When was the Earth formed?

When was the Earth formed? Modern estimates are that it formed by accretion, 4.54ish billion years ago. But I’m not going to worry about its absolute age; what I’m wondering is where we choose to draw the line between Earth-not-quite-formed and Earth-now-formed.

We don’t really know how long it took for the Earth to form. It may have been only a few million years, or it may have been upward of a hundred million. Time frames on the lower end of that range are within the margin of error for our ability to measure its age. But if it took closer to a hundred million years, it makes a difference where in that process we declare the Earth to be officially “formed”.

It’s a kind of Paradox of the Heap (also called the Sorites Paradox). Removing one grain of sand from a “heap” seems like it shouldn’t cause it not to be a heap of sand. And (as we look back in time) removing one dust particle from the Earth shouldn’t make it not-the-Earth. But, carried to its logical extreme, that implies that one grain of sand can be a heap, or one dust particle can be the Earth, which is silly.

We might want to appeal to the International Astronomical Union’s controversial 2006 definition of “planet”, but we should be careful, because that definition is not intended to be universally applicable. Consider that no exoplanets can be planets, because planets must orbit the Sun. It’s really just an ad-hoc definition intended to apply to the modern Solar System. Still, maybe the idea of “clearing its orbit” is useful. We could declare the Earth to be formed when its orbit has been substantially cleared of small objects.

The giant impact

The next question: Did Earth exist prior to the “giant impact” event? The giant-impact hypothesis says that, early in the Earth’s history, there was another large proto-planet, commonly called Theia, in the same orbit. Theia eventually collided with the Earth. Most of it merged with the Earth, while some of the debris field produced by the impact coalesced to form the Moon.

I couldn’t find a clear chronology of events. Was the orbit pretty much cleared before the impact, or is it possible that the impact occurred while Earth and Theia were still getting bigger? I’ll assume the former.

So we’re supposed to imagine that it happened like this:

Descriptions of the impact always seem to implicitly answer my question. By calling the larger object the Earth, that means the Earth must have already existed.

If we gave the objects unbiased names, it wouldn’t change what happened, but it might change how we tend to imagine it:

By the way, why does nobody call Theia a planet? It’s always an “object”, or a “body”. I suppose the IAU definition might have something to do with it, though my fuzzy memory tells me this conspicuous avoidance of the word “planet” is older than that.

Theia is invariably described as Mars-sized. That’s suspiciously specific, but I’ll go with it. Mars is (and therefore Theia was) about 10.7% of Modern Earth’s mass. Using these numbers, I estimate that Theia was around 11.9% of pre-impact Earth’s mass. The impact increased Earth’s diameter by 3 or 4%.

Of course it’s reasonable to award the name “Earth” to the larger of the two impacting objects. It’s like if you’re an explorer of old, tracing a big river to its source. When you come to a fork, you’d probably choose the tributary that supplies the most water.

There are some researchers who think that the impactors might have actually been very close to the same size as each other, because that would better explain the composition of the Earth and Moon.

I’m sure there’s some very good reason that this is not the mainstream theory, but it would be interesting if it were. Even if we wanted to, we couldn’t really call one of the impactors the Earth. Without a time machine, we’d have no way to even tell which is which.

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