Astronomical Time: Sidereal, Solar and the Equation of Time

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

A sidereal day lasts 23 hours 56 minutes and a solar day lasts 24 hours 00 minutes. How many minutes longer is the solar day?

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

The sidereal month is about 27.3 days and the synodic month is about 29.5 days. How many days longer is the synodic month? Give your answer to one decimal place.

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

This graph shows the Equation of Time in minutes (up) against the month (across), taken on the 1st of each month. September, October and December are plotted for you: about 0, +10 and +11 minutes. Plot the value for 1 November, when the sundial runs about +16 minutes ahead of the clock.

Order the reasoning

Put the explanation of the four-minute difference into a logical order.

• The Earth completes one full 360 degree turn in about 23 hours 56 minutes
• During that turn the Earth has also moved about one degree along its orbit
• A distant star is therefore back in the same place, but the Sun is not
• The Earth must turn about one degree further for the Sun to return to the meridian
• That extra degree takes about four minutes, making the solar day 24 hours

Sidereal against solar

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 _____.

Explain the sundial's quarter hour

A friend has read that a sundial in November is "a quarter of an hour wrong". Write an explanation for them showing that the sundial is not wrong at all.

• Explain the difference between apparent solar time and mean solar time
• Say what the Equation of Time is, and what a value of about +16 minutes means
• Give the two causes of the Equation of Time, and say why there are two peaks in a year rather than one
• Use the sidereal and solar day to explain why solar days are not all the same length in the first place