Talk:Gaussian gravitational constant

Where does the magic number

 0.01720209895

come from ? -- DavidCary 19:17, 12 May 2004 (UTC)

It's the gravitational constant in other units:

${\sqrt {G}}={\sqrt {6.67*10^{-11}\;\mathrm {N\,m^{2}/kg^{2}} }}$

$={\sqrt {6.67*10^{-11}{\frac {\mathrm {m} ^{3}}{\mathrm {s} ^{2}\mathrm {kg} }}}}$

$={\sqrt {6.67*10^{-11}{\frac {(86,\!400)^{2}*(1.9891*10^{30})}{(1.496*10^{11})^{3}}}{\frac {\mathrm {AU} ^{3}}{\mathrm {day} ^{2}\;\mathrm {mass} _{Sun}}}}}$

$=0.0172\;\;\mathrm {AU} ^{3/2}\;\mathrm {day} ^{-1}\;\mathrm {mass} _{Sun}^{-1/2}$

--wwoods 01:11, 19 May 2004 (UTC)

In Theoria Motus Gauss defines $k={\frac {2\pi }{t{\sqrt {1+\mu }}}}$ where t is 365.2563835, the number of days in a sidereal year, and $\mu ={\frac {1}{354710}}$, the mass of the Earth in solar masses. Gauss states the quantity is the same for all bodies orbiting the Sun. It may be a correction to Kepler's Second Law since 2π/t is the areal velocity for a body of negligible mass at 1 AU. Gauss initially gives the invariant quantity for all bodies as,

${\frac {g}{t{\sqrt {p}}{\sqrt {1+\mu }}}}=k$

with g/2 being the area swept out by the radius in time t and indicates a few pages later that p=a(1-e²) where a is the semi-major axis of the elliptical orbit.

--Jbergquist (talk) 23:46, 11 November 2011 (UTC)

How do we arrive a k analytically? The derivation of Gauss' constant expression is quite simple and requires only an elementary knowledge of orbital mechanics. From the conservation of angular momentum we know,

$r^{2}{\dot {\theta }}=h={\frac {g}{t}}$.

From the derivation of the equation for the orbit we know,

$r={\frac {p}{1+e\cos {\theta }}}\qquad p={\frac {h^{2}}{\mu }}\qquad \mu =GM\left(1+m\right)$.

Combining the two expressions for h we get,

$r^{2}{\dot {\theta }}={\frac {g}{t}}=h={\sqrt {GM\left(1+m\right)p}}$.

Dividing both sides of the equation by the knowns on the right we get,

${\frac {g}{t{\sqrt {p\left(1+m\right)}}}}={\sqrt {GM}}$.

--Jbergquist (talk) 22:18, 14 November 2011 (UTC)

What is little "m"?

To Jbergquist: You keep using

$(1+m)\,$

in your formulas. Since 1 is a dimensionless number, then so must m be. What is m? You have not defined it. JRSpriggs (talk) 07:47, 22 November 2011 (UTC)

Many problems with this article

It seems to be yet another article pasted together from several stubs, without much editing. The statement "he had already used the concept to great success in predicting the orbit of Ceres in 1801" is questionable. He probably used it for that, we have no account of what he actually did, other than what he published years later in Theoria Motus. I'm pretty sure that "It is equal to the square root of GM☉" is just plain wrong - it is equal to the square root of G, not GM. I have references for this. What does this even mean... "The Gaussian gravitational constant is related to an expression which is the same for all bodies orbiting the Sun" ...?

We have contradictions:

The Gaussian gravitational constant is now an IAU defining constant used to define the astronomical unit.

In 2012 the definition of the astronomical unit was changed again, to be equal to a precise numerical value,

Which is it?

What does this mean... "The term "gravitational constant" comes from the fact that k2 is related to the standard gravitational parameter" ...? A constant is a constant - a definition of a fundamental quantity. Many other problems. Tfr000 (talk) 02:30, 12 December 2015 (UTC)

...and more... This statement is wrong: "A different constant is needed for the objects in orbit about another body." It's a gravitational constant. Presumably it is valid throughout the universe, like G, the Newtonian constant. This is also wrong: "Their efforts led to the preparation of Newcomb's Tables of the Sun in 1895, and correspond to a value for the Gaussian gravitational constant of 0.017 202 098 14 A3/2S−1/2D−1". Here is the text directly from Newcomb's Tables of the motion of the earth on its axis and around the Sun:

The adopted value of the GAUSSIAN constant is that of GAUSS himself, namely:
k=3548".18761=0.01720209895

Tfr000 (talk) 03:33, 16 December 2015 (UTC)

I fixed the lead section, removed some of the just plain wrong information, and added a discussion of why this constant is different than Newton's. More to come. We have a paragraph here on relativity - probably that should be removed to a brief section discussing how Gauss' constant would be changed by modern information. In the astronomical world, Gauss' constant was used verbatim until it was abandoned just recently, so there is little justification for getting deeply into such things, other than intellectual curiosity. Tfr000 (talk) 14:45, 20 December 2015 (UTC)

Well I re-wrote pretty much the entire article. Hopefully it now gives a better idea of why this constant was important until recently. I still want to add a little bit about derivation from Kepler's 3rd, and about what the constant would have looked like with modern values. I removed the relativity info completely. [1] says, The system of astronomical constants as presented, for example, in IERS Standards, begins with two defining constants, i.e. velocity of light c and Gaussian gravitational constant k. [...] General relativity has no effect on these definitions when these quantities are regarded without any physical context related to them., so it doesn't seem like there is any point in keeping it. Tfr000 (talk) 14:20, 30 December 2015 (UTC)