![]() In many secondary school texts, the dimensions of G are derived from force in order to assist student comprehension: In natural units, of which Planck units are a common example, G and other physical constants such as c (the speed of light) may be set equal to 1. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the cube of the Planck length divided by the product of the Planck mass and the square of Planck time. The dimensions assigned to the gravitational constant in the equation above- length cubed, divided by mass, and by time squared (in SI units, meters cubed per kilogram per second squared)-are those needed to balance the units of measurements in gravitational equations. With relative standard uncertainty 1.2 ×10 −4, or 1 part in 8,300. ![]() ![]() In SI units, the 2010 CODATA-recommended value of the gravitational constant (with standard uncertainty in parentheses) is: The gravitational constant is perhaps the most difficult physical constant to measure to high accuracy. The constant of proportionality, G, is the gravitational constant. According to the law of universal gravitation, the attractive force ( F) between two bodies is proportional to the product of their masses ( m 1 and m 2), and inversely proportional to the square of the distance ( inverse square law) ( r) between them:
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