Earth's formation & Late Heavy Bombardment

1. Dec 27, 2008

Widdekind

According to the History Channel documentary Comets -- Prophets of Doom (DVD), Earth today accumulates "30 to 40 thousand tons of space dust per year".

CRUDE MODEL:

We imagine that the accumulation rate of space debris declines exponentially:
$$rate = T \times e^{-\frac{t}{\tau}}$$​
We then demand that:
$$T \times e^{-\frac{4.5 \, billion}{\tau}} = 40,000 \, tons \, year^{-1}$$​
and
$$\int_{0}^{4.5 \, billion} T \times e^{-\frac{t}{\tau}} dt = M_{Earth}$$ ​
Solving this sytem of equations numerically yields:
$$T \approx 3 \times 10^{13} tons \, year^{-1}$$
$$\tau \approx 200 \, million \, years$$​
This suggests, that Earth only reached ~98% of its present mass after 4$$\tau$$ = 800 million years. Since Earth is ~4.6 billion years old, this suggests, that the early Earth was accumulating considerable mass until ~3.8 billion years ago. Perhaps surprisingly, this agrees w/ Geological evidence, that Earth's Late Heavy Bombardment persisted until ~3.8 billion years ago*. Before this time, Earth was significantly (2-40%) smaller than today, explaining why no prior rocks** have (to date) been found.
* James F. Luhr. (DK) Earth -- the Definitive Visual Guide, pp. 26-29.
** ibid., Zircon crystals have been found from ~4 billion years ago.

2. Dec 27, 2008

D H

Staff Emeritus
This is far too speculative and contains far too many unjustified assumptions. In particular, what makes you think that mass accumulation in the protoplanetary disk is anything like the mass accumulation after the Sun ignited, and that mass accumulation after solar ignition follows a simple exponential decay?

If this is your own pet theory, we have rules against that. If this is something you can justify from peer-reviewed literature, please post a reference.

3. Dec 27, 2008

Staff Emeritus
You start with a model with the majority of the accretion occurring at early times. You then use this to show that the majority of the accretion occurs at early times.

OK...I guess.

4. Dec 27, 2008

D H

Staff Emeritus
What Widdekind has done here is anything but OK. It flies in the face of extant planetary formation theory. This forum is not the place for personal conjectures.

The standard model indicates that the planets formed fairly quickly. For example, see http://www.nature.com/nature/journal/v418/n6901/abs/nature00995.html.

That simple exponential decay in the accumulation rate is too simple. It indicates a maximal rate occurred when the Earth's mass was zero. This is simply wrong. Think of a snowball rolling down a hill. A snowball's mass accumulation rate increases as its mass increases (it is roughly proportional to the surface area, or m2/3). While the snowball analogy is just that -- an analogy -- there are good reasons to think that the Earth's mass accumulation rate also increased as the Earth's mass grew.

By Widdekind's simple model, there is nothing special to mark the late heavy bombardment. This, too, flies in the standard models. The late heavy bombardment period represents a distinct spike in mass accumulation. One explanation is the outward migration of Neptune and Uranus toward to Kuiper belt. For example, see http://www.nature.com/nature/journal/v435/n7041/full/nature03676.html.

Widdekind appears to have cherry-picked the number 40,000 tons/year. It's a bit hard to track down good numbers; I found estimates on non-crackpot sites ranging from 20,000 tons per year to 200 million tons per year. A higher number is not good for Widdekind's conjecture.

Finally, there is evidence of rocks considerably older than the late heavy bombardment. For example, see http://news.nationalgeographic.com/news/2008/09/080925-oldest-rocks.html. These early rocks jibe with the Earth being essentially fully formed 4.6 billion years ago. The late heavy bombardment was simply a period of increased bombardment that did not change the Earth's mass by much. The reason we don't see many very old rocks is because of plate tectonics rather than as a result of burying by continued bombardment.

Last edited: Dec 27, 2008
5. Dec 27, 2008

Staff Emeritus
I guess my point was that all that Widdenkind got out is what he put in. As you point out, that doesn't match any observations.

Well, he does have a history of that.

6. Dec 27, 2008

D H

Staff Emeritus
I've noticed that.

7. Dec 27, 2008

Janus

Staff Emeritus
locking as OP is being over-speculative