## What is sbpy?¶

sbpy is an Astropy affiliated package for small-body planetary astronomy. It is meant to supplement functionality provided by Astropy with functions and methods that are frequently used in the context of planetary astronomy with a clear focus on asteroids and comets.

As such, sbpy is open source and freely available to everyone. The development of sbpy is funded through NASA PDART Grant No. 80NSSC18K0987, but contributions are welcome by everyone!

## Why sbpy?¶

In our interpretation, sbpy means Python for Small Bodies - it’s the simplest acronym that we came up with that would neither favor asteroids nor comets. That’s because we equally like both!

sbpy is motivated by the idea to provide a basis of well-tested and well-documented methods to planetary astronomers in order to boost productivity and reproduceability. Python has been chosen as the language of choice as it is highly popular especially among early-career researchers and it enables the integration of sbpy into the Astropy ecosystem.

## What is implemented in sbpy?¶

sbpy will provide the following functionality once the development has been completed:

• observation planning tools tailored to moving objects

• photometry models for resolved and unresolved observations

• wrappers and tools for astrometry and orbit fitting

• spectroscopy analysis tools and models for reflected solar light and emission from gas

• cometary gas and dust coma simulation and analysis tools

• asteroid thermal models for flux estimation and size/albedo estimation

• image enhancement tools for comet comae and PSF subtraction tools

• lightcurve and shape analysis tools

• access tools for various databases for orbital and physical data, as well as ephemerides services

The development is expected to be completed in 2021. For an overview of the progress of development, please have a look at the Status Page.

Additional functionality may be implemented. If you are interested in contributing to sbpy, please have a look at the contribution guidelines.

## Module Structure¶

sbpy consists of a number of sub-modules, each of which provides functionality that is tailored to individual aspects asteroid and comet research. The general module design is shown in the following sketch.

The functionality of version 1.0, which will be finalized in 2021, is detailed below. Please refer to the Status Page to inquire the current status of each module.

### sbpy.data¶

The data module provides data containers used throughout sbpy for orbital elements (Orbit), ephemerides (Ephem), observations (Obs), physical properties (Phys), and target names (Names). Instances of these classes are used as input to and output for a wide range of top-level functions throughout sbpy, guaranteeing a consistent and user-friendly API. All classes in data provide query functions to obtain relevant information from web-based services such as JPL Horizons, Minor Planet Center (MPC), IMCCE, and Lowell Observatory, providing orbital elements at different epochs, ephemerides, physical properties, observations reported to the MPC, (alternative) target identifiers etc.

Additional functionality of data includes an interface to the orbit fitting software OpenOrb and an interface to SPICE for offline ephemerides calculations using SpiceyPy, for which we will provide utilities tailored to the needs of the small body community. Examples for how to use sbpy with ephemerides calculation package PyEphem and orbital integrator REBOUND (Rein and Liu 2012) will be provided as notebooks.

data also provides a range of other useful module-level functions: image_search queries the Solar System Object Image Search function of the Canadian Astronomy Data Centre, providing a table of images that may contain the target based on its ephemerides. sb_search uses IMCCE’s Skybot; given a registered FITS image, the function will search for small bodies that might be present in the image based on their ephemerides. pds_ferret queries the Small Bodies Data Ferret at the Planetary Data Systems Small Bodies Node for all existing information on a specific small body in the PDS.

### sbpy.activity¶

The activity module provides classes for modeling cometary comae, tails, ice sublimation. We have implemented the Haser gas coma model (Haser, Haser 1957), and a Vectorial model is planned (Vectorial, Festou 1981). Some parameters for commonly observed molecules (e.g., H2O, CO2, CO, OH, CN, C2), such as photo-dissociation timescale and fluorescence band strength, are included. The gas coma classes can be used to generate aperture photometry or a synthetic image of the comet.

For dust, we have simple photometric models based on the Afρ and εfρ quantities (A’Hearn et al. 1984; Kelley et al. 2013). A syndyne/synchrone model (Syndynes, Finson & Probstein 1968; Kelley et al. 2013) is planned.

The activity module includes LTE and non-LTE radiative transfer models used to determine production rates and excitation parameters, such as the temperature in the coma. In the inner regions of the coma collisions dominate molecular excitation and the resulting rotational level population is close to LTE. Beyond the LTE inner region, the level populations start to depart from the equilibrium distribution because the gas density is not high enough to reach thermodynamic equilibrium through collisions with neutrals. The inclusion of all relevant excitation processes in cometary atmospheres in a complex 3-dimensional outgassing geometry represents a state-of-the-art coma model which will provide a baseline for interpretation of cometary spectroscopy observations.

