 In how old are stars, we found that the Sun will burn hydrogen for 10 billion years. But because the Sun is a field star, we could not determine how long ago the hydrogen burning started. In how old is the Earth-Moon system, we found that the oldest solid Earth and Moon material was 4.3 billion years old. But we could not determine the age of the Earth from its original start, because the giant impact turned the mantle to magma. In this chapter, we'll cover the age of the solar system itself, which will give us both the age of the Sun and the age of the Earth. To get a handle on the age of the solar system, we'll need to review planetary formation theory. Any such theory would need to explain our solar system as we see it today. We'll start with a look at some of the key characteristics of our system. We have the Sun at the center and four relatively small rocky planets in the inner solar system and four much larger gaseous planets in the outer solar system. They are all in nearly circular orbits and they are all in the same orbital plane. None of the planets are orbiting outside the plane like some comet's asteroids and dwarf planets do. Our theory of planetary formation will need to explain these facts. In our How Older Stars segment, we've covered how the Circumsteller disk feeds the central object leading to the formation of protostars, t-tarry stars, and eventually fully formed helium fusion burning stars. The process from the beginning of the protostar phase to a fully fledged star is estimated to take from one to two hundred million years. During this period, the debris in the disk is forming planets. In the nucleosynthesis segment of the Lambda Cold-Dark Matter Big Bang Theory chapter, we covered the content of clouds like these for the first generation of stars. At that time it was limited to hydrogen, some helium, and just traces of beryllium and lithium. Planetary nebula formed when normal stars run out of hydrogen. The violent process created pressures and temperatures large enough to fuse hydrogen and helium into heavier elements and eject them into the interstellar medium from which giant molecular clouds like this are formed. These include carbon, nitrogen, and oxygen along with even smaller amounts of heavier elements like silicon, sulfur, and iron. But this kind of star transition does not have energy to fuse enough protons to create atoms larger than iron. Supernova explosions occur when supermassive stars run out of hydrogen. These seed even heavier elements into the interstellar medium like lead, zirconium, silver, tungsten, and gold. But even at these extreme energies it is unlikely that a supernova could produce elements larger than lead. This is because of the repulsive force of like charges is so strong. The Coulomb force creates the Coulomb barrier. You may recall from our last chapter on how older stars that a proton in our sun can collide a trillion times a second with other protons and still not fuse for a billion years. But neutrons have no charge and their fusing has no such barrier. It has long been theorized that the heaviest elements like thorium, protactinium, and uranium were created by neutron star mergers. In 2017, using large laser interferometers that we covered in the gravitational waves segment of the How Fast Is It? video book, just such a merger was detected. Now known as a kilonova, it's understood that neutron star mergers are the origin of the majority of all the heaviest elements found throughout the universe. For our collapsing cloud, we know that it contained all 94 natural elements because we find them here on Earth. 99% of the mass of the circumstellar disk is in the form of gas with just 1% in the form of dust. The solid dust has little effect on the star formation, but it's key to planetary formation. Dust is the only solid grains available for growing planets. Dust itself cannot be formed directly from purely gaseous material at the low densities found in interstellar molecular clouds. Instead, solid grains are known to form in planetary nebula, supernova, and in the outer atmospheres of cool supergiant stars. The dust in the interstellar medium extinguishes light from stars via absorption and scattering. The scattering leads to emissions of their own. Comparing dusty clouds to non-dusty clouds using spectral absorption and emission lines shows that almost all the iron, magnesium, silicon, much of the carbon, and some of the oxygen and nitrogen are contained in the dust. This makeup is similar to the terrestrial, amorphous, non-crystalline rocks. If the temperature permits, they are surrounded by a mantle of water ice. The original dust grains in the cloud are no longer available for direct observation. But to this day, there are similar objects in our solar system called interplanetary dust particles. They are being collected in the thermosphere by the International Space Station. Here's an electron microscope view of one of them. It's 10 micrometers in length. That's around 100 times larger than interstellar dust. NASA also uses high-flying aircraft to collect dust at high altitudes before it gets close enough to the surface to mix with earth elements. In 2018, a team of scientists from the University of Hawaii examined this dust with electron microscopes. They mapped the element distributions and discovered that these glassy grains are made up of sub grains that aggregated together prior to the formation of the comet the interplanetary dust particles came from. These represented samples of the early interstellar dust. Dust is the base material for planet formation. The dust