lesson3b orbital properties of the moon. rotation is constant, orbital speed is not
TRANSCRIPT
Lesson3b
Orbital Properties of the Moon
Rotation is constant, orbital speed is not.
0 days
21 days
14 days
7 days
Same side always faces exactly toward the Earth if the Moon is in a circular orbit.
0 days
21 days
14 days
7 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 = M x V x R• 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 Earth-
Moon 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 2 3
33% 33%33%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
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 2 3 4
25% 25%25%25%1. Yes, they went to the Moon.2. No, it was faked.3. I’m not sure but it might
have been faked4. I’ve never considered this
question
Lunar Module
What was left behind
The Lunar Rover
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, micro-meteorites which can not make it through the Earth’s atmosphere.
Young
Old
• 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)
