Pre-moon size of the earth

January 13, 2011 12:41 AM

What was the size of the earth, proportionally to it today, before whatever hit it to create the moon?
posted by Sparx to Science & Nature (12 answers total)

The theory that something crashed into Earth to make its moon is only a theory, still. So there's probably no known answer to this, but most proponents of said theory believe that Earth was actually smaller before than after, oddly enough.
posted by Dee Xtrovert at 1:15 AM on January 13, 2011 [1 favorite]

If we assume that no mass was lost in the process and simply sum the volumes of the Earth and the Moon then we have a combined volume of 1.11×10²¹ m³. This is equivalent to a sphere of radius 6413 km, compared to the current radius of Earth which is 6367 km. In volume terms it'd be about 110% the current volume.
posted by alby at 1:21 AM on January 13, 2011 [1 favorite]

alby - the impactor is hypothesized to be approximately mars-sized, so you'd need to include that as well... Vearth + Vmoon = Vpre-earth + Vmars, assuming no material was lost, very approximately...
posted by russm at 1:35 AM on January 13, 2011 [2 favorites]

Best answer: so now I'm off my phone and can look stuff up, plugging in the numbers from wikipedia, the volume of the pre-impact Earth has a lower bound of 0.869 of the current Earth (plus any material permanently ejected from the Earth/Moon system)... this gives a radius of ~96% the current radius of Earth... it's all pretty approximate though...
posted by russm at 2:10 AM on January 13, 2011

Response by poster: Fascinating. I hadn't even thought to consider the addition of the impactor. Is that why the Earth is thought to have been smaller pre-impact?
posted by Sparx at 2:11 AM on January 13, 2011

yep - if the impactor was indeed mars-sized (and I have no idea how that estimate was made) then it's quite a bit of material you're adding...

then again, if we make some unjustifiable assumptions (composition of the earth was and is uniform, and didn't change as a result of the impact event, and I'm not messing up the calculation), the surface gravity of the pre-impact earth would have been ~98% of current surface gravity (reduced since the Earth was smaller, offset by being closer to the centre of mass)... I doubt you'd even notice the difference...
posted by russm at 2:27 AM on January 13, 2011

Don't forget that the moon is less dense than the earth, presumably due to its lower compaction by gravity, and the impactor might well have had the same characteristic. So the volumes added to the Earth would not have been static.
posted by nicwolff at 5:21 AM on January 13, 2011 [1 favorite]

Best answer: A quick search on NASA's ADS site finds articles stating that dynamical simulations support the idea that the impact of the Mars-sized object occurred when the Earth was approximately 90% of its current mass.
posted by Tooty McTootsalot at 6:35 AM on January 13, 2011 [1 favorite]

The theory that something crashed into Earth to make its moon is only a theory, still.

It's actually a hypothesis.
posted by electroboy at 7:27 AM on January 13, 2011 [4 favorites]

Best answer: Earth and Venus are nearly the same size. But Earth is a lot more dense, having a lot more metal than Venus, which is why the surface gravity on Earth is about half again what it is on Venus.

There's really no way to know what pre-impact Earth was like, but the best guesses I've seen is that it was a near-twin of Venus.
posted by Chocolate Pickle at 9:27 AM on January 13, 2011

nicwolff - the density variation is due to composition, not compaction, so summing volumes does actually work in this case. (the Earth had already differentiated into a lighter crust/mantle and a heavy core when the hypothesised impact occurred, so the material that was ejected from Earth was mainly composed of the Earth's lighter elements.)
posted by russm at 12:45 PM on January 13, 2011

I just looked it up, and now they say that the surface gravity of Venus is .9G. Used to be they said it was about .7G, which is why my "half again" comment above.
posted by Chocolate Pickle at 5:48 PM on January 13, 2011