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The Solar System Clock - what is in a day?

Day (Synodic) Clock

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Rotation (Sidereal) Clock

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So, just as we got our ahead around the Solar System Clock, we have a curve ball. Our clock up until now measures a day in terms of the time it takes for the sun to return to the same position in the sky. If the sun starts is directly above us, a day has elapsed when the sun is directly above us again, roughly 24 hours later. The thing is that planets orbit the sun while they are rotating. So, the sun has moved relative to our position since the previous day and this means that a 'day' does not match a rotation. A better way to measure a day is by measuring how long it takes for some distant object (such as a star) to return to the same position in the sky. This measure of a rotation is called the synodic period. The two clocks above compare synodic (day) verses sidereal (rotation).

What can we tell by looking at these clocks?  

Slower rotation, bigger difference

The difference between the synodic and the sidereal period is more obvious in planets that rotate more slowly such as Mercury and Venus. This makes sense, because the longer the rotation period, the further that the planet moves along its orbit before it has rotated. 
Beyond Venus, the day and rotation periods are almost identical. This is because the rotational period is comparatively shorter than  the orbital period. 

Direction of rotation

The rotation period of Mercury is shorter than the day. That is, the sun returns to the same position in the sky less frequently than the planet rotates. Why is that? Well, it is because Mercury rotates in the direciton of orbit (direct rotation), so it needs to rotate further for the sun to return to the same position in the Sky. 
Venus is quite the opposite. The day is shorter than the rotation. This is because Venus rotates in the opposite direction to the orbit (retrograde rotation), so it doesn't need to rotate quite as far for the sun to reach the same position in the sky. The same applies for all planets that have the retrograde rotation (as shown by the anticlockwise clocks of Venus, Uranus and Pluto).

It is not always immediately obvious why planets with direct rotation have longer days than rotation periods and planets with retrograde rotation have longer rotation periods than days, but is easier to understand when seen in a simulation. Click 'Go' below for a simulation (then read the explanation below)Pause, continue or reset the simulation when you want to.

Explanation
The planet in the left system has direct rotation, the planet on the right has retrograde rotation. The current position of the observer is shown by the small red pyramid. There are two lines, one to show the rotation point and one to show the day point (this will always point directly to the sun). When the observer passes the rotation point, the planet has completed a rotation and when the observer passes the day point, the planet has completed a day (the sun will have returned to the same position in the sky as seen by the observer). 

Note that given that the planets have the same rotation speed, the rotation period is the same. It is the day length that will change depending on direct or retrograde rotation. 

It is quite clear now that with direct rotation, it will take the observer longer to pass the day point than the rotation point and the opposite for retrograde rotation. 

Cogs and wheels

Have a look at the simulation below showing the relative progression of the years, days and rotations and the numbers behind the calculations.

PlanetYearsDaysRotationsOrbital period (Earth days)Days per yearRotations per yearDay/Rotation

References and further reading

cseligman.com
This page was the source of the values that I used in programming The Solar System Clock. The whole site is an excellent resource for information about astronomy.
In particular, for information on the rotations of the planets, see http://cseligman.com/text/sky/rotationvsday.htm.

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