【天文】基于Matlab模拟太阳位置跟踪和日行迹现象

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⛄ 内容介绍

由于地球的倾斜和围绕太阳的轨道的偏心率，太阳在天空中的轨迹取决于一年中的时间和观测的纬度。 “analemma”是由地球轨道与太阳的偏心率和倾斜引起的现象。如果您设置相机并在一年中每隔 24 小时拍摄一次太阳照片，天空中就会出现一个“无限大”的符号。八字形表示“表观太阳时”（正午 = 太阳直接在头顶）与“平均太阳时”（时钟计算 24 小时天）之间的差异。

⛄ 部分代码

function [azimuthAngle,elevationAngle] = sunPosition(dayOfYear, ...

   timeHour,latitude)

% Copyright 2016 The MathWorks, Inc.

% Make sure time vector is oriented properly

if size(timeHour,1) == 1 && size(timeHour,2) > 1

   timeHour = timeHour';

end

% Make sure day vector is oriented properly

if size(dayOfYear,2) == 1 && size(dayOfYear,1) > 1

   dayOfYear = dayOfYear';

end

% Account for Multiple Days

numTime = numel(timeHour);

numDays = numel(dayOfYear);

timeHour = repmat(timeHour,1,numDays);

% Shift solar noon for longitude

longitudeShift = 0;

% Equation of Time - East/West timeshift associated with elliptical orbit

equationTime = 9.87*sind(2*360/365*(dayOfYear-81)) - ...

   7.53*cosd(360/365*(dayOfYear-81)) - ...

   1.5*sind(360/365*(dayOfYear-81));

solarTimeCorrection = equationTime/60 + longitudeShift/15;

solarTime = timeHour + repmat(solarTimeCorrection,numTime,1);

% Angle of Sun - Related to Solar time (0 deg - vertical sun)

hourAngle = 180*(12-solarTime)/12;

% Sun Declination - varies from +/- 23.45 during year

sunDeclinationAngle = 23.45*sind(360/365*(dayOfYear-81));

% Solar Zenith Angle Calculations

cosineZenith = bsxfun(@plus,sind(latitude)*sind(sunDeclinationAngle),...

   cosd(latitude)*bsxfun(@times,cosd(sunDeclinationAngle),cosd(hourAngle)));

zenithAngle = acosd(cosineZenith);

elevationAngle = 90 - zenithAngle;

% sunUp = elevationAngle > 0;

% Solar Azimuth Angle Calculations

eastVertical = bsxfun(@times,cosd(sunDeclinationAngle),sind(hourAngle));

southVertical = bsxfun(@plus,-sind(sunDeclinationAngle)*cosd(latitude), ...

   bsxfun(@times,cosd(sunDeclinationAngle),sind(latitude)*cosd(hourAngle)));

posAngle = eastVertical > 0;

azimuthAngle = zeros(numTime,numDays);

azimuthAngle(posAngle) = acosd(-southVertical(posAngle)./ ...

   sqrt(eastVertical(posAngle).^2 + southVertical(posAngle).^2));

azimuthAngle(~posAngle) = 180 + acosd(southVertical(~posAngle)./ ...

   sqrt(eastVertical(~posAngle).^2+southVertical(~posAngle).^2));

azimuthAngle = -azimuthAngle;

end

⛄ 运行结果

编辑

⛄ 参考文献

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