The Earth isn't 6,000 years old, but it's also impossible for it be billions of years old. The Sun loses Mass at a constant rate every year. If you add up all the mass it would have lost over millions of years, It's impossible for the Earth and Life to have even existed, with the Sun engulfing it. The only way life as we know it could have started to exist is anywhere from 100,000 to a million years ago.
Have a read.
Link
"There are two different lines of argument concerning a shrinking sun. The first one refers directly to the classical Kelvin-Helmholtz theory of the sun shining through gravitational contraction. The second line is based on a supposed change in the measured diameter of the sun.
The gravitational-contraction theory was perfectly respectable mainstream science, in the 19th century. As described in the historical section above, it was abandoned in the early part of the 20th century, for good scientific reasons that had nothing to do with creationism. Some creationists, notably Barnes (1974), appear to be unaware of developments in science beyond 1895 or so, and continue to invoke Kelvin's arguments as if they were still valid. But even if we didn't know anything about nuclear fusion (or if fusion for some reason didn't work in the sun), Eddington's (1920; 1924) refutation of the gravitational-contraction theory would still remain solid. This directly contradicts the claims of Akridge (1980), that the theory was abandoned solely because evolution required more time: "Scientists have not always attributed the energy source of the sun to thermonuclear fusion. Prior to the discovery of thermonuclear fusion, Helmholtz predicted that the energy of the sun was supplied by the gravitational collapse of the sun. This model was accepted until the theory of evolution began to dominate the scientific scene. Then Helmholtz's explanation was discarded because it did not provide the vast time span demanded by the theory of organic evolution on the earth. The substitute theory was introduced by Bethe in the 1930's precisely because thermonuclear fusion was the only known energy source that would last over the vast times required by evolution. Science may now be on the verge of disproving the substitute evolutionary model of the sun." (ibid, p 3). Akridge's last sentence is also misleading, in that the standard model of the sun isn't "evolutionary" in any sense connected with the Darwinian evolution that he's referring to elsewhere in the quote (and of course also misleading in that science is nowhere near disproving it).
Akridge (1980) is also the primary source for the other line of argument, claiming that the shrinking of the sun has been measured. He bases this claim entirely on the results of Eddy & Boornazian (1979). Remarkably enough, it nevertheless appears as if he hasn't even read their paper he does not refer directly to it, but only to a popularization (Lubkin 1980, see ref in Akridge 1980). It is also interesting to note that Akridge implies that E&B observed 400 years of shrinking, whereas the title of the E&B paper is 'Secular decrease in the solar diameter, 1863-1953', with only a 90-year period. Despite these (and other) obvious flaws, Akridge's claim has nevertheless become standard creationist fare, repeated in numerous creationist publications, from Brown (1995) to Molén (1991).
Strahler (1987) reviews the data available at the time of Akridge's writing, and contrasts it with Akridge's (1980) presentation. He notes that Eddy & Boornazian (1979) themselves do not interpret their result as evidence of an ongoing change. Their interpretation of their own data is dismissed out of hand by Akridge (1980). Other measurements, not showing any significant shrinking, were available in 1980, but were completely ignored by Akridge (1980). Subsequent measurements, published between 1980 and 1987, do not support Akridge's claim.
The issue of the solar diameter has become of some interest recently, with the arrival of precise helioseismological data. Eddington's (1920) argument against gravitational contraction, from the frequency stability of variable stars, applies with a vengeance to helioseismology, which is much more precise. Helioseismology is so precise today, that comparison between theoretical calculations and measurements require a better knowledge of the solar radius than is currently available. Furthermore, as the sun is not a solid body, it does not have a well-defined surface at which to measure the radius (Castellani & Degl'Innocenti & Fiorentini 1998). The difference between different definitions amounts to a century's worth of Akridge-shrinking, making it plausible that the apparent shrinking reported by Eddy & Boornazian (1979) might well be due to systematic errors when comparing data taken over long periods of time by different observers using different instruments and, quite possibly, different definitions.
A recent measurement of the solar diameter is that of Brown & Christensen-Dalsgaard (1998). From data taken over the period 1981-1988, they report a radius of 695,508 ± 26 km, with no evidence of change over time. The issue of surface definition is discussed at some length, leading to the conclusion that their definition is about 500 km smaller than that used in most previous estimates. Even over such a short period of time, their time series is sufficient to exclude an ongoing shrinking at the Akridge rate of five feet per hour, albeit at a modest statistical confidence level. I extracted the data from figure 2 in Brown & Christensen-Dalsgaard (1998) and did some line fitting, finding that the best fit to the data is a slight, statistically insignificant, growth of the diameter of the sun. No support whatsoever for shrinkage.
For a slightly longer time base, I'll use the value from Allen (1973), cited by both Brown & Christensen-Dalsgaard (1998) and Castellani & Degl'Innocenti & Fiorentini (1998) as the standard reference value before the 1990s. Working from Brown & Christensen-Dalsgaard (1998), I have re-calculated both their measurement, and that of Allen (1973) to what I believe is the same surface definition, obtaining a value for the angular diameter of the sun of 1919.31 ± 0.19 arcseconds in 1973, and 1919.359 ± 0.018 arcseconds on average 1981-1988. Akridge's alleged shrinkage corresponds to about 0.25 arcseconds over the same length of time, no trace of which is visible. It appears that the sun has stopped shrinking."
In a nutshell.
So basically you're assuming that the rate of shrinkage is constant. That assumption is baseless. Other stars expand and contract cyclically. Our own sun might do the same on a small scale.
There is not even any good evidence of shrinkage. The claim is based on a single report from 1980. Other measurements, from 1980 and later, do not show any significant shrinkage. It is likely that the original report showing shrinkage contained systematic errors due to different measuring techniquies over the decades.