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If the Earth rotates on its own axis, then what do we mean by sunrise and sunset?

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Yes the earth rotates around its axis, which gives rise to the motion of the sun as we see it.
To understand sun rise you'd have to start with a reference frame. For us, the earth is considered to be the inertial frame for any apparent motion in the celestial sphere, it simplifies the computations. Thus any motion of celestial bodies is defined with respect to that frame.
So in that context Sunrise would be the time when for a given latitude, when the sun first appears above the local horizon, and sun set would become the time when the sun disappears below that local horizon.

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Sunrise is the moment when the point you are located on, on Earth, gets to receive its part of the sunlight (due to the Earth's rotation you spoke about). And sunset is the moment when the point you are located on, on Earth, has made its turn and faces away from the Sun, then preventing you from receiving its light.

When the Earth will have made another half of its rotation, you will get to see another sunrise.

The Earth makes a full rotation in a 24h cycle. This is why you get a sunrise and a sunset everyday :)

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    $\begingroup$ and the technical definition is: Sunrise is the moment the first direct rays of sunlight reach you. Sunset is the moment the last rays of sunlight fail to reach you. So on the Equinoxes "daylight" is actually longer than "night" by several minutes. They'd be equal if Sunrise and Sunset were measured at the point the Sun was "half set" and "half risen". $\endgroup$ – Jim2B Jan 12 '16 at 20:22
  • $\begingroup$ Thank you, @Jim2B. Is it true that there's another element in the difference in the lengths of day and night (even at an Equinox)? Namely that atmospheric diffraction means that when, for example, we see the sun's disk balanced on the horizon at sunset, the sun has actually already set? $\endgroup$ – David Garner Jan 18 '16 at 20:53
  • $\begingroup$ Yes :) I forgot that diffraction affects the timing too. $\endgroup$ – Jim2B Jan 18 '16 at 21:44
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This is only one way Possible due to Rotation of Earth.## Rotation Of Earth ## The time of sunset varies throughout the year, and is determined by the viewer's position on Earth, specified by longitude and latitude, and elevation. During winter and spring, the days get longer and sunsets occur later every day until the day of the latest sunset, which occurs after the summer solstice. In the Northern Hemisphere, the latest sunset occurs late in June or in early July, but not on the summer solstice of June 21. This date depends on the viewer's latitude (connected with the Earth's slower movement around the aphelion around July 4)

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    $\begingroup$ This doesn't appear to answer the question. $\endgroup$ – James K Jan 14 '16 at 18:26
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Its simply mean ,when earth rotates (as Sun don't move) ,the instant when the light of sun falls on the earth called sunrise and its just opposite mean sunset.

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