Gravitation, Constant of

the proportionality constant G in the formula for Newton’s law of gravitation, F = G(mM/r²), where F is the force of attraction, M and m are the masses of the bodies attracting one another, and r is the distance between them. Other symbols used for the constant of gravitation are y and f (less frequently k²).

The numerical value of the constant of gravitation depends on the choice of the system of units of length, mass, and force. In the cgs system,

G = (6.673 ± 0.003) × 10⁻⁸ dyne • cm² • g⁻²

or cm³ • g⁻¹ sec⁻²; in the International System of Units,

G = (6.673 ± 0.003) × 10⁻¹¹ newton • m² • kg⁻²

or m³ • kg⁻¹ • sec⁻². The most accurate value of the constant of gravitation is obtained from laboratory measurements of the attractive force between two known masses by means of torsion balances.

The geocentric constant of gravitation is used to calculate the orbits of celestial bodies, such as artificial satellites, relative to the earth. It is the product of the constant of gravitation and the mass of the earth (including its atmosphere):

GE = (3.98603 ± 0.00003) × 10¹⁴m³ • sec⁻²

The heliocentric constant of gravitation is used to calculate the orbits of celestial bodies relative to the sun. It is the product of the constant of gravitation and the mass of the sun:

GS_S = 1.32718 × 10²⁰ m³ • sec⁻²

The values of GE and GS _S are in accordance with the system of fundamental astronomical constants adopted in 1964 at the meeting of the International Astronomical Union.