Gravitational coupling constant

In physics, a gravitational coupling constant is a constant characterizing the gravitational attraction between a given pair of elementary particles. The electron mass is typically used, and the associated constant typically denoted $α G$ . It is a dimensionless quantity, with the result that its numerical value does not vary with the choice of units of measurement, only with the choice of particle.

$α G$ is typically defined in terms of the gravitational attraction between pair of electrons. More precisely,

where:

In natural units, where $4π G = c = ħ = ε 0 = 1$ , the expression becomes

This shows that the gravitational coupling constant can be thought of as the analogue of the fine-structure constant; while the fine-structure constant measures the electromagnetic repulsion between two particles with equal charge, the magnitude of which is equal to the elementary charge, this gravitational coupling constant measures the gravitational attraction between two electrons.

There is no known way of measuring $α G$ directly, and CODATA does not report an estimate of its value. The above estimate is calculated from the CODATA values of $m e$ and $m P$ .

While $m e$ and $ħ$ are known to one part in 7007200000000000000♠20000000, $m P$ is only known to one part in 7004200000000000000♠20000 (mainly because $G$ is known to only one part in 7004100000000000000♠10000). Hence α_G is known to only four significant digits. By contrast, the fine structure constant $α$ can be measured via the anomalous magnetic dipole moment of electron with a precision of few parts per 10¹⁰. Also, the meter and second are now defined in a way such that $c$ has an exact value by definition. Hence the precision of $α G$ depends only on that of $G$ , $ħ$ , and $m e$ .

...
Wikipedia