It looks like they chose to use the "universal gravitational constant" "k" instead of Newton^s constant, "G": p.23, "k^2 = universal gravitational constant, 1.32452139x10^20, m^3/(sec^2)(sun mass units)"
I think "k" was also known as "Gaussian gravitational constant" https://en.wikipedia.org/wiki/Gaussian_gravitational_constan...
But the value and unit of "k" given in the Wikipedia page is different. Do you know what NASA document means by "universal gravitational constant" in modern sense?
The code appears to use in some places GK2M, which is the Newtonian constant of gravity, and in other places SQRDK, which is inappropriately described as a "gravitational constant", but it actually is the mass of the Sun expressed in some special units.
Newton's constant is known only with a very high uncertainty, i.e. a very low precision.
For the great bodies of the Solar System, e.g. the Sun and the planets, one knows with a high accuracy the product between their mass and Newton's constant, because that can be measured by the force with which they attract a body of known mass, e.g. an artificial satellite or an interplanetary probe.
Computing their mass in kilograms would be pointless in most cases, because that would introduce great uncertainties in the computations. So for the Sun and the planets one expresses their masses by the products between their mass and Newton's constant, whenever that is possible, i.e. whenever one needs to compute their attraction force exerted upon a small object.
Wikipedia names the product mass-Newtonian constant as "the standard gravitational parameter of a body", but I believe that this is a misleading name, because this product is just the mass of the body expressed in different (non-SI) units. Expressing a mass by its product with the Newtonian constant is not different from expressing the mass in pounds instead of kilograms. Using the Newtonian constant instead of some random unit conversion factor just has the advantage of removing the uncertainties from some expressions computing forces of gravity.
It's just regular old G, defined in mass-of-sun units: https://en.m.wikipedia.org/wiki/Gravitational_constant (fourth item in the first table: NASA also uses meters whereas Wiki uses km)
Gauss's constant k is defined as sqrt(G), but for a while the international standard was to define k and then compute G as k^2, which is why NASA refers to it that way.
I think it's just units. From wikipedia: "and its value in radians per day follows by setting Earth's semi-major axis (the astronomical unit, au) to unity, k:(rad/d) = (GM)0.5·au−1.5."
the value given in the paper assumes the distance in meters I think.