Mathematica 2015

you are no longer in the central European time zone, so it is 13.00 zone time. Weird? To find your position you need to find the altitude of the sun at the solar noon and determine the UTC time when the solar noon occurred in your place. This means that you need to estimate your solar time first. When being at the sea, you just need to observe the sun and find the UTC time that approximately correspond to the solar noon. When that is ready, you can take your first measurements. You need to prepare graph paper with y-axis labelled angle and the x-axis labelled GMT time (when a given altitude occurred). Remember that you need to take the measurement between the horizon and the lower border of the circumference of the sun. Taking a measurement every 5 minutes throughout an hour when you estimate to have your solar noon you are likely to see a parabola made of points on the graph. Its highest point has the coordinates (x,y) which mean the solar noon in GMT time and the altitude of the sun. Finally, you need to calculate the longitude and the altitude using your Nautical Almanac for the declination of the sun in the given day. Finding longitude is relatively easy. First, you need to determine the time distance between you and Greenwich (you know the UTC time when the solar noon occurred, so you need to subtract 12 hours from it). Then, you need to convert the time in hours minutes and seconds to hours with decimals and multiply by 15 (as every time zone has 360/24=15Β°).Then, there is just one more step left. You need to apply so called equation of time. In fact, we do not see the sun moving with completely constant velocity. Hence, the difference between the expected position of sun (calculated) and the real one must be applied. You will find it in the tables. You needn’t worry about the negative values of the longitude calculated – they just indicate western hemisphere. Latitude is more work, but it is not that hard. You probably know that the angle between your latitude and the declination is equal to the missing angle between the altitude and the right angle. In other words: πœ‘ ( 𝑖 ) = 90Β° βˆ’ 𝛼 ( 𝑖 ) + (𝑖 𝑖) . Declination for a given day is given in the almanac, so the only missing variable is your altitude. To your measured value you need to apply 3 corrections: Index correction (IC) (to prevent the zeroing error – you have to determine it by yourself), height of eye correction (HC) (you will find it in the appropriate tables) and the diameter error (DE) (because the declination is given for the middle of the sun and we are measuring the altitude from the lower border in order to increase the accuracy) which is about +16’.

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