How to calculate the latitudinal and longitudinal coverage of the area of the circle that subtends an angle of 4 degree at the location on the surface of the Earth?

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megha 2024-1-3

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https://ww2.mathworks.cn/matlabcentral/answers/2065856-how-to-calculate-the-latitudinal-and-longitudinal-coverage-of-the-area-of-the-circle-that-subtends-a

评论： megha 2024-1-3

For example, [-11.9459279123647, -76.84862390044384] are the geographical lat-long of the location of the ground station on the surface of the Earth. Consider it taking an observation above 100 km from the surface of the Earth with 4 degree field of View. Applying parallax method, I calculated that at 100 km altitude the radius of the circle will be (100km * sin(4 degree)) = 3.49 km, and hence the area of the circle will be (pi*r^2) = 38.24551 km^2.

Now, I would like to obtain the range of geographical latitude and longitude that will be covered under this circle at 100 km.

Similarly I would like to obtain the coverage at 200 km, 300 km and so on. But, first things first. Let's start from just 100 km. I can loop it for diffrernt altitudes by my own.

Any suggestions are appreciated.

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Answer 1

Sulaymon Eshkabilov 2024-1-3

在 MATLAB Online 中打开

It is something like this way:

% Given Data:

centerLatLong = [-11.9459279123647, -76.84862390044384]; % Latitude and Longitude of the center

ALT100 = 100; % Altitude in 100km

ALT200 = 200; % Altitude in 200km

ALT300 = 300; % Altitude in 300km

Angle = 4; % Field of view angle in degrees

ALT = [ALT100, ALT200, ALT300];

% Plot Line Style Options:

L = {};

LT = '--:-.-';

MT = 'vodp';

CT ='rgbk';

LW = 3:-.75:.5;

for ii = 1:numel(ALT)

% Radius of the circular area:

R = ALT(ii) * sind(Angle);

% Latitudinal and longitudinal coverage:

latCoverage = asin(R / 6371) * (180 / pi); % 6371 km is Approx. Earth radius

longCoverage = R / (6371 * cosd(centerLatLong(1)));

% Range of latitudes and longitudes covered:

minLat = centerLatLong(1) - latCoverage;

maxLat = centerLatLong(1) + latCoverage;

minLong = centerLatLong(2) - longCoverage;

maxLong = centerLatLong(2) + longCoverage;

LATCov = [minLat; maxLat];

LONCov =[minLong; maxLong];

STYLO = [CT(ii), LT(ii), MT(ii)];

plot(LONCov, LATCov, STYLO, 'LineWidth',LW(ii))

L{ii} = ['Altitute at ' num2str(ALT(ii)) ' km'];

hold on

legend(L{:}, 'Location', 'Best')

% Display the results:

disp(['Coverage in ' num2str(ALT(ii)) ' km altitude']);

disp(['Latitude Range: ', num2str(LATCov(1)), ' to ', num2str(LATCov(2))]);

disp(['Longitude Range: ', num2str(LONCov(1)), ' to ', num2str(LONCov(2))]);

end

Coverage in 100 km altitude

Latitude Range: -12.0087 to -11.8832

Longitude Range: -76.8497 to -76.8475

Coverage in 200 km altitude

Latitude Range: -12.0714 to -11.8205

Longitude Range: -76.8509 to -76.8464

Coverage in 300 km altitude

Latitude Range: -12.1341 to -11.7577

Longitude Range: -76.852 to -76.8453

xlabel('Longitude')

ylabel('Latitude')

grid on

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Sulaymon Eshkabilov 2024-1-3

在 MATLAB Online 中打开

If you want the values of R as well, this is the change in the code:

for ii = 1:numel(ALT)
% Radius of the circular area:
R(ii) = ALT(ii) * sind(Angle);
fprintf('Radius:  %f km at the Altitude of %d km \n', R(ii), ALT(ii));
% Latitudinal and longitudinal coverage:
latCoverage = asin(R(ii)/ 6371) * (180 / pi);  % 6371 km is Approx. Earth radius
longCoverage = R(ii)/ (6371 * cosd(centerLatLong(1)));
...
end