grains run into each other and stick, forming larger and larger grains, mixing compounds and eventually forming mineral-rich pebble-sized objects that grow to boulder size. The near-earth asteroid 2015 TC-25 is an example of an object this size. With a 4 meter diameter, that's 13 feet, it's one of the smallest asteroids ever detected. The process continues to grow the rocks into rubble heaps, large enough for a little gravity to hold them together. Ryugu is an example of an object this size. It's one kilometer wide and weighs in at just under a half a trillion kilograms. Japan landed rovers on this asteroid in 2018. You can see the rubble nature of the object with this picture taken from the surface. By the time enough matter has accumulated into objects like these, we have what astronomers call planetesimals. These can extend from several to hundreds of kilometers in diameter. Object 67P, visited by the Rosetta mission in 2014, is thought to be a combination of two planetesimals that bound together in a slow speed collision. Their combined mass is just under 10 trillion kilograms. This is Aurocoth. It was discovered in 2014 out in the Kuiper Belt by the New Horizons search team using the Hubble Space Telescope. This object is 36 kilometers across, that's 22 miles. It's considered a minor planet like Pluto. Like P67, it has two lobes that collided slowly. A close examination of the surface shows lighter lines separating sections of the lobe. These indicate that Aurocoth was built piece by piece by the coalescing of over a dozen smaller planetesimals. By the time this collide and merge process creates objects with enough mass to produce a gravitational strength that exceeds the structural strength of the rocks, the object is forced into a spherical shape. Series is a good example of this. And once the mass reaches around 14 billion trillion kilograms, solid mass convection activates. The temperatures and pressures inside the object liquefy matter, and the core becomes molten. Mercury, our smallest planet, is a good example of this. The star, Formelhout, is a good example of this process. Its circumstellar disc morphed into a protoplanetary disc with at least one object large enough to be considered a planet, Formelhout B. Over time these larger objects continue to grow by accumulating matter from the disc. We find that in each region, each orbit, each distance from the sun, everything coalesces into one massive object. These larger objects sweep out the remaining debris in their orbits. This is a defining characteristic for planets. All the little deviations averaged out as the smaller particles with varying elliptical orbits combined. This explains orbits being nearly circular, and all in the same plane. But the actual process is very chaotic. Not as simple and straightforward as this illustration. The process of accumulating matter in the disc into larger objects came to an end when the sun ignited as a main sequence star, and its strong solar winds blew away any remaining loose material. Other model estimates for how long this process takes range from 100 million to 200 million years. Here's a computer simulation created by Caltech that illustrates this chaos. Planets interact with the rotating disc and lose momentum moving their orbits closer to the sun, or gain momentum increasing their orbital distance from the sun. Changing orbits create collisions between planets, moons form and collide with each other and with planets. Comets and asteroids form and smash into everything. But out of this chaos, we get our current order. There is an expected difference between how this works out for planets forming in the inner parts of a solar system, and how it works out for planets forming in the outer parts of the solar system. In the inner parts closer to the central star, it's hot. At these temperatures, with no pressure, water molecules cannot take liquid or solid form. The solar wind from the forming star pushes these molecules along with helium and hydrogen molecules into the outer solar system. Planetesimals in this inner region wind up with little to no gas or water. That leaves metal and rock for these planets. In the outer parts, further from the central star, the water is frozen solid and therefore behaves like rocks. Planets out here have metal, rocks and ice. This means that they're substantially more massive. This extra mass produces enough gravity to hold on to the gas as well. The dividing line is called the frost line, or the snow line, and its distance from the star is temperature dependent. It will be located where the temperature falls to around 250 degrees Kelvin, that's minus 10 degrees Fahrenheit. The hotter the star, the further out this line will be. This explains the difference between the rocky planets in the inner solar system and the gas giant planets in the outer solar system. Our frost line is between four and five astronomical units. That puts it at the far rim of the asteroid belt. Meteorites are asteroid or comet material that have fallen to Earth. There are over 40,000 meteorites that we know about. Some have no uranium. They can be used to measure the solar system's initial lead ratios. The Kenyon Diablo meteorite fits in this category. Some contain intact material from the circumstellar disk during the planetesimal building process. These are the ones that never went through a melt and re-hardening process, like all the rocks on the Earth and the moon. The meteorite Allande fits into this category. We'll start with Kenyon Diablo, the meteorite that was responsible for meteor crater in Arizona. It is