

**Why are there too few (or too many) digits in the orbital elements?**- Our HTML screen displays are designed for human
readability. If you need machine precision (for machine readability),
then you should download the ASCII files. However, the actual
precision of the files is described by the "1-sigma variation" column
in the HTML orbital element tables, which will generally be different
from either of the element formats.

**I don't have an observatory code. What should I enter in the services forms?**- If you are doing only occasional
observing, then you can use the default code of 500, or find an
observatory near you and use their code. If you are intending to
submit observations to the Minor Planet Center then you must contact
them and obtain an observatory code. See their Guide to
Minor Body Astrometry.

**Your home page says that it was last updated a long time ago, but I thought your site was updated daily. What's up?**- The database is updated daily, and hence all orbital information is kept current. The home page is not changed on a frequent basis.

**My question isn't here. Whom can I ask?**- We would like to include your question here! Use the contact interface with the astdys staff, and we will try to answer your question as promptly as possible.

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