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@brandon-rhodes
Created April 14, 2013 20:32
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A quick iPython Notebook showing the algorithm that libastro, and thus PyEphem, uses to adjust the visual altitude of objects that are 15° or higher in the sky. (For objects closer to the horizon, a different formula is used; see `refract.c`.)
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{
"metadata": {
"name": "refraction"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "# Atmospheric angle correction in libastro and PyEphem\n\nThe following graph shows the difference, as one moves up the sky from 15\u00b0 to overhead at 90\u00b0, between the apparent position of a celestial body and its actual position."
},
{
"cell_type": "code",
"collapsed": false,
"input": "%pylab inline",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "\nWelcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\nFor more information, type 'help(pylab)'.\n"
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": "pr = 1010.0 # pressure, millibar\ntr = 25.0 # temperature, C",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": "# Difference between True angle and Apparent angle\n\ndef ta(aa):\n return 7.888888e-5 * pr / ((273 + tr) * tan(aa))",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 26
},
{
"cell_type": "code",
"collapsed": false,
"input": "# aa = Apparent angle\n\naa = linspace(15.0 * pi / 180.0, 90.0 * pi / 180.0, 200)\nplot(aa, ta(aa))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 27,
"text": "[<matplotlib.lines.Line2D at 0xb41728c>]"
},
{
"output_type": "display_data",
"png": 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}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So the big question is, does this adjustment drive towards zero fast enough that the adjustment does not push the answer \u201cover to the other side of the sky\u201d even for a moment as it nears 90\u00b0?"
},
{
"cell_type": "code",
"collapsed": false,
"input": "# aa = Apparent angle\n\naa = linspace(89.99 * pi / 180.0, 90.0 * pi / 180.0, 200)\nplot(aa, ta(aa))",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 28,
"text": "[<matplotlib.lines.Line2D at 0xb4f03ac>]"
},
{
"output_type": "display_data",
"png": 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ubq43X2rA8Pc9LyvH/v37z/tYThMo9xz0Pi/rd6p6z/fv30+/fv2YO3cuERER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\nh9NALyLicBroRUQcTgO9iIjD/R/7nP6n8giVJQAAAABJRU5ErkJggg==\n"
}
],
"prompt_number": 28
},
{
"cell_type": "markdown",
"metadata": {},
"source": "So it looks like the approach towards 90.0\u00b0 is, at the very end, linear \u2014 without any possibility of overshooting and then working its way back. Good!"
}
],
"metadata": {}
}
]
}
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