From: roberts@cmr.ncsl.nist.gov (John Roberts)
Newsgroups: sci.space
Subject: More lunar gravity questions
Date: 8 Nov 92 20:03:07 GMT
Article-I.D.: cs.BxEyEE.6C9.1
Distribution: sci
Organization: National Institute of Standards and Technology formerly National Bureau of Standards
X-Added: Forwarded by Space Digest
Original-Sender: isu@VACATION.VENARI.CS.CMU.EDU


-From: andy@osea.demon.co.uk (Andrew Haveland-Robinson)
-Subject: Ten embarrassed questions about the moon (very long)
-Date: 8 Nov 92 03:34:44 GMT
-Organization: Haveland-Robinson Associates

-In article <BxD5Hz.Ewt.1@cs.cmu.edu> roberts@cmr.ncsl.nist.gov writes:
-...
-An excellent article!  I have a couple of questions...

-What is the ratio of density of the mascons to the "masdeps" (depletions)?

Here's what I can find in the reference:

p.27: "The laser altimetry experiment also revealed that the center of mass
[of the moon] was displaced 2-3 km from the geometric center, toward the
earth. This offset cannot be accounted for by the mascons, which shift the
center of mass only about 40 m. The displacement is compatible with a thicker
far-side crust of highland material."

p.277: "The mean lunar radius is 1738 km and the mean density is 3.34 g/cm^3.
The density of the highland rocks lies within the range 2.75-3.0 with a mean
value of 2.95. The maria basalts have higher densities (3.3-3.4), about equal 
to the bulk density of the moon. The density of the lower crust ...is probably
about 3.0-3.1. Assuming that the crustal average density is 2.95, the bulk
density of the moon below the crust will be 3.39 g/cm^3." [Latest value of
coefficient of moment of inertia (0.395 +- .005) does not rule out the
possibility of a core.] "The data permit the existence of an iron core
of radius 450 km, for which there is no seismic evidence, or of a Fe-FeS
core of radius 700 km, which corresponds to the S wave seismic discontinuity."

p.277: "The smallest example [of a filled crater with a positive mascon]
is Grimaldi (150 km diameter). The positive gravity anomaly over the mare
basin Grimaldi (+60 mgal) is just the reverse of the -60 mgal anomaly over
the crater Copernicus. The largest anomalies are +220 mgal, under Mare Imbrium
and Mare Serenitatis. Smaller positive anomalies exist under the following
circular maria: Crisium, Nectaris, Humorum, Humboltianum, Orientale, Smythii,
and under Sinus Aestuum and Grimaldi, and some other minor features. [Have 
to do something about those names, if people ever colonize the place. :-) ]
Frequently, the anomalies possess a ringlike structure... as shown by Mare
Orientale. In this example, the positive anomaly of +150 mgal is confined to
the central, basalt filling. Commonly, negative anomaly rings surround the
mascons.

"...Filled craters less than about 200 km in diameter have negative gravity
anomalies. Sinus Iridium, the Bay of Rainbows on the coast of the Sea of
Rains (Mare Imbrium), possesses a negative anomaly of -90 mgal.

"Large mountain ridges, such as the Apennines, have small positive anomalies.
This great feature, standing 7 km above Mare Imbrium, has a small positive
gravity anomaly of +85 mgal. If the mass of the Apennines were totally
uncompensated, a positive anomaly of +300 mgal would result, so that some
isostatic readjustment has occurred."

[I don't know what a "mgal" is, but I guess this gives some idea of the
relative magnitudes.]

-Are the mascons responsible for the locked orbit? If so, then that would
-explain why the Marias are dense and are only found facing the Earth.

The book doesn't say, but I would suspect that the maria and the current 
mascons were formed only after the moon's rotation was locked to its orbit 
around the Earth. From the previous post, the maria are disproportionately 
common on the near side because the crust is thinner there, making the flow
of lava easier. The difference in crust thickness is presumably the result
of the Earth's gravitational influence, which would be uneven only if the
moon's rotation were already locked to the Earth. (This would also account
for the above-mentioned displacement of the center of mass.)

The mascons could only form after the point at which the outer part of the 
moon had solidified sufficiently that isostatic adjustment would not take
place. From the quote above, the Apennines must have formed around the
beginning of that period.

-References I've seen indicate that Earth's tides are responsible for
-locking the moon's rotation to the orbit.

I believe the main effects of the tides on Earth are to slow the Earth's
rotation and to cause the moon to gradually move further from the Earth.
If one assumes that the moon once rotated faster than it revolved, then the
tidal forces must have been much greater than those we see on Earth, because
of the greater mass of the Earth. If the moon were liquid at the time (which
would fit the Earth impact model), then those tides would have stirred the
entire body of the moon, generating tremendous friction.

One aspect I'm more uncertain of: if the moon continues to move outward
from the Earth, then the period of its revolution about the Earth must
be increasing. If its rotation continues to remain tidally locked, then
there must be some currently active mechanism that maintains this state.
It would be a subtle effect, and I can think of several possible mechanisms
to explain it, but I'm not sure of the relative magnitudes. Perhaps drag
from the "rocking" (what's the word?) of the moon relative to the Earth is
sufficient to account for it.

John Roberts
roberts@cmr.ncsl.nist.gov
Newsgroups: sci.space