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* Add physics script for the light abberation calculation. * updating DIRECTORY.md --------- Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: cclauss <cclauss@users.noreply.github.com>
51 lines
1.4 KiB
Python
51 lines
1.4 KiB
Python
"""
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Title : Calculate Light Aberration (astronomy)
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Description :
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The below algorithm calculates astronomical light aberration as obtained
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using Special Relativity.
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"""
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from math import atan, sqrt, tan
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def get_aberration_angle(angle_rest: float, velocity_over_c: float) -> float:
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"""
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This method calculates astronomical light aberration.
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The angle at rest 'angle_rest' is given in radians [rad]
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and is in the range (-pi, pi).
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The relative velocity of observer w.r.t. to the light emitting object is
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expressed by 'velocity_over_c' that is given as ratio for velocity
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w.r.t. the speed of light c and is in the range (0, 1).
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https://en.wikipedia.org/wiki/Aberration_(astronomy)
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tan(phi/2) = sqrt((1 - v/c)/(1 + v/c)) * tan(theta/2)
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Where v is the relative velocity, phi is the observed angle with respect to the
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velocity vector (affected by light aberration), and theta is the angle observed
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angle in the limit of veclocity being equal to 0.
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Examples:
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>>> get_aberration_angle(0.2, 0.1)
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0.18102
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>>> get_aberration_angle(0.2, 0)
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0.2
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>>> get_aberration_angle(0, 0.2)
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0.0
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>>> get_aberration_angle(-1.5707963267948966, 0.7)
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-0.7954
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"""
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factor = sqrt((1 - velocity_over_c) / (1 + velocity_over_c))
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angle_ab = 2 * atan(factor * tan(angle_rest / 2))
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return round(angle_ab, 5)
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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