HG1G2 tools

This page includes documentation and tools for H,G₁,G₂ and H,G₁₂ photometric systems. These systems are empirical functions that are used to fit the observations (visual magnitudes) of asteroids as a function of the phase angle. The main purpose for these systems, together with the previous H,G system, is to predict the magnitude H of an asteroid at the exact backscattering direction as the phase angle is 0. This so-called absolute magnitude H is related to the size and albedo of an asteroid, and one of these three can be computed if the other two are known.

The H,G₁,G₂ system was chosen to replace the old H,G system as the tool recommended by the IAU at its general assembly in Beijing, August 2012. The system is described in Muinonen et al. (2010). For smooth adaptation of this system, we have implemented tools that can be used to fit observations with the H,G₁,G₂ and H,G₁₂ functions. We are distributing so-called reference implementations of the system on different languages/platforms. The main idea is that they should all implement the same functionality, despite the programming language or computing platform.

Reference implementations

• Fortran 2003 version (HG1G2tools module and Example fit, or zip file for codes, readme and example data.) (version at 2013-08-29)
• Mathematica version (HG1G2tools package and Example fit) (version at 2013-08-29)

Other tools

• Online implementation of the H,G₁,G₂ system in flux space (2015) with automatic model selection
• For Python, we recommend the Python-package sbpy, an Astropy affiliated package for asteroid and comet researchers. It has the H,G₁,G₂ and H,G₁₂ photometric systems implemented. An example how to fit observations using sbpy is here (Python Jupyter notebook or PDF), using scipy.optimize function minimize.
• Example data from (44) Nysa
• Original Fortran 77 version
• (Deprecated) Python version (HG1G2tools package) (version at 2016-04-20)

Contribute

You are more than welcome to contribute. If you are interested in creating a reference implementation using some language or platform that is currently lacking an implementation, please read guide for developers and send your source code here for distribution. All other tools that are somehow related to H,G₁,G₂ system are also welcomed!

You can contact Antti.I.Penttila( a t )helsinki.fi for more information.

References

Reference to this page: A. Penttilä, Collection of tools for H,G₁,G₂ system, http://wiki.helsinki.fi/display/PSR/HG1G2+tools (2012).

Reference to IAU-adopted version: K. Muinonen, I.N. Belskaya, A. Cellino, M. Delbò, A.-C. Levasseur-Regourd, A. Penttilä, E.F. Tedesco (2010). A three-parameter magnitude phase function for asteroids, Icarus 209(2), 542-555. DOI:10.1016/j.icarus.2010.04.003 (local copy)

Reference to 2015 flux space extension and online implementation: A. Penttilä, V.G. Shevchenko, O. Wilkman, K. Muinonen (2016). H,G₁,G₂ photometric phase function extended to low-accuracy data, Planetary and Space Science 123, 117-125, DOI:10.1016/j.pss.2015.08.010 (local copy)