A Text-Book of AstronomyComstock, George C. (George Cary)
Science
A Text-Book of Astronomy
Comstock, George C. (George Cary)
Astronomy
95. DENSITY OF THE MOON.--It is believed that in a general way the moon
is made of much the same kind of material which goes to make up the
earth--metals, minerals, rocks, etc.--and a part of the evidence upon
which this belief is based lies in the density of the moon. By density
of a substance we mean the amount of it which is contained in a given
volume--i. e., the weight of a bushel or a cubic centimeter of the
stuff. The density of chalk is twice as great as the density of water,
because a cubic centimeter of chalk weighs twice as much as an equal
volume of water, and similarly in other cases the density is found by
dividing the mass or weight of the body by the mass or weight of an
equal volume of water.
We know the mass of the earth (§ 45), and knowing the mass of a cubic
foot of water, it is easy, although a trifle tedious, to compute what
would be the mass of a volume of water equal in size to the earth. The
quotient obtained by dividing one of these masses by the other (mass of
earth ÷ mass of water) is the average density of the material composing
the earth, and we find numerically that this is 5.6--i. e., it would
take 5.6 water earths to attract as strongly as does the real one. From
direct experiment we know that the average density of the principal
rocks which make up the crust of the earth is only about half of this,
showing that the deep-lying central parts of the earth are denser than
the surface parts, as we should expect them to be, because they have to
bear the weight of all that lies above them and are compressed by it.
Turning now to the moon, we find in the same way as for the earth that
its average density is 3.4 as great as that of water.
96. FORCE OF GRAVITY UPON THE MOON.--This number, 3.4, compared with the
5.6 which we found for the earth, shows that on the whole the moon is
made of lighter stuff than is the body of the earth, and this again is
much what we should expect to find, for weight, the force which tends to
compress the substance of the moon, is less there than here. The weight
of a cubic yard of rock at the surface of either earth or moon is the
force with which the earth or moon attracts it, and this by the law of
gravitation is for the earth--
W = k × (m m´) / (3963)^{2};
and for the moon--
w = k × {m (m´/81)} / (1081)^{2};
from which we find by division--
w = (W / 81) (3963 / 1081)^{2} = (W / 6) (approximately).
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