Question

How did Kepler work improve on or support Copernicus's heliocentric theory?

Answer 1

Kepler was an assistant to Tycho Brane, Brane had given Kepler the planet Mars to study, where he found out that the orbit of the planets around the sun wasn't just a plain circle, instead, where ellipses. 

This being said, Kepler's work supports Copernicus because when Copernicus was working on the solar system, he simplified Ptolemy's version by putting the sun near the center, and then Kepler said that the planet orbits were elliptical. 

(Basically, Kepler's idea was based on Copernicus.....I think)

hope this helps :)