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March 3

Gravitational constant in terms of energy

The Gravitational constant is usually written in terms of mass, but it seems to me it would be more naturally written in terms of energy, because after all it's energy that gravitates, not [just] mass.

In those terms the value would be: 8.2627195×10^-45 m/J. (i.e. G / c^4) Which is a much simpler unit. With this formulation of G you can just plug in the energy of a photon, for example, and get results, no need to resort to complicated curvature of space explanations.

The article on the Gravitational constant does not have it written this way - before I add it, I just wanted to see what others thought. Ariel. (talk) 22:50, 3 March 2024 (UTC)[reply]

You should only add this if you can cite reliable sources that present the constant in units of this dimension. See WP:OR. Is your unit correct? Shouldn't it be

m\cdotkg -1

? Given the uncertainty in the value of

G

, the number of digits in the numerical value you give is unwarranted. I think it should be something more like

8.26271(19) \times 10 -45

. --Lambiam 00:18, 4 March 2024 (UTC)[reply]

m/J

is the correct unit for

G/c^{4}

, although it's not clear to me why G is being divided by

c^{4}

. It seems this is introducing a new constant G', which complicates other things, like Newton's law of gravitation would change from

F=G{\frac {m_{1}m_{2}}{r^{2}}}

to

F=G'{\frac {m_{1}m_{2}c^{4}}{r^{2}}}

As to the OP question, it should definitely not be added to the article unless there is a reliable source that presents it in this way; otherwise it would be original research. CodeTalker (talk) 01:08, 4 March 2024 (UTC)[reply]

Agreed about the significant digits, I was going to do that if I added it.

It's not a new constant, rather instead of the mass you would put in the energy of the object, and then use this form of G instead of the original. It's more correct that way because it's energy that gravitates, not just mass.

Is it really possible that this is OR, and that no one else thought of defining G in terms of energy instead of mass? That would surprise me. Ariel. (talk) 02:06, 4 March 2024 (UTC)[reply]

You can express the gravitational constant in the unit

m^{5}J^{-1}s^{-4}

, but that doesn't change its numerical value. As long as you use SI units, the numerical value remains the same. When you divide the gravitational constant by

c^{4}

, you get a new constant G', and if you want to that instead of G, you have to compensate every formula with another

c^{4}

. For Newton's law of gravity, that makes things more complex. Newton's theory, which is is older and more widely used than General Relativity, suddenly gets a ridiculously small constant and a weird lightspeed to the fourth, despite having nothing to do with the speed of light. In General Relativity, these factors

c^{4}

may compensate for others, but the theory is still full of powers of

c

, most of which get cleverly absorbed somewhere.

That mass is equivalent to energy doesn't mean that expressing things in energy is more correct. You can just as well express energy as relativistic mass, which is the more common method in GR (not in particle physics, but that doesn't deal with gravity). Physicists tend to use what's most practical and I've never seen anyone use this constant G'.

BTW, have you noticed how the accuracy of G is improved when expressed in parsec per solar mass times (km/s) squared? That's because the uncertainty in the solar mass compensates for the uncertainty in G, the product of which is known much more accurately than either of them separately. PiusImpavidus (talk) 10:48, 4 March 2024 (UTC)[reply]

I see now that there is something called the Einstein gravitational constant, which has the same dimension as your energetic constant but differs by a scalar factor:

\kappa ={\frac {8\pi G}{c^{4}}}\approx 2.076647442844\times 10^{-43}\,{\textrm {N}}^{-1}.

It is referred to in section Gravitational constant § Definition. (The precision is unwarranted.) --Lambiam 19:12, 4 March 2024 (UTC)[reply]