Lesson3b
Orbital Properties of the Moon
Rotation is constant, orbital speed is
not.
7 days
14 days
0 days
21 days
Same side always faces exactly toward the Earth
if the Moon is in a circular orbit.
7 days
14 days
0 days
21 days
In 14 days the Moon completes one rotation on
its axis.
But since the orbit is elliptical, the moon’s
orbital speed slows.
It is not quite half-way around the orbit in 14
days.
This means the Moon has over rotated on its
axis and as a result, we see the Moon appear
to wobble.
Tidal Forces
• It is not a coincidence that the Moon rotates
once every orbit.
• This is due to tidal interactions between the
Earth and the Moon.
• The tidal interactions allow the transportation
of angular momentum between the two
bodies.
As the Moon orbits the Earth, the Earth moves
in a very small circle
Two oceanic bulges, Earth rotates
underneath the water bulges
Mt. Saint Michael
Normandy, France
Angular Momentum
• This is the momentum that keeps things
spinning. It depends on the mass (M), the
radius (R) and the velocity (V).
• L=MxVxR
• Angular momentum for a system is always
conserved.
• M, V or R can change, but L has to stay
constant.
The Earth-Moon System
• The total angular momentum of the EarthMoon system is conserved.
• LErotation – Angular momentum from Earth
spinning on its axis
• LEorbital – Angular momentum of Earth moving
in small circle
• LMrotation -- Angular momentum from Moon
spinning on its axis
• LMorbital -- Angular momentum of Moon
moving in orbit
Total Angular Momentum
• Ltotal = LErotation + LEorbital + LMrotation + LMorbital
• The total angular momentum is conserved,
but the system can exchange angular
momentum from one component to the
other.
Tidal bulge is not perfectly aligned with the
direction to the Moon
Result
• Moon pulls back on the Earth, slowing the
Earth’s rotation.
• But total angular momentum in a system is
always conserved.
• If the Earth’s rotation slows, then the
rotational angular momentum of the Earth
decreases.
• The Moon has to pick up that angular
momentum. It does this by an increase in the
Moon’s orbital angular momentum. The
Moon speeds up in its orbit.
Lot’s of energy in the tides, and it all
comes from the Moon
• Lunar ranging program shows the Moon is
receding from the Earth at 3.8 cm/year.
Lunar Ranging
• Lunar ranging program shows the Moon is
receding from the Earth at 3.8 cm/year.
• If this rate were constant then over 1 million
years (1 x 106 years) the Moon would increase
the size of its orbit by 3.8 x 106 cm or 3.8 x
104 meters, or 38 km.
• At the same time the Earth’s rotation has
slowed by 22 seconds. So 1 million years ago
the Earth’s day was 22 seconds shorter.
• Extrapolating to 4.6 billion years and assuming
the rate of transfer of angular momentum was
constant (which it wasn’t) the Moon would
have been 175,000 km closer. (Current
distance is 384,403 km)
• The Earth’s rotation at this time was 6.5 hours.
• Note: This is complicated. The effect of tides
was greater in the past and that means the
exchange in angular momentum was not
constant throughout the life time of the
system.
• The ground also bulges along a line
connecting the Earth and the Moon. The
Moon’s surface bulges toward the Earth and
away from the Earth, just like the oceans due
on the Earth.
• Long ago, when the Moon use to rotate on its
axis faster than it does today, the Earth tugged
on the Moon’s tidal bulge and forced the
Moon to slow its rotation until it finally
became tidally locked. (synchronous orbit)
• This is the lowest energy state for the Moon.
• Why wouldn’t zero rotation for the Moon be
the lowest energy state? If the Moon didn’t
rotate on its axis it would have zero rotational
angular momentum. Wouldn’t this be a lower
energy state for the Moon?
• Why isn’t zero rotation the lowest energy
state for the Moon?
Back to Libration
• The Moon isn’t quite in a circular orbit. It
wobbles because its orbit is slightly elliptical.
• When the Moon is farthest away, it moves
more slowly in its orbit. But the rotation
around its axis is at a constant rate.
• This means the Moon over rotates compared
to us on Earth.
• Could this be related to some Moon Quakes?
Subtle (or not so subtle) effect
• The rotation of the Earth causes it to bulge at the
equator. The difference in diameter is not huge,
but measureable.
• Earth Equatorial diameter: 12,756 km
• Earth Polar diameter: 12,713 km
• Difference: 43 km.
• What was this difference like billions of years
ago?
.
1. The Earth was flatter (more
oblate) because it was
spinning faster
2. The Earth was more
spherical because it was
more molten
3. It was the same as today
33%
1
33%
2
33%
3
Material moves to poles as rotation
slows
Material moves to poles as rotation
slows
• If the Earth were not rotating it would be a
sphere, not an oblate sphere.
• As the Earth’s rotation has slowed, the shape
of the Earth has slowly changed from a more
flattened sphere to more spherical.
• This changing shape forces the lithosphere to
move to the polar regions.
• This helps to propagate plate tectonics on the
Earth. It is not the only effect, but one of
them.
• RESULT: The Moon has helped to drive plate
tectonics on the Earth.
Apollo landing sites
• Do you think the Apollo astronauts really
went to the Moon or was it faked?
.
1. Yes, they went to the Moon. 25%
2. No, it was faked.
3. I’m not sure but it might
have been faked
4. I’ve never considered this
question
1
25%
25%
2
3
25%
4
Lunar Module
What was left behind
The Lunar Rover
• Lunar Reconnaissance Orbiter (LRO)
Lunar Reconnaissance Orbiter
Lunar Reconnaissance Orbiter
Regolith is why we can see the tracks
Old illustration of the Moon
Reality
• Although the Moon has no atmosphere there
is still a form of erosion.
• Meteorite impacts. In particular, micrometeorites which can not make it through the
Earth’s atmosphere.
Old
Young
• Older craters begin to lose their sharp edges
because constant “sand blasting” by
micrometeorites break off small pieces.
• The resultant small pieces become the Lunar
Regolith.
• The layer of regolith varies in depth from a
few meters deep in the youngest maria to
over 20 meters deep (~ 60 feet) in the
highlands.
• Only the top few inches are a fine powder.
The rest in compressed by the weight of the
overlying regolith.
• Regolith is composed of bits of rocks found in
that particular area of the Moon.
Mare Regolith
• Glass beads come from volcanic lava
• Impact glass is more distorted, and comes
when the heat of impact melts some of the
rock into glass
• Rock fragments are just little pieces of rock
from the surface around the area
• Plagioclase feldspar is typically found in
crustal material. (sodium, calcium, aluminum,
silicon, oxygen) (light elements)
Lunar Rocks
• Most rocks on the Moon are Breccia. They are
composite rocks that are made of differing
materials which have been fused together.
Mare Breccia rock
Mare Basalt Rocks – Mantle material such as
Oviline – rich in iron and magnesium
Mare Breccia Rock Formation
Highland Breccia rocks -- composed of
feldspars and plagioclase (a silica)