rotation and orbit of the Earth To say that the Earth rotates on its axis once per day and completes one orbit of the Sun each year is to encapsulate but also to simplify the situation. In making such a description, the main naïvety is the overlooking of a fixed reference frame. From a vantage point far above its north pole, the Earth would be seen to rotate on its axis in an anticlockwise fashion, and to be moving round the Sun in the same direction (Fig. 1).
By the time the Earth has rotated exactly once, its orbital motion of nearly 30 kilometres per second has carried it approximately 1/365th of the way round its orbit. The result of this is that after exactly one rotation of the Earth, the Sun (seen from the Earth) is no longer in quite the same direction as it was before. Because rotation and orbital motion are in the same sense, it actually takes a fraction more than a complete rotation to complete a day, as defined by the time between successive noons (when the Sun is at its highest point in the sky) at a single point on the Earth's surface. Noon to noon is exactly 24 hours (this is the basis of the definition of the unit of time we call an hour), and this period is referred to as a ‘solar day’. The slightly shorter period in which the Earth completes an exact rotation (a ‘sidereal day’) is approximately 23 hours 56 minutes 4 seconds. An effect of this is that seen from a location on the Earth's surface a given star will rise 3minutes 56 seconds earlier each day, which is why the stars visible in the evening sky change gradually through the year.
Seasons are caused by the fact that the Earth's rotation axis is not at 90° to its orbital plane, but is inclined at 23½° and (on a human timescale) points to a fixed direction in space. On about 21 June each year the north pole is tilted as close towards the Sun as it ever gets, and the Sun thus reaches its farthest north point in the sky, which corresponds to the summer in the northern hemisphere and to winter in the southern hemisphere. This is the northern summer solstice, when northern latitudes experience their maximum duration of daylight. Conversely, on about 21 December the north pole is pointed away from the Sun, and the northern hemisphere experiences winter (and the shortest hours of daylight) while the southern hemisphere has summer. This is the northern winter solstice. A quarter of an orbit between these dates, the axial tilt is sideways to the Sun and day and night are of equal length at all places on the Earth; these equinoxes occur on about 21 March and 21 September each year. Calendar dates of events vary slightly because there is not an exact number of solar days in a year. The exact figure is 365.25636 solar days per year, or strictly speaking, per ‘sidereal year’. This is close enough to 365¼ for the calendar to be kept in step with the seasons by declaring the ‘civil year’ to be normally 365 days but 366 days every fourth year (when the year number is divisible by four). These 366-day years are ‘leap years’. Our current system of declaring century years to be leap years only if divisible by 400 was introduced by Pope Gregory XIII in 1582, and is known as the Gregorian Calendar. This compensates for most of the 0.00636 of a day difference between the year length and the 364¼ day approximation, leaving a discrepancy of only 7 hours 16 minutes per thousand years.
An additional complication is that the Earth's orbit is not quite an exact circle, but an ellipse. At its nearest point to the Sun,
perihelion (which falls on approximately 3 January), the Earth–Sun distance is 147.1 million km; the distance reaches a maximum of 151.1 million km at
aphelion on about 4 July. The speed of a planet's orbital motion is greatest at perihelion and least near aphelion, but its rotation is at a constant rate. The Sun therefore usually appears slightly out of position in the sky as compared with the fictitious ‘mean Sun’ required for regular timekeeping; a sundial will consequently read 14 minutes slow in February and 16 minutes fast in November.
The Earth's orbit and rotation are not constant in the long term, but are affected by factors such as the pull of the Sun and Moon on the Earth's equatorial bulge and, to a much lesser extent, by the gravitational attraction of the other planets. The direction of tilt of the Earth's rotational axis traces out a complete circle in the sky over a period of 22thousand years; the amount of tilt varies between 21.8° and 24.4° over a period of 40 thousand years; and the shape of the orbit becomes slightly more and slightly less elliptical over a period of 110 thousand years. The combined effect of these cycles is probably an important factor in driving global climate change. It takes much longer for the rate of rotation to change. The main cause is the tidal pull of the Moon, which has slowed the day length by about two hours over the past 400 million years.
David A. Rothery
