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Defining Rotation and Revolution of the Earth
Rotation is where the Earth spins on its own axis. The axis is an imaginary line through the center of the planet between the north and south poles. As the Earth rotates, the Sun looks like it's travelling around the Earth, rising in the east and setting in the west - but what really happens is the other way around. As the Earth rotates, the spot where you're standing is moving past the Sun from west to east.
Each rotation of the Earth - roughly the length of time for the Sun to come back to the same point in the sky a second time - is called a day. Specifically, it's called a solar day. There is also a day length measurement called a sidereal day, which we'll get back to in a moment.
Revolution is where the Earth travels, or revolves, around the Sun in a roughly circular path. (Mathematically, it's actually an ellipse rather than a circle.) Each revolution takes the Earth around one complete orbit of the Sun, back to the same point a second time, and is called a year.
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Rotation and Revolution at the Same Time
To recap, the Earth rotates once upon its axis each day, and revolves once around the Sun each year. These two motions happen at the same time - that is, while the Earth is rotating, it's also revolving, so that by the time it completes one full rotation, it's no longer in the same place along its orbit. This is the key to the difference between a solar day and a sidereal day.
A solar day is the length of time that it takes for the Sun to be in the same spot in the sky (as seen by an observer on Earth) a second time - for example from noon to noon. On Earth, a solar day is 24 hours long.
A sidereal day is the length of time that it takes for the Earth to make one full 360-degree rotation around its axis. By the time it's done, it has moved a short distance on its orbital path - and the Sun isn't in the same place. A sidereal day is about 4 minutes shorter than a solar day. It takes the first 4 minutes of the next rotation for the Sun to be back to the same spot in the sky relative to the stars.
In the diagram to the left, #2 marks a full sidereal day, and #3 marks a full solar day.
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Rotation and Revolution of Other Planets
On Earth, a solar day and a sidereal day are almost the same length. This is not the case for every planet and moon in our Solar System. Some rotate faster and others slower. For example, Jupiter rotates completely around in only 10 Earth hours, which makes the difference between sidereal and solar day very short indeed.
Meanwhile, Mercury takes 59 Earth days to complete one full rotation, and it revolves quite a distance during that time; by the time the Sun is back to the same spot for a completed solar day, two Mercury years (88 Earth days each) have passed.
Closer to home, our own Moon rotates exactly once for every revolution around Earth. One full rotation is the same length as one full revolution. This is why we always see the same side of the Moon facing us.
Other planets also revolve around the Sun at different rates. The planets far away have much longer years than the planets up close because they have greater distances to travel.
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One Last Word about Revolution
While the Earth (and other planets) revolve around the Sun, the Sun is also revolving around the center of the Milky Way Galaxy. One revolution of the Solar System takes 200-250 million Earth years and is called a galactic year. In an absolute sense, a completed revolution around the Sun does not actually bring us back to the same point in the Universe a second time.
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Solar vs. sidereal diagram by GDR, used under CC-A-SA 3.0 unported license.