estimated to have fallen to Earth around 50,000 years ago. Fragments of the meteorite have been actively collected since the mid-1800s. The largest fragment is the Hollinger meteorite, with a mass of 639 kilograms or 1,400 pounds. This iron meteorite contains treylite, an iron-sulfide mineral that has almost no uranium. Since the mineral contains no uranium, all the lead present in the treylite is the lead originally present when the meteorite formed. This includes the radiogenic isotope lead 206 and 207 that decayed from uranium before the meteorite formed, as well as the natural, non-radiogenic lead 204. Thus, using mass spectrometry as always, this Kenyon Diablo treylite gives us the primordial ratios for lead 206 over 204 and 207 over 204. In fact, these two numbers are generally used as the standard for our solar system's original lead concentrations. In 1969, Allande created a fireball over the northern Mexico sky. As the meteorite burst, numerous fragments rained down around the small village of Pueblito de Allande. Over 2,000 kilos of debris have been found, and new pieces are still being discovered every now and then. It's a type of meteorite called carbonaceous chondrite. That's a stony meteorite with lots of carbon and containing small mineral granules called chondrules. A lot of meteorites have experienced significant heat that melted and reorganized their minerals. But Allande was not one of them. Its pieces remained as they were when they formed. Here's a slice of it. We're particularly interested in the little pale whitish-gray bits called calcium-aluminum inclusions, CAIs for short. These are thought to be the very first solids condensed in the circumstellar disk. Dating these would give us the starting date for the solar system. Other interesting pieces of the meteorite are these round darker-gray bits. These were the first liquid droplets to condense out of the disk gas. They are also some of the oldest minerals that formed in the solar system, but not as old as CAIs. We are interested in two findings associated with Allande. One is the ratio of Uranium-238 to Uranium-235 isotopes. In Allande, it was around 137.88 Uranium-238 for each Uranium-235. This ratio has held up across Earth, Moon, and meteorite rocks. The other is the ratio of radiogenic lead 207 and 206 to non-radiogenic lead 204. A large number of these ratios were determined from the various CAIs and condrules, but we'll use just one, with lead 207 over 204 at 22.76 and 206 over 204 at 30.06. These ratios for Uranium and lead from Allande and primordial lead from Canyon Diablo are very important for dating meteorites. In the How Old is the Earth-Moon System, we covered radioactivity, half-life, and the law of radioactive decay. It showed that the present amount of radiogenic lead in a sample will equally initial amount, plus however much gets created by the decay of the parent Uranium. For lead 207, the parent is Uranium-235. For lead 206, the parent is Uranium-238. With this equation we used Arthur Holmes' system for Uranium decay into lead inside Zircon crystals to date the oldest rocks on the Earth and the Moon. But that won't work for meteorites. They don't have any Zircon crystals. So by the mid-1940s, Arthur Holmes and others had extended the Uranium-lead dating method into a lead-lead method called the Holmes-Houderman system that took into account lead 204 the natural non-radiogenic lead isotope. This is the system that tells us the age of meteorites, the Earth, planets, and the entire solar system. So we'll take a minute to show how it works. The idea is to start with the Uranium-to-lead growth equations and produce an equation that fits the definition for the slope of a line. We start by dividing both sides of the growth equation by the number of lead 204 isotopes. We move the lead term on the right side of the equation to the left side, leaving only Uranium on the right. We then divide the top equation by the bottom. This creates ratios on the left and right. We then replace the Uranium ratio on the right with the known value, 1 over 137.88, found in a Yonde and elsewhere. This knocks out the need to measure Uranium content altogether. If we graph this equation using the 207-204 ratio as the Y-axis and the 206-204 ratio as the X-axis, we see that the left-hand side of our Holmes-Houderman's equation is the slope of a straight line. The right-hand side depends only on time. For any given time, t will have a straight line. Replacing the initial lead ratios with the standard from Canyon Diablo, we see that all lines pass through this point. Now if we have t stand for the amount of time since the material formed, we can use the present-day lead ratios from the Yonde CAI for the other point on the line. Other ratios from Yonde CAIs also fall on this line. In fact, all the materials formed around the time these CAIs formed will fall on this line. That's why this isochron is called a geochron. It represents the age of the solar system's planetesimals building blocks. So now we have an equation for this earliest time, t. It's a transcendental equation, it cannot be solved algebraically, but computer iteration processing gets us as close as we want. The solution gives us t equal to 4.567 billion years, plus or minus 70 million years. This is the oldest age of all meteorites, meteors, asteroids, comets, moons, planets, including the earth, as well as the sun. In fact, whenever you hear that the sun is 4.5 billion years old, that number came from this Holmes-Houderman's process for radiometric rock dating. Now that we have a handle on star development, from