# Website documentation

## Symbols and units

We consistently use the following notations and units across the MP3C service:

Quantity Short name Unit
Semi-major axis a au
Orbital eccentricity e None
Inclination, J2000.0 i deg
Perihelion distance q au
Aphelion distance Q au
Argument of perihelion, J2000.0 ω deg
Longitude of the ascending node, J2000.0 Node deg
Mean anomaly at the epoch m deg
Mean daily motion n deg · day−1
Epoch Epoch TT
RMS residual rms None
Arc length (single-opposition orbits) Arc length days
Number of observations (MPC) nobs None
Number of oppositions (MPC) nopp None
Absolute magnitude (from HG system or not) H None
Slope parameter (from HG system, or not; usually set to 0.15 in latter case) G None
Diameter D km
Inverse diameter 1/D km−1
Geometric visible albedo pV None
Mass Mass kg

## Filtering

The Properties search, Best values search, XY plots and histogram forms allow applying filter rules to bodies. For the Properties search, the procedure is made of two steps since the rows from a property table, such as the albedos table, do not represent bodies, but measurements, so that a body may have several albedo measurements. In this, case, we first apply filter rules to determine a list of filtered bodies. Then, the property table is filtered to limit results to rows corresponding to any body from the list of filtered bodies.

How bodies are filtered depends on the filter field used. When multiple fields are filled, they are treated individually, and they each limit further the set of results.

### Filter by “Names list”

Any term in this comma-separated list of names is matched against all names, including body synonyms. For example, entering “Juno”, “00003”, “1804RA” or “I04R00A” would in all cases limit the search to Juno. The search is case-sensitive.

### Filter by “Numbers list”

This list of ranges of numbers limits the results to bodies with a matching body number from MPC. For example, entering “1, 3-5” will limit results to Ceres, Juno, Vesta and Astraea.

### Filter by “Parents (families) list” or “Parents names list”

For each of these fields, results are filtered to only show bodies for which any family measurement matches an element from the list in the field. For example, filtering by parent name “Baptistina“ will include a match for Stateira, because one of its attributed family is Baptistina, although its best family is set to Flora.

For the Parents names list, the search is case-sensitive.

### “Constraints on quantities” filter rows

These fields allow filtering by any numeric data in the best values table. For bodies with several measurements of a quantity such as the mass, the filter is applied to the best mass of the body and may therefore not match all individual mass measurements for that body. An important consequence is that, in the Properties search, filtering for example the masses table by a range of masses may display rows with the mass outside that range.

## Family physical property

Asteroid families may be defined differently depending on the author, and/or analysis, and/or the data used. Please refer to the publications reported in the family table. In the table of families we report the number and name of the family member with the lowest number (parent body number and name) and the family ID and name of the family according to the author classification.

When available, we also provide in the $$C_j$$ parameter a measure of the likelihood of each family member to be real or interloper on the basis of its position on the so-called family V-shape (or V-plot). Bodies with low $$\left| C_j \right|$$ are more likely to really be a member of the attributed family.

For example, for the David Nesvorny HCM families, asteroid (1745) Ferguson has family number 605, family name Koronis, parent body number 158, parent body name Koronis, and $$C_j = -0.5900$$.

## Best values

Best values are calculated for physical properties. The algorithm depends on the property, as detailed below.

### Family numbers and names

The best family of a body is only calculated when data is available from one of the following sources (there is only one at the moment):

1. “doi.org/10.26033/6cg5-pt13”: Nesvorny HCM families

If data exist for more than one of the references above, we only consider the first available reference from the list above. The best family is then set to the family given by the row with lowest $$\left| C_j \right|$$.

Note that best family numbers and names in the "best values" table refer to parent body numbers and names from the families table, which were determined by us to provide consistent naming of families across different data sources. Family IDs and names set by the authors' data sources are not available in the best values.

### Other properties

All properties not already mentioned in one of the previous sections are numeric. For any measurement, the standard error of the measured value is defined as half the difference between the upper and lower uncertainties. For each body and quantity, the rules for computing the best value and its standard error are the following:

• If there are no measurements, the best value and its standard error are undefined.
• If none of the measurements have uncertainties, the best value is set to the average of the measurements with an undefined standard error.
• In all other cases:
• For the considered body, a “default” standard error, $$\sigma_{\mathrm m}$$ is calculated. It is defined as the average of the standard error over all measurements that have it defined. For the measurements without uncertainties, we set their standard error to $$\sigma_{\mathrm m}$$.
• The best value is then calculated as the average of the measurements ($$x_i$$), weighted by their inverse standard errors, $$\sigma_i$$: $x = \frac {\displaystyle \sum_i \frac{x_i}{\sigma_i^2}} {\displaystyle \sum_i \frac 1 {\sigma_i^2}}$ The associated error bar is: $\sigma = \left(\sum_i \frac{1}{\sigma_i^2} \right)^{-1/2}$