Scientific Background
=====================

.. contents:: Table of Contents
   :local:
   :depth: 1

Overview
--------

This document provides the scientific foundations for Planet Ruler's photographic planetary 
radius measurement method. We begin with historical context establishing the geodetic challenge, 
introduce the geometric concept of the limb arc, examine whether cameras can resolve this signal,
 and detail the mathematical methods for extracting radius from images.

.. _historical_methods:

Historical Methods
------------------

.. include:: science/historical_methods.rst

.. _geometry_basics:

Basic Geometry
--------------

.. include:: science/geometry_basics.rst

.. _camera_specifications:

Camera Specifications
---------------------

.. include:: science/camera_specifications.rst

.. _methodology:

Methodology
-----------

.. include:: science/methodology.rst

.. _detection_methods:

Detection Methods
-----------------

.. include:: science/detection_methods.rst

.. _gradient_field:

Gradient Field
--------------

.. include:: science/gradient_field.rst

References
----------

- Snyder, J. P. (1987). *Map Projections: A Working Manual*. U.S. Geological Survey Professional Paper 1395.
- Torge, W., & Müller, J. (2012). *Geodesy* (4th ed.). De Gruyter.
- Hartley, R., & Zisserman, A. (2004). *Multiple View Geometry in Computer Vision* (2nd ed.). Cambridge University Press.
- Luhmann, T., et al. (2014). *Close-Range Photogrammetry and 3D Imaging* (2nd ed.). De Gruyter.
- Szeliski, R. (2022). *Computer Vision: Algorithms and Applications* (2nd ed.). Springer.
- Kirillov, A., et al. (2023). Segment Anything. *arXiv preprint* arXiv:2304.02643.
- Young, A. T. (2006). Understanding astronomical refraction. *The Observatory*, 126, 82-115.
- Bohren, C. F., & Fraser, A. B. (1986). At what altitude does the horizon cease to be visible? *American Journal of Physics*, 54(3), 222-227.