It's not just money; its the needs of a civilization. Two thousand years ago, the Greeks invented the first computer. The computer was used to record the motions of the celestial bodies. This development was not applied to other areas of expertise.
The other day I was running some numbers for adding a Mars orbit to the mechanism, and there were several pretty good solutions. 284 (71*4) Earth years almost exactly equals 151 Mars years (150.99 or so), with an error of about an hour at the end of the 284 years, and those gears are pretty easy to cut.
37,157 Earth years hits an even number of Mars years even closer, despite the longer time span, accurate to about 0.05 seconds per year, but requires something like a 449 tooth gear.
So anyway, to get better orbital data I downloaded the latest and greatest method we use for planetary orbits, VSOP87. As it turns out, VSOP87 is just a computerized way of calculating with a bunch of little gears. A planet's orbital elements are simply the sum of a bunch of terms Q = Q + k1 * COS(k2 + k3*T) where T is time. There's nothing inherently elliptical about it.
So the clockwork method lives!!!