The Cowan & A’Hearn (1979) ice sublimation model (sublimation), used to describe comet activity, and common parameters will also be added.

### sbpy.photometry¶

The photometry module implements a number of light scattering models for asteroidal surfaces and cometary coma dust. The goal of this module is to provide a facility to fit light scattering models to observed brightness data of asteroids, and to estimate the brightness of asteroids and cometary comae under specified geometry based on scattering models. Specifically, we include a number of disk-integrated phase function models for asteroids, bidirectional reflectance (I/F) models of particulate surfaces, and phase functions of dust grains in cometary comae. The disk-integrated phase function models of asteroids include the IAU adopted (H, G1 , G2) system (Muinonen et al. 2010), the simplified (H, G12) system (Muinonen et al. 2010), as well as the classic IAU (H, G) system. The disk-resolved bidirectional reflectance model includes a number of models that have been widely used in the small bodies community, such as the Lommel-Seeliger model, Lambert model, Lunar-Lambert model, etc. Surface facet geometries used in the different models can be derived with methods in shape. We also include the most commonly used 5-parameter version of the Hapke scattering model. Empirical cometary dust phase functions are implemented, too (Marcus 2007; Schleicher & Bair 2011, https://asteroid.lowell.edu/comet/dustphase.html). Some single-scattering phase functions such as the Henyey-Greenstein function will also be implemented.

### sbpy.shape¶

The shape module provides tools for the use of 3D shape models of small bodies and the analysis of lightcurve observations. The user can load asteroid shapes saved in a number of common formats, such as VRML, OBJ, into Kaasalainen, and then calculate the geometry of illumination and view for its surface facets, and manipulate it. Furthermore, Kaasalainen will provide methods for lightcurve inversion. shape will provide an interface to use shape models for functions in photometry.

In addition to the shape model methods, shape also provides methods for the analysis and simulation of simple lightcurve data. The Lightcurve class provides routines to fit rotational period (based on Lomb-Scargle routines implemented in stats and other frequency tools), Fourier coefficients, and spin pole axis orientation. The class will also be able to simulate a lightcurve at specified epochs with a shape model class and the associated information such as pole orientation, illumination and viewing geometry as provided by the Phys class, and a scattering model provided through classes defined in the photometry module.

### sbpy.spectroscopy¶

As part of spectroscopy, we provide routines for fitting measured spectra, as well as simulating synthetic spectra over a wide range of the electromagnetic spectrum. The spectral models include emission lines relevant to observations of comet comae, as well as reflectance spectra of asteroid and comet surfaces. The module provides functions to fit and remove baselines or slopes, as well as to fit emission lines or reflectance spectra.

In addition to the aforementioned functionality, we provide a class Hapke that implements Hapke spectral mixing functionality.

This module also provides spectrophotometry methods as part of Spectrophotometry. This functionality includes the transmission of spectra (empirical, generated, or from the literature) through common photometric filters, and the derivation of photometric colors from spectral slopes with SpectralGradient.

### sbpy.thermal¶

Thermal modeling capabilities for asteroids are available through the thermal module. The module provides implementations of the Standard Thermal Model (STM, Morrison & Lebofsky 1979), the Fast-Rotating Model (FRM, Lebofsky & Spencer 1989), and the popular Near-Earth Asteroid Thermal Model (NEATM, Harris 1998) which can all be used in the same way for estimating fluxes or fitting model solutions to observational data.

### sbpy.imageanalysis¶

The imageanalysis module will focus on the analysis of telescopic images. Centroid provides a range of centroiding methods, including a dedicated comet centroiding technique that mitigates coma and tail biases (Tholen & Chesley 2004). Code will also be developed to incorporate ephemerides into FITS image headers to facilitate image reprojection in the rest frame of the moving target (moving_wcs) for image co-addition, e.g., using SWARP (Bertin 2002). We will modify and integrate cometary coma enhancement code from collaborator Samarasinha (CometaryEnhancements; Samarasinha & Larson 2014; Martin et al. 2015). The coma enhancements will be coded into a plugin for the Ginga Image Viewer.

imageanalysis will also provide PSF subtraction functionality that is utilizing and extending the Astropy affiliated package photutils; this class will provide wrappers for photutils to simplify the application for moving object observations. Results of imageanalysis.PSFSubtraction routines can be directly used in imageanalysis.Cometary- Enhancements for further analysis.

