Today in Astronomy 111: Mercury
 The properties of Mercury
 Comparison of Mercury
and the Moon
 Water on Mercury and the
Moon
 Ice in the polar craters of
Mercury and the Moon
 Tidal locking and
Mercury’s eccentric orbit
 Moment of inertia and
differentiation in
terrestrial planets
15 September 2011
Half Mercury, half Moon. (Image
from Mariner 10, NASA.)
Astronomy 111, Fall 2011
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Mercury’s vital statistics
Mass
3.302 × 10 26 gm (0.055M⊕ )
Equatorial radius
2.4397 × 108 cm (0.383R⊕ )
Average density
Albedo
5.427 gm cm -3
0.12
Average surface
temperature
442.5 K
Orbital semimajor axis
Orbital eccentricity
Sidereal
revolution period
Sidereal
rotation period
15 September 2011
MESSENGER
(JHU-APL/NASA)
5.791 × 1012 cm
(0.387 AU)
0.2056
87.969 days
58.785 days
Astronomy 111, Fall 2011
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Visits to Mercury
There have been two:
 NASA’s Mariner 10 conducted
three close fly-bys in 1974-1975.
 Since 17 March 2011, the NASA
MErcury Surface, Space
ENvironment, Geochemistry and
Ranging (MESSENGER) satellite
has been in orbit around
Mercury and will return detailed
imaging, topographic,
compositional, and magneticfield data for about a year
thenceforth.
15 September 2011
Astronomy 111, Fall 2011
MESSENGER displays its
scientific instrument
complement as it passes by
(NASA/JHU-APL).
3
Moon
Mercury
Mass (gm)
7.349 × 10 25
3.302 × 10 26
Radius (cm)
1.7381 × 108
2.4397 × 108
Mean density (gm cm -3 )
Albedo
Mean temperature (K)
Orbital
semimajor axis (cm)
Orbital eccentricity
Obliquity to Solar orbit
Tidally-locked rotation?
Mean surface
magnetic field (G)
Atmosphere
Surface visited?
3.350
0.12
274.5
5.427
0.12
442.5
3.844 × 1010
5.791 × 1012
0.0549
1.54°
Yes
0.2056
0.04°
Yes
0
2.2 × 10 -3
None
Yes
None
No
15 September 2011
Astronomy 111, Fall 2011
Moon vs.
Mercury
Image by Tunç Tezel
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Moon vs. Mercury (continued)
 From the appearance, albedo, and
reflectance spectra, we conclude that
the surfaces are similar in
composition: feldspar and pyroxene
– bearing rocks.
 From the density, we conclude that
Mercury has more than its share of
iron, in the form of a core with radius
about ¾ that of the planet.
 From the magnetic field, we
conclude that Mercury’s core is
probably liquid, for a dynamo
mechanism to operate.
Diagrams by UCAR (U. Michigan)
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Tectonic activity:
Mercury vs. Moon
From observations of rilles
and scarps, we conclude that
both have a “plastic” mantle,
but that Mercury has been
tectonically active and the
Moon has not.
 Recently, volcanoes have
been seen on Mercury,
within the giant Caloris
impact basin. The moon
has none.
MESSENGER
(JHU-APL/NASA)
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Water on airless Solar system bodies
It is easy for hydrogen to escape from small bodies like the
Moon and Mercury, and easy for sunlight to dissociate water
into H and O. So is there any water at or just underneath the
surface of Mercury and the Moon? There are two good
reasons to think there should be, despite the difficulties:
1. The solar wind. The Sun is constantly spewing out about
10 −14 M year −1 in the form of the Solar wind, mostly as
protons and electrons.
 The protons, travelling at high speeds, bury themselves
several cm below the surface of any airless body they
encounter.
 It doesn’t take long for each proton to become H, and for
two of these to make water with a nearby O.
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Water on airless Solar system bodies (continued)
 This is probably the origin
of the widespread water
recently detected on the
Moon by the NASA Deep
Impact and ISRO
Chandrayaan-1 spacecraft.
 Quantity: about one liter per
ton of rock or regolith.
What’s closest to the surface
seems to come and go with
darkness and sunlight .
Temperature (left) and water concentration (right) on the Moon, a quarter
of a lunar day apart. From Jessica Sunshine and the EPOXI team.
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Polar ice: Mercury vs. Moon
2. Comet and asteroid impacts. In principle comets and
asteroids could deliver larger amounts of water to the Moon
and Mercury than the Solar wind can.
 It wouldn’t last long in the sunshine on either body – it
would be evaporated, dissociated, and in short order the
hydrogen would escape.
 But because the Moon and Mercury both have very small
obliquity (tilt of rotation axis from the orbital axis), there
are permanently-shaded parts of craters near the north
and south pole, where some of the delivered water can
last – in Mercury’s case, practically forever.
