Formation of the Earth's Moon

How did this get here?

The earth has a bulk density of 5.5 grams per cubic centimeter. This density reflects the composition of material at the location in the solar system where the Earth was assembled via accretion. Logically one would therefore expect the moon to the have the same density. However,the moon has a density of 3.3 grams per cubic centimeter. Is this a problem?

Yes! This implies a special formation history for the Moon which is difficult to understand from first principles.

The Origin of the Moon:

Until recently, the origin of the Moon was not understood. The moon has long been an anomaly because its mass is 1/80th of Earth's mass and volume is 1/50th of Earth's volume. This is very large for a planetary satellite. For instance, the moon to planet mass ratio for Ganymede, the largest moon in the Solar System, to it's planet Jupiter is less than 1/1000th. Their volume ratio is almost 1 to 20,000.

Possibilities for Lunar Origin:

Formed in place by accretion NO! its composition/density is wrong
Formed someplace else where the average density is 3.5? Implies formation near Mars how did it get here?
Fissioned from the earth's mantle (note the density of the earth's mantle is around 3.5) - but by what mechansism?

The above 3 scenarios for lunar formation are all physically implausible so why is the moon there?

Let's imagine the following sequence:

Shortly after the formation of the earth a leftover planetisimal roughly the size of Mars had either struck the earth or had a close passage to it. What might happen?

Here is the Sequence if there was an impact

	Step 1: The Mars planetisimal is poised to strike the molten protoplanet earth which has been differentiated.
	Step 2: The impact into the molten earth sends large molten lumps of debris out of the earth - mostly from the middle layers of the differeniated earth.
	Step 3: The debris ring of molten ejecta coalesces, by accretion, into a single object. The density of that object would be similar to the density of the middle layers of the earth (e.g. about 3.5 grams/cc). In computer numerical models, this coalescence occurs fast, on a timescale of about 100 million years.

The problem with this scenario is that the probability of a direct collision is small. However, the same result can occur if there is not a direct collision but instead there is a close passage by the Mars sizes object.

Here is the Sequence if it was a close passage:

	This shows the encounter path.
	Step 1: A tidal force is exerted on the molten earth which causes an obvious deformation.
	Step 2: The deformation actually separates from the earth initially as a whole molten blob whose composition again reflects the middle layers of the Earth
	Step 3: However, this molten blob is gravitationally perturbed by the combined forces of the Earth and the still near Mars size object so it distengrates into a debris ring.
	After a 100 million years or so, the debris ring has coalesced into the moon, and the Earth has cooled so that water vapor in its atmosphere (combined with bombardment by comets) has produced the oceans.

Since the moon formed from the condensation of a debris ring in relatively near-earth orbit, the moon was initially quite close to the earth. At this time (4.6 billion years ago) the earth was rotating quite rapidly (about once every 5 hours). The nearby moon exerted large tidal forces on the spinning earth causing it to slow down. This process continues to day. To conserve total system angular momentum, the response of the moon is then to move farther away from the earth.

How did this get here?

Step 1: The Mars planetisimal is poised to strike the molten protoplanet earth which has been differentiated.

Step 2: The impact into the molten earth sends large molten lumps of debris out of the earth - mostly from the middle layers of the differeniated earth.

This shows the encounter path.

Step 1: A tidal force is exerted on the molten earth which causes an obvious deformation.

Step 2: The deformation actually separates from the earth initially as a whole molten blob whose composition again reflects the middle layers of the Earth

Step 3: However, this molten blob is gravitationally perturbed by the combined forces of the Earth and the still near Mars size object so it distengrates into a debris ring.

After a 100 million years or so, the debris ring has coalesced into the moon, and the Earth has cooled so that water vapor in its atmosphere (combined with bombardment by comets) has produced the oceans.