There are 3 naturally occuring types of carbon, called isotopes, ¹²C, ¹³C, and ¹⁴C. These are all basically the same except for the number of neutrons in the nucleus of the atom. Living things can use all 3 types to build sugars and proteins and all those other organic molecules needed for life. Animals get it from the food they eat, plants get it from the air. These 3 isotopes all exist in nature in a pretty consistent ratio
¹⁴C, however, is unstable (radioactive) and over time decays into more stable elements.
But it also is constantly getting replenished from cosmic rays interacting with other gases in the atmosphere to in the atmosphere, so as long as something is alive the ratio of carbon 14 in that plant or animal to the other types of carbon stays pretty consistent.
But once it dies, it’s not taking any new carbon in, so what was there when it died is all it’s ever going to have until it decomposes away entirely or gets eaten by scavengers or whatever. The ¹²C and ¹³C are basically going to stay put, while the ¹⁴C slowly decays.
So to date something you just need to look at the ratio of the different types of carbon and you can figure out how old it is.
Let’s say ¹⁴C has a half life (the time it takes for half of it to decay) of 1 year (its actually something like 5 or 6 thousand years but this makes the math easy with smaller, easier to digest numbers)
And let’s say the ratio is 1:1, ¹²C+¹³C to ¹⁴C (again, it’s more like 1% carbon 14 IRL)
So after a year, half of the ¹⁴C will be gone, and the ratio will be 2:1
After another year half of that remaining ¹⁴C will be gone and it’ll be a 4:1 ratio, another year and it’s 8:1, etc.
This of course has limitations. After a long enough time basically all of the carbon 14 will be gone and you can’t really date things that way anymore. I think the limit is something like 50,000 years.
It’s also only really useful for plants, animals, and stuff made from them (leather, textiles, the straw in mud brick buildings, food, etc.)
So not really useful for dating rocks from a few billion years ago like we would need to date remnants of Theia.
There’s also a few things that can cause more ¹⁴C to form than normal, humans caused one with our nuclear testing, there was another event around the 8th century that we’ve discovered from measuring the carbon 14 in tree rings from that time that we think may have been caused by a supernova sending more cosmic rays our way than usual. So those events also need to be accounted for.
But there’s other similar techniques using elements with longer half lives that we can use to date older or inorganic materials.
For example uranium-lead dating. When the mineral Zircon forms, it tends to include uranium but exclude lead. But over time uranium decays into lead, so if you have a sample of zircon, you can measure how much lead is in it and figure out how long ago it must have formed because that lead must have once been uranium that has decayed at a steady pace over the centuries.
So we can use methods like that to determine when certain rocks formed.
We know pretty well what the earth and moon are made of (X% silica, Y% Iron, Z% aluminum, etc. with certain amounts of different isotopes) so if we were to find some deposit of minerals that deviates a lot from what you’d find elsewhere on earth or the moon, it’s pretty safe to say that that material might have originated elsewhere, like on theia.
There are 3 naturally occuring types of carbon, called isotopes, ¹²C, ¹³C, and ¹⁴C. These are all basically the same except for the number of neutrons in the nucleus of the atom. Living things can use all 3 types to build sugars and proteins and all those other organic molecules needed for life. Animals get it from the food they eat, plants get it from the air. These 3 isotopes all exist in nature in a pretty consistent ratio
¹⁴C, however, is unstable (radioactive) and over time decays into more stable elements.
But it also is constantly getting replenished from cosmic rays interacting with other gases in the atmosphere to in the atmosphere, so as long as something is alive the ratio of carbon 14 in that plant or animal to the other types of carbon stays pretty consistent.
But once it dies, it’s not taking any new carbon in, so what was there when it died is all it’s ever going to have until it decomposes away entirely or gets eaten by scavengers or whatever. The ¹²C and ¹³C are basically going to stay put, while the ¹⁴C slowly decays.
So to date something you just need to look at the ratio of the different types of carbon and you can figure out how old it is.
Let’s say ¹⁴C has a half life (the time it takes for half of it to decay) of 1 year (its actually something like 5 or 6 thousand years but this makes the math easy with smaller, easier to digest numbers)
And let’s say the ratio is 1:1, ¹²C+¹³C to ¹⁴C (again, it’s more like 1% carbon 14 IRL)
So after a year, half of the ¹⁴C will be gone, and the ratio will be 2:1
After another year half of that remaining ¹⁴C will be gone and it’ll be a 4:1 ratio, another year and it’s 8:1, etc.
This of course has limitations. After a long enough time basically all of the carbon 14 will be gone and you can’t really date things that way anymore. I think the limit is something like 50,000 years.
It’s also only really useful for plants, animals, and stuff made from them (leather, textiles, the straw in mud brick buildings, food, etc.)
So not really useful for dating rocks from a few billion years ago like we would need to date remnants of Theia.
There’s also a few things that can cause more ¹⁴C to form than normal, humans caused one with our nuclear testing, there was another event around the 8th century that we’ve discovered from measuring the carbon 14 in tree rings from that time that we think may have been caused by a supernova sending more cosmic rays our way than usual. So those events also need to be accounted for.
But there’s other similar techniques using elements with longer half lives that we can use to date older or inorganic materials.
For example uranium-lead dating. When the mineral Zircon forms, it tends to include uranium but exclude lead. But over time uranium decays into lead, so if you have a sample of zircon, you can measure how much lead is in it and figure out how long ago it must have formed because that lead must have once been uranium that has decayed at a steady pace over the centuries.
So we can use methods like that to determine when certain rocks formed.
We know pretty well what the earth and moon are made of (X% silica, Y% Iron, Z% aluminum, etc. with certain amounts of different isotopes) so if we were to find some deposit of minerals that deviates a lot from what you’d find elsewhere on earth or the moon, it’s pretty safe to say that that material might have originated elsewhere, like on theia.