And thereby hangs a tale.
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Polar ice: Mercury vs. Moon (continued)
The BMDO Clementine satellite passed
over the poles of the Moon in early 1994,
and took images that were interpreted as
showing surface ice in polar craters.
 This would be of asteroidal/cometary
origin but the required amount was
surprising large – typically 5 m deep,
105 m2 in area– and the results
remained controversial.
 Clementine was the DoD’s first try at
the “faster– better – cheaper ”
philosophy of spacecraft development.
Images of the Moon’s south pole, from Clementine
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Polar ice: Mercury vs. Moon (continued)
In 1998, NASA’s Lunar Prospector
satellite repeated the imaging observations, added neutron spectroscopy, and apparently confirmed
the Clementine findings.
 Again plausible, but the lowenergy neutron method of
detecting water (hydrogen in
Lunar Prospector neutronthe ice) had never been tried
spectrometer scans during an
before under any conditions,
orbit over both poles (Feldman
and thus was also controversial. et al 1998).
 Lunar Prospector was one of NASA’s first tries at “faster –
better – cheaper.” Like Clementine there were difficulties in
calibrating and interpreting its measurements.
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Polar ice: Mercury vs. Moon (continued)
In 1999, radar astronomers at
Arecibo Observatory made a longwavelength, radar-polarimetric
study of the north pole of Mercury,
and found that the perpetuallyshadowed crater floors were very
reflective in a way most easily
explained by clean water ice.
 For ice detection, this technique
is less controversial than the
means employed by the Lunar
satellites. But it was shocking Radar-reflectivity image of the
nonetheless: ice on Mercury?
north pole of Mercury (Harmon
et al. 2001)
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Polar ice: Mercury vs. Moon (continued)
So Arecibo tried to confirm the
Clementine and Lunar Prospector
results. They were able to show that
there isn’t any surface ice in the
Moon’s polar craters.
 Recently confirmed from space by
the JAXA Kaguya/SELENE and
NASA LRO satellites.
 Clementine-Prospector results were
confounded by steep illumination
angles, calibration difficulties.
 The “you get what you pay for” Radar image of the Moon’s
satellite-development philosophy south pole (N.J.S. Stacy, Ph.D.
is making a comeback.
dissertation, Cornell U.)
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Polar ice: Mercury vs. Moon (continued)
What about subsurface ice, mixed
with dirt, in the Lunar polar
craters? To expose this was the job
of NASA’s Lunar Crater
Observation and Sensing Satellite
(LCROSS):
 Make a small crater within a
permanently-shadowed region,
with the impact of a spent
rocket stage.
 Analyze the composition of the
ejecta, from measurements by
satellites right overhead.
15 September 2011
A permanent shadow on the moon
(yellow contour), compared to neutron
signal (blue) and the LCROSS impact
site (red dot). (NASA and ISR/RAS)
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Polar ice: Mercury vs. Moon (continued)
Results show water ice present at the
Species Abundance in
ejecta (percent
level of about 50 liters of water per ton of
by mass)
ejecta, in this polar-crater floor.
H2O
5.4
 This would be on the high end of soil
H2
1.4
water content for the driest deserts on
CO
5.7
Earth, like the Sahara and Atacama.
Hg
1.2
 There’s as much molecular hydrogen Ca
1.6
(H2) in the soil as water ice, molecule Mg
0.4
for molecule. Much of the neutron
signal was from this H2.
Colaprete et al. 2010,
 The water ice comes with very large
Gladstone et al. 2010
amounts of other volatiles like CO,
calcium, magnesium and mercury.
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Polar ice: Mercury vs. Moon (continued)
This is far less water than was claimed on the basis of the
Clementine and Lunar Prospector results, and is consistent with
the Arecibo radar observations.
 There’s enough to be scientifically interesting, and the
mixture of volatiles will usefully constrain models of
delivery and the thermal history of the crater floors.
 An entire permanently shaded region contains 106-107
gallons, which would fill a large municipal water tower.
This would go a long way toward the needs of a Lunar
base. Has to be laboriously extracted and purified, though.
 Coming soon: MESSENGER observations of the shadows,
topography and composition of the polar-crater floors on
Mercury. (Not going to create any craters, though.)
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Tidal locking and Mercury’s orbit
In celestial mechanics, tidal locking means that the heat
dissipated during an orbit, by variation in tidal forces, is
minimized.
 Tidal forces are the gravitational force differences between
one end and another of one body, owing to different
distances away from a second body, and from one side
and another of one body, owing to different directions
toward the second body.
 The result is a stretch along the line between the two
bodies, and a compression in the perpendicular directions
(see next page).
 We will derive formulas for tidal forces – and much more
on tides – later this semester.
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Imagine yourself in orbit around Earth,
feeling tidal forces
To you, it
seems as if
you are
stretched in
the direction
of the
earth’s
center, and
squeezed in
the other
direction.
