Tycho's circumstances

Tycho had many advantages and disadvantages in his effort to measure the heavens.

Disadvantages in the late 1500s:

recent emergence from the Dark Ages
pre-enlightenment culture, no science tradition, the utility of mathematics not widely understood
astrology prevailed over astronomy
primitive technology
no accurate clocks
no optics
no computing devices
no electricity
no thermometers
paper was a luxury, he had to make his own
no tables of logarithms or trig functions to ease computations
hand calculations to 6 significant figures were needed
no prior instrumentation available, every instrument was a new design
only prior star catalog was 17 centuries old and had one degree of accuracy

Advantages available to Tycho:

excellent funding - total expenditures over 20 years was a 'ton of gold' by Tycho's estimation
He spent about 1% of Denmark's GDP annually - about $3M per year (current$)
available assistants - typically ten astronomy-savvy helpers on-site to help with observations and calculations
20 year timespan - allowed multiple opportunities for re-measurements and optimal geometries of the planets
construction of multiple instruments, to improve accuracy and to permit cross-checking