how older stars, and some key dates from uranium-led analysis of rocks and meteorites, we can estimate the age of the solar system as a whole. Give or take a few million years here and there. Our first data point is provided by uranium decay. A neutron star merger would have seeded our cloud with relatively equal amounts of uranium 235 and uranium 238. The time it takes for the ratio to reach today's value of 1 uranium 235 for every 137.88 uranium 238 is 6 billion years. For almost 1.4 billion years, the cloud orbited the Milky Way in hydrostatic equilibrium. And then, for some as yet unknown reason, the equilibrium was broken and it started to collapse. In a million years, the colliding giant molecular cloud broke up into fragments, with our fragment being one of them. Over the next million years, a circumstellar disk formed around a central object accreting mass from the disk material orbiting around it. From here on, we'll cover the development of the core object and the circumstellar disk in parallel. Over the course of the next million years, the central object continued to accumulate matter and its core temperature reached 10,000 degrees Kelvin. At this temperature, it began to shine by a normal, non-nuclear means. That made it a protostar. It may have looked like this one, just 950 light-years away. During this time, most of the matter continues to reside in the circumstellar disk. It's losing large quantities of material to the central object, but by the time the protostar forms, the disk still has 99% of the solar system's mass. Some dust may have been colliding and sticking together, but the vast majority of whatever formed in the disk during this period was eventually lost to the forming star. The protostar phase does not last long for stars the size of our sun. Over the next million years, it accumulated massive amounts of matter from the disk and shrank significantly as gravity took hold. Its core temperature rose to 5 million degrees. This put the sun into its T-Tari phase, named after the star, T-Tari. In fact, it may have looked like T-Tari. The young sun was still growing by accumulating large amounts of material from its surroundings, so it was not yet stable. Unlike the short life span for protostars, T-Tari stars can last for 100 million years. During this phase, the disk experienced a growing solar wind from the developing star. This wind started pushing on the lighter gas and dust close to it, forming a snow line beyond which water ice could form. With the sun at only 5 million degrees Kelvin, this line would be much closer to the star than it is today. Over the next 30 million years, the sun's core temperature would have reached 10 million degrees. Throughout the disk, some dust grains began to stick together, forming larger particles. These particles continued to randomly collide and stick, creating planetesimals, reaching the size of boulders or small asteroids. The oldest of the starting material found so far was in the Elande meteorite and dated via lead isotope contents to be 4.567 billion years old. By convention, astronomers used this date for the age of the sun and its solar system, often rounded up to 4.6 billion years. Estimates are that the sun remained in its T-Tari phase for an additional 67 million years as it migrated to the main sequence. In that time, it reached 15 million degrees Kelvin at its core. As the sun's solar wind picked up, it dispersed the remaining gas and dust around it back into the interstellar medium. This ended mass accumulation and the sun settled into hydrostatic equilibrium. During this period in the disk, the forming of planetesimals increased as the objects began to attract each other via gravity. The disk grew to planet sizes and swept out the debris in the vicinity of their orbits. The disk experienced a chaotic period of collisions that resulted in 9 major planet-sized objects along with dozens of moons and millions of asteroids and comets. In addition, as the sun heated up, the snow line moved out to where we find it today, just outside the asteroid belt. This line separated the four waterless inner solar system planets from the five water-rich outer solar system planets. The giant impact hypothesis has a collision between the Earth and a Mars-sized planet liquefying the crust of both planets and forming the moon from ejected matter. Based on uranium-led dating of zircon crystals found in Australia and on the moon, this happened 4.3 billion years ago. That would be 200 million years after the original Earth formed. Given the mass of our sun, we know that in the beginning it had enough hydrogen to shine for a total of 10 billion years. We now figure that it has been burning for 4.6 billion years. Therefore we can expect that it will burn for 5.4 billion more years before it runs out of fuel. I am impressed by how we have been able to reconstruct our solar systems formation. We started with a giant molecular cloud rotating around the Milky Way every 213 million years, 26,000 light years from the center. It was seated with uranium around here, a little over an eighth of a revolution from our current position. It rotated an additional six and a half times before the cloud segment started to collapse here where we find the Perseus arm today. It took only half of a revolution more to form the entire solar system. Today we have a beautiful planet with a sun that will sustain us for billions of years. But even more spectacular than the rise of the Earth over a 300 million year period is what happened in the 4.3 billion years since our temperate, watery Earth formed. Life.