Requirements for Comet/asteroid Orbit Determination and Ephemeris Software

1. Inputs - The user will have the option of either modifying the record of an existing minor planet, deleting an existing minor planet, or creating a new minor planet
   1. Up to 1000 minor planets will be supported.
   2. The user will have the ability to designate whether an existing minor planet is a comet or an asteroid
   3. The user will have the ability to directly enter the orbital elements of an existing minor planet
      1. The user will either supply a barycentric equatorial position/velocity state vector, or classical heliocentric equatorial elements, referred to ICRF/J2000
      2. The user may optionally specify the one-sigma covariances in these orbital elements
   4. The user will have the ability to enter observations of an existing minor planet from which an orbit can be calculated
      1. The user will have the option of entering either optical or radar observations
         1. For each optical observation, the user will supply the following:
            1. The Coordinated Universal Time (UTC) of the optical observation
            2. The right ascension and declination, as well as the observational uncertainties in these data, referred to a user-specified mean ecliptic and equinox
            3. (Optionally) The visual magnitude
            4. The geodetic lat/east long/alt from which the optical observation was made
            5. (Optionally) The Earth Orientation Parameters for the timeframe of the observation
         2. For each radar delay or doppler observation, the user will supply the following:
            1. The Coordinated Universal Time (UTC) of the radar observation
            2. The radar transmission frequency
            3. The radar delay or radar doppler shift, as well as the observational uncertainties in these data
            4. The geodetic lat/east long/alt of the transmitter and receiver from which the radar observation was made
            5. The Earth Orientation Parameters for the timeframe of the observation
      2. Up to 1000 observations will be supported for each minor planet
      3. Observations will be supported in the timeframe B1900 - J2200
      4. Optical observations can be referenced to either FK4, FK5 or ICRF (with FK5 regarded as equivalent to ICRF for optical purposes). Radar observations must be referred to ICRF.
      5. CODES will also process tabulated observations from either Minor Planet Electronic Circulars (MPECs), MPCOBS files, or Near Earth Object Dynamics Site (NEODyS) files. CODES will provide default EOPs for these observations; other data specified in 1.4.1 will be extracted from the file records.
2. Initial Orbit Determination - The user will have the ability to attempt to calculate an initial two-body orbit of an existing minor planet for which at least three optical observations are available. Due to the nature of the problem, the process will be interactive, and possibly iterative.
   1. The user will select which three observations of the minor planet will be used
   2. The user will select whether to use the Gauss method, conditioned Gauss method, or Laplace method
   3. When the output of the selected method is displayed, the user will have several options:
      1. Save the calculated initial orbital elements for the minor planet,
      2. Refine the orbit using differential correction,
      3. Try a new value of the semi-major axis (conditioned Gauss only),
      4. Try another method, or
      5. Try another set of three observations
   4. CODES will indicate whether the initial orbit implies that the minor planet is a Potentially Hazardous Asteroid (PHA) or comet, using the MPC definition of a PHA.
3. Final Orbit Determination - The user will have the ability to attempt to calculate the least-squares best-fit orbit (including one-sigma covariances) of an existing minor planet, using all available (>3) optical and/or radar observations (plus observational uncertainties), provided that a preliminary set of orbital elements (either user-defined in 1.3 or calculated in 2.3) is available.
   1. The user will choose whether to calculate a solution using non-gravitational thrust parameters, to account for comet outgassing
   2. If sufficient visual magnitude observations are available, CODES will also attempt to solve for the best-fit visual brightness parameters (absolute visual magnitude and slope parameter).
      1. If insufficient visual magnitude observations are available, or if no reasonable best-fit solution can be obtained, CODES will adopt a default value (dependent on whether the minor planet is an asteroid or a comet) for the slope parameter, and derive the resulting absolute visual magnitude
      2. If sufficient visual magnitude observations are available, and if a satisfactory best-fit solution can be obtained, CODES will calculate the best-fit absolute visual magnitude and slope parameter
      3. In the case of an asteroid, the calculated values of absolute visual magnitude and slope parameter will be used to estimate the radius of the minor planet
   3. CODES will indicate whether the final orbit implies that the minor planet is a Potentially Hazardous Asteroid (PHA) or comet, using the MPC definition of a PHA.
   4. CODES will indicate if the least-squares process has diverged, returning the preliminary orbit in such a case.
4. Compare optical observations to known minor planets - The user will have the ability to search the Minor Planet Center comet/asteroid catalogs, to determine which candidates best match the optical observations of the subject minor planet
   1. Candidates will be restricted to those comets/asteroids whose RMS position residuals are less than 1 arc degree
   2. The brightness residuals for each candidates will also be calculated and displayed, though they will not be used in the determination of valid candidates
   3. In searching for comet candidates, the user will have the following options
      1. two-body mechanics
      2. integrated n-body mechanics
   4. In searching for asteroid candidates, the user will have the following options:
      1. two-body mechanics
      2. integrated n-body mechanics, consider all asteroids
      3. integrated n-body mechanics, consider only Near-Earth Asteroids
      4. integrated n-body mechanics, consider only Main-Belt Asteroids
      5. integrated n-body mechanics, consider only Centaurs and Trans-Neptunian Objects
5. Ephemeris - The user will have the ability to create an ephemeris for an existing minor planet, provided that a set of orbital elements (initial or final, calculated or user-defined) is available
   1. The user will specify the desired time(s) at which output will be calculated (CODES supports dates between 1900-2200)
   2. The user will specify the perspective of the observer (geocentric, or topocentric with lat/east long/alt)
   3. If the state vector's one-sigma covariances are available, the ephemeris will include predicted ra/dec one-sigma covariances
   4. If the absolute visual magnitude and slope parameter are available, the ephemeris will include predicted visual magnitude
6. Collision/Near-Miss Detection
   1. The user will have the ability to predict collisions and/or near-misses between an existing minor planet and the nine major planets (plus Earth’s Moon) through J2200, provided that a set of orbital elements (initial or final, calculated or user-defined, one-sigma covariances included) is available. The near-miss threshold will be user-specified.
   2. Output will include:
      1. Barycentric Dynamical Time (TDB) of the event,
      2. minimum distance,
      3. linearly-estimated probability of impact, and
      4. linearly-estimated one-sigma position covariances.
7. Settings - The user will have the ability to adjust the following:
   1. Perturbing bodies in numerical integration. The choices will include
      1. Sun, nine planets, and Earth’s Moon,
      2. Sun, nine planets, Earth's Moon, and asteroids Ceres, Pallas and Vesta (default selection),
      3. Sun, nine planets, Earth's Moon, and all asteroids with well-approximated masses (235),
      4. Sun, nine planets, Earth's Moon, and all available asteroids (300).
   2. Estimated radius of the minor planet, in km. (used for radar calculations)
   3. Absolute visual magnitude and slope parameter
8. The user will have the ability to display both the orbital elements (plus one-sigma covariances, if available) and the state vector (plus one-sigma covariances, if available) of an existing minor planet
9. The user will have the ability to propagate the state vector/orbital elements (plus covariances) of an existing minor planet from one epoch to another
10. The user will have the ability to calculate the observational residuals for an existing minor planet, based on the current orbital elements/state vector
11. The user will have the ability to review and/or delete observations of an existing minor planet
12. Trajectory calculations will use a high-precision numerical integrator
    1. Step-size error control of the numerical integrator shall be used to ensure that, in any calculation involving the perturbed trajectory of a minor planet, the integration error in the final position shall not exceed 0.00000001 AU, regardless of the length of the interval of integration.
    2. Positions and velocities of the Sun, nine planets, and Earth's Moon will be calculated from the JPL DE405 ephemeris tables
    3. Positions and velocities of perturbing asteroids will be calculated from their mean orbital elements

