## Time from the Sun The Equation of Time

Solar time is based upon the apparent solar day, which is the time between two successive local noons at the same longitude. The length of the solar day varies, partly because the earth's orbit is an ellipse, and also because the earth's axis is tilted to the celestial equator.

The mean solar day is fixed at 24 hours, but the actual solar day can be nearly 22 seconds shorter or almost 29 seconds longer. These differences can build up to around 17 minutes early or 14 minutes late, (see Figure 10.1). The difference between apparent and mean solar time is called the equation of time:

Mean Solar Time = Apparent Solar Time +/— The Equation of Time

If you want greater accuracy and if you have a pocket calculator, the Equation of Time for any day can be found (approximately) using the equation:

Equation of Time = 9.87 * sin (2B) — 7.53 * cos (B) — 1.5 * sin (B)

Where:

N = day number, January 1 = Day 1and count from there.

During daylight the best means of estimating the passage of time, as opposed to telling the time, is the sun's position. The sun rises in the east and travels westwards in a great arc reaching its zenith (highest point) at noon before setting in the west. There are 360° in a circle and in each hour the sun appears to travel 15°, which lets you divide the horizon into 15° (or hourly) blocks.

Equation of Time on |
5th |
15th |
25th |
Average Change (secs) |

January |
-5m 03s |
-9m 10s |
-12m 12s |
20 |

February |
-14m 01s |
-14m 16s |
-13m 18s |
5 |

March |
-11m 45s |
-9m 13s |
-6m 16s |
16 |

April |
-2m 57s |
+0m 14s |
+ 1m 56s |
18 |

May |
+3m 18s |
+3m 44s |
+3m 16s |
4 |

June |
+ 1m 46s |
-0m 10s |
-2m 20s |
16 |

July |
-4m 19s |
-5m 46s |
-6m 24s |
20 |

August |
5m 59s |
-4m 33s |
-2m 14s |
11 |

September |
+ 1m 05s |
+4m 32s |
+8m 04s |
20 |

October |
+ 11m 20s |
14m 01s |
+ 15m 47s |
13 |

November |
+16m 22s |
15m 28s |
+13m 11s |
10 |

December |
+9m 38s |
+5m 09s |
+0m 13s |
10.1 Equation of Time Local Noon Local noon should give you one accurate time check each day but as the sun appears to hang around its zenith, timing local noon by observing the sun's zenith provides a hazy answer. If you have a compass, know its deviation and your local variation, then in theory you can find local noon by determining when the sun points due south in the northern hemisphere, or due north in the southern hemisphere. In practice this works not very well, or not at all. |

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