## What are the common methods for chronology, or measuring time?

In cosmochemistry, chronology involves determining the timing of events that resulted in the formation of the Sun and the planetary bodies that orbit it. There are two different types of ages: relative and absolute.

Relative ages tell you the sequence of the events based on the geological principle of superposition, which states that in a sequence of undisturbed sedimentary layers or lava flows, the oldest layers are at the bottom. See the image of the Grand Canyon below for an example. We know that CAIs and chondrules must have formed before the chondrites because the chondrites cannot be older than their components (see images below for clarification)

Layers of sediment in the Grand Canyon is a nice example of the Law of Superposition. The layers on the bottom are older than layers on the top.

The circular components of this chondrite (e.g., CAIs and chondrules) formed before the chondrite.

The law of superposition is also used for crater counting, the main way we determine the relative ages of planetary surfaces like the Moon, Mars and Mercury. The more craters on the surface, the older that surface. Crater counting assumes that new surfaces are smooth and that craters form over time at a constant rate. The light and dark surfaces of the Moon are a simple example of this idea. The dark smooth surfaces on the Moon are younger than the heavily cratered, light surfaces.

The Moon has smooth and cratered surfaces. The cratered surfaces are older than the smooth dark surfaces.

Measuring the accumulation of daughter products from their unstable parent nuclides (or radionuclides) provides a more quantitative way of determining ages. We measure the abundances of the parent and daughter isotopes that are present. If the decay rate of the radioactive parent is known, we can calculate the time necessary for the daughter to accumulate using the radioactive decay equation (see example here).

The only way to get absolute ages is by analyzing long lived radionuclides systems in the object of interest. Absolute ages give you the time (in years, usually) when an object formed. These radionuclides have half-lives greater than 100 million years, which means that a significant amount of the radioactive parent nuclide is still exists today. The most commonly used long lived radionuclide system in cosmochemistry today is the 206Pb-207Pb system (based on the U-Pb system). The age of the Earth was calculated by Clair Patterson to be 4.55 billion years old based on Pb-Pb dating of meteorites and terrestrial rocks.

Short-lived radionuclides (SLRs) have half-lives less than 100 million years. They are also called “extinct” or “fossil” radionuclides because the radioactive parent nuclides are no longer present in detectable abundances in the solar system (see diagram below).  For SLRs, the presence of the radioactive parent is estimated by measuring the excess of the daughter nuclide relative to the terrestrial value. SLRs can provide quantitative relative ages, not absolute ages. The commonly used SLR system in cosmochemistry is 26Al-26Mg, which has a half-life of 0.7 million years. Primitive meteorites, also called chondrites, have circular inclusions that were originally dust particles in the protoplanetary disk.  The large white circular inclusions in meteorites (see image of chondrite above) are called calcium-aluminum-rich inclusions (CAIs). The other smaller circular inclusions are called chondrules. The Al-Mg system has been used to date these inclusions. Studies have found that CAIs have larger amounts of excess 26Mg than chondrules. The difference in the excess 26Mg corresponds to >2 million years difference in their ages. Therefore, chondrules formed >2 million years after CAIs. In fact, absolute ages of CAIs from Pb-Pb measurements indicate that CAIs are the oldest material in our solar system at 4.56 billion years old. This gives us an upper limit on the age of the solar system.

Aluminum-26 is a short-lived radionuclide that decays to 26Mg. It has a half-life of 0.73 Myr. This diagram shows that as the number of 26Al atoms decreases with time due to radioactive decay, the number of  atoms of the daughter product, 26Mg, increases.