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Q & A: Gravity: units and constants

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Most recent answer: 09/14/2012
In your answer on gravitational mass, you say that G might be the proportionality constant between inertial mass and grav mass, as it was set by Newton to make the two kinds of mass the same. If so, why isn’t it G^2, rather than G, in the grav force equation, involving two masses, ie GMm/r^2 ? Shouldn’t it come twice in there?
- John
This is really purely a matter of linguistic convention. The standard choice for G is 'the constant needed to calculate the force from the product of the inertial masses'. You could define a different constant 'the constant you need to multiply each inertial mass by so that when you take their product you get the right number to calculate the force". That definition would give sqrt(G) for the value. Either one would work fine so long as everybody understands the definitions.

Incidentally, in some parts of physics, people redefine the units of mass, length, time, etc, so that the multiplier is one. Those 'Planck units', where the speed of light is also one and Planck's constant, from quantum mechanics, is one, are convenient for work on quantum gravity.

Mike W.

(published on 09/14/2012)

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