Hi FE

Just been reading this thread and thought I'd throw in a few facts.

Firstly the Astronomical Unit is defined as 149,597,870,691 metres (plus or minus 3 metres) and it's directly measured by radio signalling between Earth and space-probes as well as a bit of geometry. That particular figure is defined as the orbital radius of a massless particle with the same orbital period as the Earth's year. As a result Earth orbits a little more than 1 AU.

Usually the standard orbit equation has enough accuracy to tell us how far apart the Earth and Sun are, as well as watching where it is with respect to other planets and the stars. But for extreme accuracy - like comet appearances millennia ago - the orbits of all significant objects in the Solar System are computed numerically.

If you don't already know the basic equation for the duration of Earth's orbital year is t = 2*pi*sqrt[R^3/(G*(M+m))] - where R is the average orbital radius, G the gravitational constant, M the mass of the Sun, and m the mass of the Earth. But most computations by NASA's JPL use the value of G*(M+m) derived from observation, because the value of G is notoriously uncertain beyond a few decimal places.

The main thing to remember is that the year is determined by the Earth-Sun distance - and it has been observed to be steady for millennia. Or steady enough to compute eclipses with high accuracy, but as Tom has noted the basic shape of the orbit does slowly change over thousands of years. Chaos effects can cause a very gradual change over millions of years - there's a slight chance Mercury will move out of its orbit in a few billion, for example - but there's no observable change quick enough to cause current global warming.

Adam

PS the Earth-Sun tide is about 1/3 of the Earth-Moon tide in strength, but about 12-13 times lower in frequency and so its decceleration of Earth's axial rotation is much slower in effect than the Earth-Moon tide. The rate of decline of the rotation is proportional to the frequency and much smaller in magnitude than the Earth's angular momentum around the Sun.