In Kepler’s model, the Sun lies at one focus of each planet’s elliptical orbit.
This statement is Kepler’s first law of planetary motion, published in 1609 in Astronomia nova. It replaced the long-standing assumption that celestial orbits had to be perfect circles. Kepler reached the result by analyzing Tycho Brahe’s exceptionally precise observations, especially the difficult motion of Mars. An ellipse is an oval-shaped curve with two focal points; the Sun occupies one, while the other is empty.
The Sun is therefore not at the geometric center of a planet’s ellipse. Because the orbit is usually only slightly eccentric, most planetary paths look nearly circular, which can hide the offset. Earth’s orbit is a modest example, while a comet such as Halley’s has a much more elongated ellipse.
The focus should not be confused with the center, vertex, or directrix. Kepler’s second law adds that a planet sweeps out equal areas in equal times, so it moves faster near the Sun and slower farther away. In a more exact two-body treatment, the focus corresponds to the system’s barycentric arrangement.