form a MATLAB function which calculates the difference between TAI

Please, form a MATLAB function which calculates the difference between TAI (International Atomic Time) and UTC (Universal Time Coordinated) for any given date. The date should be given in Year, Month, Day, Hour, Minute and Second format. https://www.timeanddate.com/time/leap-seconds-future.html

Answer 1

[Arjun]

Hi @Oktay,

I see that you want to create a MATLAB function to calculate the time difference between the TAI and UTC time.

To calculate the time difference between TAI and UTC you have to consider the list of leap seconds which are updated from time to time and also the initial time difference which is 10 seconds. Kindly refer to the code below for better understanding:

function tai_utc_diff = calculateTAI_UTC(year, month, day, hour, minute, second) 
    % List of leap seconds added to UTC since 1972 
    leap_seconds = { 
        datetime(1972, 7, 1), 10; 
        datetime(1973, 1, 1), 11; 
        datetime(1974, 1, 1), 12; 
        datetime(1975, 1, 1), 13; 
        datetime(1976, 1, 1), 14; 
        datetime(1977, 1, 1), 15; 
        datetime(1978, 1, 1), 16; 
        datetime(1979, 1, 1), 17; 
        datetime(1980, 1, 1), 18; 
        datetime(1981, 7, 1), 19; 
        datetime(1982, 7, 1), 20; 
        datetime(1983, 7, 1), 21; 
        datetime(1985, 7, 1), 22; 
        datetime(1988, 1, 1), 23; 
        datetime(1990, 1, 1), 24; 
        datetime(1991, 1, 1), 25; 
        datetime(1992, 7, 1), 26; 
        datetime(1993, 7, 1), 27; 
        datetime(1994, 7, 1), 28; 
        datetime(1996, 1, 1), 29; 
        datetime(1997, 7, 1), 30; 
        datetime(1999, 1, 1), 31; 
        datetime(2006, 1, 1), 32; 
        datetime(2009, 1, 1), 33; 
        datetime(2012, 7, 1), 34; 
        datetime(2015, 7, 1), 35; 
        datetime(2017, 1, 1), 36; 
        datetime(2023, 1, 1), 37; 
    }; 
    % Create a datetime object for the input date 
    input_date = datetime(year, month, day, hour, minute, second); 
    % Initialize TAI-UTC difference 
    tai_utc_diff = 10; 
    % Loop through leap seconds and find the applicable difference 
    for i = 1:size(leap_seconds, 1) 
        if input_date >= leap_seconds{i, 1} 
            tai_utc_diff = leap_seconds{i, 2}; 
        else
            break; 
        end 
    end
end 

% Example: Calculate TAI-UTC difference for January 1, 2024, at 12:00:00 
diff = calculateTAI_UTC(2024, 1, 1, 12, 0, 0); 
fprintf('TAI-UTC difference: %d seconds\n', diff); 

Kindly refer to the documentation of “datetime” function of MATLAB to for better understanding of handling dates and time: https://www.mathworks.com/help/releases/R2021a/matlab/ref/datetime.html

I hope this will help!

[Walter Roberson]

You do not need the loop.

idx = find(input_date >= cell2mat(leapseconds(:,1)), 1, 'first');
tai_utc_diff = leap_seconds{idx,2};