Absolute dating is used to determine a precise age of a rock or fossil through radiometric dating methods. This uses radioactive minerals that occur in rocks and fossils almost like a geological clock. It's often much easier to date volcanic rocks than the fossils themselves or the sedimentary rocks they are found in.
The ecliptic is the plane of Earth's orbit around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars.