When is nightime the same length as daytime?

19 March, 2010

Sunrise
Image of a sunrise from the University Corporation for Atmospheric Research Digital Image Library
Image: University Corporation for Atmospheric Research
Source: University Corporation for Atmospheric Research

Question: When is the nighttime exactly the same length as the daytime?

Answer: You might think this is an easy question, but sometimes simple questions can have complicated answers.

Many people would say that the day with the same amount of daytime and nighttime, exactly 12 hours each, is called the equinox. But astronomers would say that there are three things wrong with this statement!

Firstly, the equinox is not a day, but is a single moment in time. At that moment, the Sun appears to lie directly over the celestial equator, the imaginary line in the sky that divides the southern hemisphere from the northern hemisphere in the sky. Before the March equinox the Sun appears to be in the southern hemisphere in the sky; after the equinox the Sun appears to be in the northern hemisphere in the sky. In 2010 the equinox occurs at exactly 6:32am AEDT on March 21st. So this day is not 'the equinox'. Instead, it is the day on which the equinox occurs.

Secondly, this day does not have exactly 12 hours of daylight and 12 hours of night, because this day is not exactly 24 hours long! A previous question discussed the difference between clock time and Sun time. At the March equinox, the length of the day is just slightly less than 24 hours, and so the daytime plus nighttime are not exactly 24 hours long.

Thirdly, on the 21st the daytime is longer than the nighttime, by around 12 minutes. There are two reasons for this.

We define sunrise to be when the top edge of the Sun first hits the horizon, and sunset to be the moment that the top edge of the Sun finally goes below the horizon. This is because the Sun is so bright that even a tiny fraction of the Sun being above the horizon makes an enormous difference to the light levels. But because the Sun takes around 2 minutes to cross the horizon, it means that, if everything else was equal, daytime would be 4 minutes longer than nighttime. (To make daytime equal to nighttime we would have to define sunrise or sunset as being when the Sun was halfway across the horizon.)

However everything else is not equal. The atmosphere bends the light from the Sun in a way that means that we see the Sun rise a few minutes earlier than it would if the sunlight was traveling in a perfectly straight line. The amount of this refraction varies according to atmospheric conditions, but for standard conditions we see the Sun rise about 4 minutes earlier than it would if there was no atmospheric refraction.

The combination of these two effects means that on the 21st, the day on which the equinox falls, the daytime is 12 minutes longer than the nighttime. The day on which nighttime and daytime are of equal length, and on which the sunrise is seen due east and the sunset is seen due west is three days later, on March 24th.

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