Earth pulls
all things
toward its
center, and
pulls
harder on
nearer
things.
Figure from Thorne, Black holes and time warps
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Tidal locking and Mercury’s orbit (continued)
 A body in circular orbit, with
rotation period equal to
revolution period, suffers no
change in tidal forces as it
travels its orbit. Thus there is
no heat dissipated from
stretching and shrinking.
 The Moon’s orbit about Earth
has a fairly small eccentricity
(0.055), so it can be considered
circular to good approximation.
 The Moon’s rotation and
revolution periods are
identical, so it is tidally locked.
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Tidal locking and Mercury’s orbit (continued)
 But Mercury’s orbit has a much larger eccentricity
(0.2056), and thus is more distinctively elliptical.
Reminder of the properties of ellipses:
Equation
x2
y2
1
+ 2 =
a
b
2
Foci at x =
c=
a2 − b 2
±c :
Eccentricity
Focal lengths
(aphelion and
perihelion distances)
15 September 2011
c
ε= =
a
a2 − b 2
a
f= a ± c
= a (1 ± ε )
Astronomy 111, Fall 2011
(Semimajor
axis)
20
ε =0
ε = 0.2056
(Circle)
(Mercury)
ε = 0.055
ε = 0.5
(Moon)
15 September 2011
Astronomy 111, Fall 2011
Orbit
comparison
Drawn to scale, in
units of
semimajor axis
length (a);
coordinate axis
origin on one
focus.
21
Tidal locking and Mercury’s orbit (continued)
 Since the distance between
Sun and Mercury varies by
so much through an orbit,
it’s not possible to have no
change in tides.
 Nevertheless, astronomers
used to think that Mercury’s
rotation and revolution
periods were equal (at 88
days), because that’s what
observations seemed to
indicate, and because it
agreed with naïve
expectations based on
circular orbits.
15 September 2011
Astronomy 111, Fall 2011
Aphelion
a = 0.387 AU
f 2 = 0.467 AU
Sun
b=
0.379 AU
f 1 = 0.307 AU
Perihelion
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Tidal locking and Mercury’s orbit (continued)
 In the mid-1960s, though, radar astronomers at Arecibo
Observatory showed that the rotation period of Mercury
is actually closer to 59 days.
 Shortly thereafter it was realized by theoreticians that the
minimum in tidal heating for Mercury’s eccentric orbit
was reached for an orbital period exactly 3/2 times the
rotation period.
 In the mid 1970s the fly-bys by Mariner 10 yielded the
rotation period much more precisely and bore out this
prediction. Mercury rotates exactly three times, every two
orbits.
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Tidal locking and Mercury’s orbit (continued)
 Like the Moon, the tidal forces to which it is subjected has
made Mercury slightly oblong. The orbit is arranged so
that the long axis always points toward the Sun at
perihelion. This keeps the tidal stretching to a minimum,
though the minimum isn’t zero.
 Other trivia: the perihelion of Mercury’s orbit precesses
slowly in the prograde direction. Long a mystery, the
precise accounting for this orbital precession by warping
of space by the Sun’s gravity was one of the first triumphs
of Einstein’s general theory of relativity (1915).
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Moment of inertia and planetary differentiation
For a given spin rate, different distribution of a given mass
within the bounds of a planet would lead to different values
of the planet’s spin angular momentum. The relation between
total angular momentum L and angular frequency ω is
where
L = Iω
z
I = ∫ r⊥2 dm
r⊥ = r sin θ
dm
The moment of inertia can be measured
from the fine details of a planet’s
gravitational field, as we will discuss
in detail later this semester.
15 September 2011
Astronomy 111, Fall 2011
θ
r
φ
x
y
25
Moment of inertia and planetary differentiation
(continued)
Here are some simple spherical configurations of mass – all
with mass M, radius R – and the corresponding moment of
inertia.
2
 Constant-density sphere: I = MR 2
5
2
 Spherical shell, with constant mass per unit area: I = MR 2
3
 Density maximum at center, declining linearly to zero at r
= R:
4
=
I =
MR 2 0.267 MR 2
15
The more strongly concentrated the mass is at the center, the
smaller the leading factor in the expression for I.
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Moment of inertia and planetary differentiation
(continued)
Results:
2
2
 The Moon has I = 0.394 MR , close enough to I = MR 2
5
that its density must be nearly constant.
 Mercury has I = 0.33 MR 2 , significantly smaller than the
uniform-density value, and probably reflective of a much
larger density in the center than at the surface. An iron
core, of the sort described above, would work fine.
The moment of inertia and the average density can be
used to calculate, fairly confidently, the properties of the
core.
 A planet that is not concentrated at the center, but tends to
have uniform density, is called undifferentiated. The
process of concentration of heavier minerals and metals at
the center is called differentiation.
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