Time apparent Sun and mean Sun the Equation

Time ‘apparent Sun’ and ‘mean Sun’ the Equation of Time

Solar time Solar Day: Interval of time between successive passages of the Sun Here, the brown mountain on the Earth is pointing at the Sun Mean solar day = 24 hours Q: When does the mountain next point at the Sun? A: After 360 O, the motion along the orbit means it has to turn a little more to point at the Sun The Earth moving in its orbit as it spins

Apparent Sun & Mean Sun the simple facts Earth spins on its axis at a constant rate Earth does not orbit the Sun at a constant speed so Sun’s doesn’t change position at a constant rate (and the length of each day would vary slightly). Apparent Sun = real position of Sun. Mean Sun = imaginary position of Sun if the Earth’s orbital speed was constant This would mean the Sun would move across the sky at a constant rate and that all days would be same length.

Here’s a more detailed explanation… Why make things complicated by using words like ‘apparent Sun’ and ‘mean Sun’? Things to remember. . 1) The words ‘apparent’ and ‘mean’ don’t have their common everyday meanings. 2) The ‘apparent Sun’ does not mean something that is thinks it’s the Sun but isn’t really, and the ‘mean Sun’ does not refer to the Sun being in a bad mood!! ‘Mean’ actually means average in this case. 3) To make our lives easier, we might prefer it if the length of a solar day was the same for every day of the year. (solar day is the time between when the Sun is overhead one two successive day). Unfortunately, the length of the solar day depends on where the Earth is in its orbit because the Earth’s orbital speed changes, depending on where it is in its orbit. (The following slides will explain this using animations). Apparent Sun refers to where the Sun actually is. But we like the idea of all days being the same length of time, so we came up with the idea of ‘mean Sun’ and ‘mean solar time’… Mean Sun is the imaginary position in the sky where the Sun would be if its orbital speed was constant. This would mean all days would be exactly the same length. Mean solar time is the time it would be using the position of the (imaginary) mean Sun.

Although the planet rotates on its axis at a constant speed, its speed in orbit varies because the orbit shape is elliptical Planet’s orbital speed is decreasing Planet’s orbital speed is slowest when planet is furthest from Sun sun Planet’s orbital speed is increasing Planet’s orbital speed is fastest when planet is closest to Sun

When the orbital speed is slow, When the orbital speed is fast, the length of the solar day is shorter the length of the solar day is longer

Equation of time isn’t an equation; it’s a fudge factor which links mean solar time (as shown on a clock) and apparent solar time (as shown by a sundial). Apparent solar time and Mean solar time would be the same if Earth’s orbit was circular and Earth’s axis was perpendicular to its orbit… BUT IT ISN’T… Earth’s orbit is elliptical It’s orbital speed varies the Sun is at one focus not at the centre Slower speed in this part of the orbit Clock time sundial time Faster speed in this part of the orbit fiddle factor Mean Solar Time = Apparent Solar Time – Equation of Time The difference is zero 4 times a year (15 April, 14 June, 1 September, 25 December. The maximum is 16 minutes in early November