Kepler, having invented the word “focus” with regard to elipses, used it to describe parabolas in a unique way. Kepler stated that a parabola had two foci, with one at infinity. [2]

Kepler’s second law of astronomy is that as a planet orbits its focus (or the sun), the area that the planet sweeps with respect to the sun as it passes between two points must be equal regardless of the planet’s distance from the sun. This means that a planet has to orbit more quickly when it is near the sun so as to sweep out “enough” area, compared to the slower orbit when the planet is far away. This particular property is relevant to infinity in that Kepler considered the case when the two points in question are infinitely close together. This rings of a premature calculus where the rate of change of the planet is examined by taking two points infinitely close to each other. With this process, Kepler described the orbit of Mars in his book The commentaries on Mars.The main consequence of Kepler’s third law of astronomy is that a planet must move faster when it is closer to its sun than when it is farther. Kepler was inspired to this proces by Archimedes, who famously inscribed shapes inside of a circle to approximate the area of the circle and pi. [2]

Taken from http://www.inference.phy.cam.ac.uk/teaching/dynamics/p0.html

All the blue regions have the same area, and by Kepler’s second law of astronomy the planet must traverse those regions in the same amount of time. For this reason the planet must speed up when it is nearer the sun.

On a lighter note, Kepler famously used a similar method involving potential infinity to determine the volume of wine bottles in the year 1612, when there was high demand for wine. [3] He also used similar methods to determine the areas of other abstract revolved surfaces. In particular he examined revolving circles about a chord, calling the surfaces “citrons” if the chord was less than a semicircle and “apples” if the chord exceeded a semicircle. [2]