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# Diurnal motion

Diurnal motion is an astronomical term referring to the apparent daily motion of stars in "orbit" around the Earth, caused by the Earth's rotation around its axis. It is a rotation around the axis between the two celestial poles.

It takes Earth 23 hours, 56 minutes and 4.09 seconds (1 sidereal day) to rotate around the axis connecting the North Pole and the South Pole.

Direction of the motion on the Northern hemisphere:

• looking to the north, below the North Star: left-right, west-east
• looking to the north, above the North Star: right-left, east-west
• looking to the south: left-right, east-west

Thus northern circumpolar stars move anti-clockwise around the North Star.

At the North Pole, north, east and west are not applicable, the motion is simply left-right, or looking vertically upward, anti-clockwise around the zenith.

For the southern hemisphere, interchange north/south and left/right, and replace North Star by southern celestial pole. The circumpolar stars move clockwise around it. East/west are not interchanged.

At the equator both celestial poles are at the horizon and motion is anti-clockwise (i.e. to the left) around the North Star and clockwise (i.e to the right) around the southern celestial pole. All motion is from east to west, except for the two stationary points.

The daily path of an object on the celestial sphere, including the possible part below the horizon, has a length proportional to the cosine of the declination. Thus the speed of the diurnal motion of a celestial object is this cosine times 15 °/hr = 15'/min = 15"/sec, i.e. (compare angular diameter):

• up to a Sun or Moon diameter every two minutes
• ca. four seconds for the largest planet
• 2000 diameters of the largest stars per second

Diurnal motion can be seen in time-exposure photography [1]. Circumpolar stars close to the celestial pole move only slowly. Conversely, following the diurnal motion with the camera, to eliminate it on the photograph, can best be done with an equatorial mount, which requires adjusting the right ascension only; a telescope may have a motor to do that automatically (sidereal drive).