Carl Sagan’s book Cosmos explains a bit about how some people in the 15 & 1600s have spent a good deal of time trying to find out the truths about Earth’s position in the cosmos. Kepler is one of them who have contributed significantly to our current understanding with help of years of observation about the night sky and lots of mathematics. Kepler did not have enough resources to get hold of good telescopes so he had to rely on readings from people who had access to it. Tycho was one of the few who had access to good telescopes and made detailed observations. Kepler had a great interest in Tycho’s mars observation, Tycho was impressed by Kepler’s work still guarded all his data because of the work he put in. Kepler left Tycho after it was becoming increasingly difficult to get data from Tycho to test his theory and trouble to get into a formal agreement to work with each other.
Some time later Tycho’s unexpected demise landed Kepler the task of finishing what has been left by Tycho. Kepler began testing his theory of earth going through circular orbit around the Sun and backed that with the date of Tycho’s observation of Mars. At one point he observed that his theory fit perfectly fine except a couple of reading which were off by 8 minutes of arc in angular degree. 8 minutes of arc deviation in a 90 degree observation field is just 0.15% deviation.
Kepler not only had faith in Tycho’s observations but also had the courage to question his assumptions even though the deviation was only 0.15%. Kepler felt that his fascination with the circle was a delusion and he abandoned his circular orbit theory and went for other curvy shapes. Eventually when he came up with an elliptical orbit with Sun at one of its foci, all the data from the observation and theory matched perfectly fine. He could have easily patched up 0.15% deviation and closed his work, but the trust he had on his fellow researcher’s data and his perseverance to find the right brought in a reformation in astronomy. His laws of planetary motion still hold good.
Many at times in school I have succumbed to the temptations of approximating or convincing myself that others could be wrong and prematurely ended feeding my curious brain. This definitely has delayed many things which I could have understood better had I spent enough time on it. If Kepler could question 0.15% deviation and come up with a revolution, then we have ample opportunities to break paths every day.
Below is Kepler’s quote
Divine benevolence has bestowed the most diligent of observers, Tycho Brahe, from whose observations this eight-minute error of Ptolemy’s in regard to Mars is deduced, it is fitting that we accept with grateful minds this gift from God, and both acknowledge and build upon it. If I had believed that the we could ignore these eight minutes (0.15% deviation), I would have patched up my work accordingly. But, since it is not permissible to ignore, those eight minutes pointed the road to a complete reformation in astronomy.
More Kepler’s quotes here
Novi's 
You might enjoy a book called the sleepwalkers by Arthur kostler. Looks at the historical context of Kepler and others in detail.
Tycho didn’t have any telescope when he was logging his observations upon the sky. Brahe died before Galileo used a telescope to see the stars; what he used were gigantic cuadrants and sextants from his own ingenuity.