Statement: The Earth rotates on its axis 366.25 times per year
That is, when the Earth completes one whole revolution around the Sun (360 degrees), which is a year, it has rotated on its own axis 366.25 times.
This is going to be old news to some people, but I think it will still catch a lot of people out. The obvious thing I am hoping you are wondering here is that you thought there were only 365 days in a year. Some of you will know there are actually 365.25 days in a year, hence the reason for a leap year every 4 years. But where does that extra rotation come from to make it 366.25?
Have a think before reading the solution below. Hopefully the wonders of jQuery will have hidden it from you until you click.
The first clue is to know the difference between a Solar day and a Sidereal day.
A Solar day is 24 hours. This is measured as the time it takes for the Sun to move across the sky from a fixed position until it returns the following day to the exact same location. So for (a famous) example, 12:00 (midday, noon) UTC is defined when the Sun is directly south from Greenwich, London, UK. When the Sun returns the next day to be exactly south in Greenwich again, 1 Solar day has elapsed.
A Sidereal day on the other hand is 23.93446959 hours, which is the time it takes for the Earth to complete one rotation. That is, the time it take to rotate through 360 degrees. This is different to a Solar day in a way that will be explained.
Referring to the image shown (click to enlarge); The Earth's starting reference position is shown as facing the Sun vertically (in this image). You can see that as the Earth completes one rotation, which is 360 degrees, which is a Sidereal day, it is facing the same way, i.e. vertically up, BUT...you have to take into account the fact that the Earth is also revolving around the Sun at the same time. So after the Earth has revolved 360 degrees, it has also shift approximately 1 degree around the Sun, so it is not facing the Sun anymore. It needs to rotate that extra 1 degree to bring the Sun back inline with its reference point, i.e. to complete 1 Solar day.
This happens every day. Every day the Earth rotates 360 (Sidereal) + ~1 (to complete Solar day) = 361 degrees.
Over the span of a year, it does this 365.25 times. So, approximately, that extra 1 degree the Earth has to rotate every day adds up to just over a whole extra rotation.
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