Glossary of Terms:

ICRF – International Celestial Reference Frame. The current astrometric frame of reference, defined by the positions of over 200 deep-space quasars, presumably with no perceptible proper motion.

J2000 – The date Jan 1.0, 2000 in the Julian calendar. Currently, astrometric measurements are made in relation to the mean ecliptic and equinox of this date; thus, "ICRF/J2000" means that a ra/dec is referred to the ICRF frame, where the origin is defined as the mean equinox of J2000.

Earth Orientation Parameters – A set of data allowing the extremely precise determination of the position and velocity of an Earth-based observer. These include polar motion coefficients, UT1-TAI time measurements, leap seconds, Earth angular rotational velocity, and departures from the 1980 IAU values for nutation and obliquity.

TDT – Terrestrial Dynamical Time. A time-scale used for observations made at the surface of the Earth; since 1984, TDT has replaced Ephemeris Time as the standard for Earth-based ephemerides. From 1984 onward, TDT = TAI + 32.184 seconds, where TAI is atomic clock time.

TDB – Barycentric Dynamical Time. A time-scale used for ephemerides referred to the barycenter of the solar system. TDB and TDT differ due to relativistic effects.

UTC – Coordinated Universal Time. Civilian time scale. Differs from atomic clock time (TAI) by an integral number of leap seconds (currently 32).

topocentric – An observation made from a specific Earth geodetic lat/east long/alt; as opposed to geocentric, in which the observer would be at the center of the Earth.

FK4 – Fundamental Katalog 4. A stellar astrometric reference frame replaced in 1984 by the more precise FK5 (which has since been supplanted by ICRF).

B1900 – The date Jan 1.0, 1900 in the Besselian calendar (which differs slightly from the Julian calendar, in that a Besselian day is defined as a mean solar day, while a Julian day is defined as precisely 86,400 TAI seconds).

J2200 – The date Jan 1.0, 2200 in the Julian calendar.