Online Astronomy eText: Appendices
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      Most astronomical and physical terms are defined in a simple way, but they sometimes require modification, to achieve greater precision. For most purposes, there is no reason for a member of the general public to be aware of such modifications. Occasionally, however, this can lead to confusion. For example, the Astronomical Unit was originally meant to be the semi-major axis of the Earth's orbit, but the actual size of its orbit is 1.00000013 AU, which is the same as "one" AU to 7-digit accuracy, but not exactly the same.
      The reason for this is that in calculations of the orbital motions of the planets it is helpful to use a number called the Gaussian gravitational constant, which is equal to the average daily angular motion of the Earth around the Sun, expressed in radians per day. Even in the 19th century this number could be measured with great accuracy, but as time went on it became possible to measure the motion of the Earth still more accurately, and the average motion was found to be very slightly less than the amount originally used to define the Gaussian gravitational constant.
      One solution to the problem raised by this very small error would be to keep the AU equal to the semi-major axis of the Earth's orbit and change the Gaussian gravitational constant to a more accurate value. But doing that would require redoing all previous orbital calculations, and particularly at a time when such calculations were done by hand that was a painful prospect. Worse yet, if that method were used to take care of the problem, any later improvement in measuring the Earth's motion would require still further recalculations. It was therefore deemed preferable to say that while the AU was the size of the Earth's orbit in principle, for precise calculations the AU should be redefined as the radius of a circular orbit whose average daily motion was equal to the Gaussian gravitational constant, and the numerical size of the Earth's orbit was changed to whatever it had to be (currently 1.00000013 AU) to make the new definition of the AU correct.