Astronomical Time: Sidereal, Solar and the Equation of Time
Why a day measured against a star is four minutes shorter than a day measured against the Sun, and why a sundial can be a quarter of an hour out and still be right.
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How long is a day? 🕰️
A day is one turn of the Earth. That sounds like one number, but it is two, and they differ by about four minutes. The difference is not a flaw in the Earth's spin. It comes from the fact that the Earth is also **going somewhere** while it turns. Get that one idea and most of this topic follows from it, including why the Moon takes longer to go through its phases than to go round the Earth.
Star time and Sun time ⭐
The two days are measured against different things. Neither is wrong; they answer different questions.
The gap ➖
An interactive activity.
Where do the four minutes come from? 🌍
The Earth completes one full turn in 23 hours 56 minutes. Why does it then take a further four minutes for the Sun to return to the same place in the sky?
- The Earth has moved about a degree along its orbit, so it must turn slightly further to face the Sun again
- The Earth's spin slows down slightly each day
- The atmosphere bends the sunlight and delays sunrise
- The Sun is moving through the galaxy and drags the Earth behind it
The same idea, for the Moon 🌙
The Moon has two months for exactly the same reason the Earth has two days. While the Moon goes round the Earth, the whole system moves along the Earth's orbit, so the Moon needs extra time to line up with the Sun again.
The other gap 🧮
An interactive activity.
Three kinds of time ☀️
Once you accept that solar days are not all exactly the same length, you need more than one kind of time:
The Equation of Time 📝
Apparent Solar Time is the time shown by a _____. Mean Solar Time runs at a perfectly _____ rate all year. The Equation of Time is AST _____ MST, so a positive value means the sundial is _____ the clock. It reaches about _____ minutes in early November.
Two causes, not one ⚖️
The Equation of Time is not one effect but **two**, added together. **1. The Earth's orbit is an ellipse.** The Earth moves fastest when it is closest to the Sun, so the Sun appears to run through the sky at a changing rate during the year. **2. The Earth's axis is tilted** by about 23.5 degrees. The Sun's apparent path is the ecliptic, which is tilted against the celestial equator that our clocks are effectively measured along. Because the two effects have different periods, they add to a curve with **two unequal peaks** in a year: about **+16 minutes in early November** and about **-14 minutes in mid-February**.
Which two produce it? ✅
Select the TWO effects that combine to produce the Equation of Time.
- The Earth's orbit is elliptical, so its orbital speed changes through the year
- The Earth's axis is tilted, so the ecliptic is inclined to the celestial equator
- The Earth's axis precesses over about 25,800 years
- The Moon pulls the Earth slightly out of position each month
Plot the maximum 📈
An interactive activity.
Order the reasoning 🪜
An interactive activity.
The summary 🖊️
A sidereal day is about _____ minutes shorter than a solar day, because the Earth must turn a little _____ to face the Sun again. The sidereal month is about _____ days and the synodic month is about _____ days. The correction between sundial time and clock time is called the _____.
Your turn ✍️
An interactive activity.