The constant of proportionality G or k appearing in formula for the force of attraction between two bodies. If the bodies can be considered points with masses M₁ and M₂, the formula is f = G M₁ M₂(r₂ - r₁)/r₃ , in which r₁ and r₂ are the vectors from the origin to masses M₁ and M₂, respectively, and r is the distance between the two masses. The value of the numerical constant depends upon the units in which the force f, the vectors r₁ and r₂ and the distance r, and the masses M₁and M₂ are expressed. The value adopted for G by the International Astronomical Union in 1976 is 6. 672 x 10^-11 m3/(kg s²). Recent measurements of the variation of gravity with depth in the Earth, and data from nuclear experiments, suggest that a fifth force, similar to gravitation, may exist or that the inverse square law for the variation of gravitation with distance is not quite correct. The uncertainties in the data, however, are such that no definite conclusions are possible at present. The symbol k² is reserved for the gravitational constant when the masses are expressed in units of the mass M_s of the Sun, distances are expressed in terms of the astronomical unit (A. U. ), and time is expressed in ephemeris days (E. D. ; 86 400 ephemeris seconds). The quantity k, also called the Gaussian constant or Gaussian gravitational constant, has the defined value 0. 017 202 098 950 (A. U. )3/(M_s (E. D. )²). This value then specifies the astronomical unit through Kepler's third law k² M_s (1 + M1/Ms) = (2ð/To)² a₃, in which To is the period of an orbiting point mass of mass M₁ and a is the radius of the circular orbit. Note that the astronomical unit is not the same as the average semi major axis of the Earth's orbit. The difference arose because Gauss, in calculating k, used a value for the mass of the Earth about 7% too small. If k is calculated instead of being defined, it can be determined to many more significant figures than can G because, with the units adopted, k is equal to the average angular speed of the Earth in its orbit, divided by (1 + mass of Earth in units of solar mass). The mass of the Earth in these units is a very small quantity and is known to better than 6 significant figures; the average angular speed is immediately calculable from the period of revolution of the Earth, which is known to better than 10 significant figures.