# Why is there a deviation between the ratio of $a^3$ and $T^2$ for the outer planets?

The Wikipedia article about Kepler's third law includes a nice table about the ratio between $$a^3$$ and $$T^2$$. However, for Mars, Jupiter, Saturn, Uranus, and Neptune, the ratio $$\frac{a^3}{T^2}$$ in $$10^{-6} \text{AU}^3 \text{ day}^{-2}$$ deviates from the supposed constant $$7.495564252$$. For instance, Mars' ratio is $$7.4950842239$$ when applying the formula, which is off by $$0.0004800281$$, while Jupiter's ratio is $$7.50430207179$$. Why is this happening? I don't think that it's because of orbital eccentricity because Mercury contradicts this hypothesis, nor is it gravitational perturbations between the body and the Sun because of Mars' case. I'm suspecting it to be inaccurate orbital measurements, but I would like to know for sure.

Kepler's third law is not that $$a^3/T^2$$ is a constant. It is that $$\frac{a^3}{T^2} \propto (M_\odot + M_{\rm planet})$$ and so the left hand side depends on which planet you are looking at and should be larger for Jupiter than it is for the Mars for example.
Does that account for your discrepancy? Almost. It should change the 4th significant figure, because for Jupiter, $$(M_\odot + M_{\rm planet}) = (1 + 0.000954)M_\odot$$, whilst for Mars it is $$(1 + 0.0000003)M_\odot$$ - this gives a ratio of 1.00095 between the RH sides of Kepler's third law for Jupiter vs Mars, compared with the discrepancy you have found that has a ratio of 1.0012.