### sbpy.obsutil¶

The obsutil module enables the user to conveniently check observability of moving targets and to plan future observations. Using Ephem functionality, obsutil provides tools to identify peak observability over a range of time based on different criteria, create observing scripts, plot quantities like airmass as a function of time, and create finder charts for an individual target. These functions and plots will be easily customizable and will work identically for individual targets and large numbers of targets. Finder charts will be produced from online sky survey data, providing information on the target’s track across the sky, it’s positional uncertainty, background stars with known magnitudes for calibration purposes, and other moving objects.

### sbpy.bib¶

bib provides an innovative feature that simplifies the acknowledgment of methods and code utilized by the user. After activating the bibliography tracker in bib, references and citations of all functions used by the user are tracked in the background. The user can request a list of references that should be cited based on sbpy functionality that was used at any time as clear text or in the LATeX BibTex format.

### sbpy.calib¶

sbpy.calib includes calibration methods, including the photometric calibration of various broad-band filters relative to the Sun’s or Vega’s spectrum.

## Design Principles - The Zen of sbpy¶

In the design of sbpy, a few decisions have been made to provide a highly flexible but still easy-to-use API. These decisions are summarized in the Design Principles, or, the Zen of sbpy.

Some of these decisions affect the user directly and might be considered unnecessarily complicated by some. Here, we review and discuss some of these principles for the interested user.

### Physical parameters are quantities¶

sbpy requires every parameter with a physical dimension (e.g., length, mass, velocity, etc.) to be a astropy.units.Quantity object. Only dimensionless parameters (e.g., eccentricity, infrared beaming parameter, etc.) are allowed to be dimensionless data types such as floats.

The reason for this decision is simple: every astropy.units.Quantity object comes with a physical unit. Consider the following example: we define a Phys object with a diameter for asteroid Ceres:

>>> from sbpy.data import Phys
>>> ceres = Phys.from_dict({'targetname': 'Ceres',
...                         'diameter': 945})


Of course, everybody knows that Ceres’ diameter is 945 km. But this is not clear from this definition:

>>> ceres['diameter']
945


Any functionality in sbpy thus has to presume that diameters are always given in km. This makes sense for large objects - but what about meter-sized objects like Near-Earth asteroids?

Following the Zen of Python (explicit is better than implicit), we require that units are explicitly defined:

>>> import astropy.units as u
>>> ceres = Phys.from_dict({'targetname': 'Ceres',
...                         'diameter': 945*u.km})
>>> ceres
<QTable length=1>
targetname diameter
km
str5    float64
---------- --------
Ceres      945.0


This way, units and dimensions are always available where they make sense and we can easily convert between different units:

>>> ceres['diameter'].to('m')
[945000.] m


### Epochs must be Time objects¶

The same point in time can be described by a human-readable ISO time string ('2019-08-08 17:11:19.196') or a Julian Date (2458704.216194403), as well as other formats. Furthermore, these time formats return different results for different time scales: UT ISO time '2019-08-08 17:11:19.196' converts to '2019-08-08 17:12:28.379' using the TDB time scale.

In order to minimize confusion introduced by different time formats and time scales, sbpy requires that epochs and points in time are defined as Time objects, which resolve this confusion:

>>> from sbpy.data import Obs
>>> from astropy.time import Time
>>> obs = Obs.from_dict({'epoch': Time(['2018-01-12', '2018-01-13']),
...                      'mag': [12.3, 12.6]*u.mag})
>>> obs['epoch']
['2018-01-12 00:00:00.000' '2018-01-13 00:00:00.000']


Time objects can be readily converted into other formats:

>>> obs['epoch'].jd
[2458130.5 2458131.5]
>>> obs['epoch'].mjd
[58130. 58131.]
>>> obs['epoch'].decimalyear
[2018.03013699 2018.03287671]
>>> obs['epoch'].iso
['2018-01-12 00:00:00.000' '2018-01-13 00:00:00.000']


… as well as other time scales:

>>> obs['epoch'].utc.iso
['2018-01-12 00:00:00.000' '2018-01-13 00:00:00.000']
>>> obs['epoch'].tdb.iso
['2018-01-12 00:01:09.184' '2018-01-13 00:01:09.184']
>>> obs['epoch'].tai.iso
['2018-01-12 00:00:37.000' '2018-01-13 00:00:37.000']


See Epochs and the use of astropy.time and Time for additional information.

### Use sbpy DataClass objects¶

Finally, we require that topically similar parameters are bundled in DataClass objects, which serve as data containers (see this page for an introduction).

This containerization makes it possible to keep data neatly formatted and to minimize the number of input parameters for functions and methods.