Tycho's observations of the planets throughout their orbit with unprecedented accuracy allowed Kepler to discover that planets move in elliptical orbits.
In 1609, the telescope was invented, opening new worlds to human scrutiny.
But the telescope alone wasn't of much use for measuring angles. It took some time to devise an instrument which would make use of the improved sight available with the telescope, but which would also permit a high angular accuracy.
In the 17th century the filar micrometer was invented, consisting of two wires mounted in the field of view of a telescope which moved towards and away from each other with a screw. The number of turns of the screw indicated the angle subtended by the object in the sky. This allowed breaking the barrier of accuracy imposed by the limited resolution of the human eye, which cannot distinguish angles below 1 minute of arc.
In the 18th century, knowledge of materials and workshop techniques improved significantly allowing instrument makers to engrave angular scales like the astronomical circle with high precision. Accuracies improved to the order of arcseconds, which allowed the detection of stellar aberration in 1725, the first direct proof that the Earth was moving through space. This finally confirmed the controversial Copernican theory which stated that the Earth goes around the Sun, and not vice versa. Another important discovery of this century was Edmund Halley's detection of the motion of stars through space.
Click on the thumbnail below to see how a telescope can resolve two stars that are too close together to be seen by the naked eye: