Lesson 3a

Properties of the Moon

Comparison to Earth

• The Moon’s radius is 27% that of the Earth (about one-fourth as big)

• The mass of the Moon is 1.2% the Earth’s mass (about 100 times less massive)

• If you spread the Moon out on the Earth it would roughly fill in the Pacific Ocean.

• The average density of the Moon is 3.34 gm/cm3

• The Moon has no atmosphere• The same side of the Moon always faces the

Earth

• How can the Moon’s radius be 27% of the Earth, but the mass be 1.2% that of Earth?

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1. The moon is made up of much less dense material

2. The moon must be inflated in some way

3. The moon’s volume is 64 times smaller than the Earth’s

• Volume = (4/3)πR3

• RE = 4RM

• VE/VM = (RE3)/(RM

3)

• VE/VM = (43RM3)/(RM

3)

• VE/VM = 64

• VE = 64VM

• If the Moon had the same composition as the Earth, the Earth would be 64 times more massive. (Moon 1.6% of Earth’s mass)

• What can you conclude from the Moon’s density being 3.34 gm/cm3 compared to the Earth’s density of 5.5 gm/cm3?

Moon has a very small iron core

Seismic information from Apollo

• The moon has small “moon-quakes” which are likely caused by Earth’s gravity.

• The interior of the Moon is not fully stratified or differentiated like the Earth.

• It has a small solid inner core of iron, a possible partially molten outer core and a mantle that is almost 1000 km thick.

GRAIL – Gravity Recovery and Interior Laboratory

GRAIL was launched on Sep 11, 2011

• As twin spacecraft orbit the Moon, they will exchange radio signals. This will allow them to compute the distance between the space craft.

• As one spacecraft passes over a different density region of the Moon it will either speed up or slow down because the gravity will increase or decrease.

This will allow mapping or Moon’s interior

Mantle is not uniform

Nearside of the Moon

Large impacts and Maria formation

• Large asteroid impacts made the Lunar crust very thin in some locations.

• These impacts occurred when the Moon was still molten inside. (around 4 billion years ago)

• Over time (hundreds of millions of years) the thin and weakened crust allowed magma to extrude up to the surface through fault fractures

• The mare filled with lava and later impacts caused craters in the Maria.

Lava filled large

impact craters

and also spread across

low- lying surface

Farside of the Moon

Why are there very few mare on the far-side of the Moon?

• Far-side: Maria covers 2.5% of surface• Near-side: Maria covers 31.2% of surface

Why are there very few mare on the far-side of the Moon?

• Far-side: Maria covers 2.5% of surface• Near-side: Maria covers 31.2% of surface

• The crust on the far-side is thicker (~80 km) than on the near-side (~60 km).

• It is currently unclear why this is the case but a controversial idea may explain this.

Two moon hypothesis – Aug 2011

• The Earth may have had two moons. The smaller moon (diameter ~ 750 miles) orbited with our Moon.

• Slowly they merged together.• Since they had nearly the same speed and

direction it was a slow motion event that spread the smaller moon all over the far side of our Moon.

GRAIL will give us the answer

Lunation and Libration

Things to notice

• The same side of the Moon always faces the Earth.

• The Moon grows and shrinks in apparent size as it orbits.

• The Moon wobbles (libration) as it orbits the Earth.

Lunation and Libration

• Given the same side always faces the Earth, does the Moon rotate on its axis and if so how long does it take to complete one rotation?

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1. To keep the same side toward us the Moon can not rotate on its axis

2. It has to rotate once every 24 hours

3. It has to rotate once every orbit

Time to discuss gravity and orbits.

The International Space Station (ISS)

Why are the astronauts in the ISS, weightless?

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1. There is no gravity in outer space2. There is no gravity in a vacuum.3. The ISS is to far away for Earth

gravity to effect it4. The astronauts are too small to be

effected5. The astronauts are falling

• Before answering the question:

Why are the astronauts in the ISS weightless?

Let’s look at a little physics.

• If you were to drop a heavy hammer and a feather at the same time, which one will hit the ground first? This is assuming that there is no air to make the feather slow up.

Please make your selection...

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1. The hammer2. The feather3. They hit at the same

time.

Galileo

• A feather and a hammer

Let’s examine our answers• There is no gravity in outer space• Question: Why is the ISS going around

(orbiting) the Earth? Because the force of gravity is holding it in orbit.

If there is no force of gravity in outer space then Newton’s first law tells us the ISS will travel in a straight

line. But it doesn’t

Let’s examine our answers• There is no gravity in outer space• Question: Why is the ISS going around

(orbiting) the Earth? Because the force of gravity is holding it in orbit.

• Earth is so far away that gravity is very weak• There is no gravity in a vacuum• Question: Why is the ISS orbiting the Earth?

Clearly Gravity works in a vacuum and at the distance of the ISS.

Now a little more thinking

• They (the astronauts) are too small for gravity to affect them.

Now a little more thinking

• They (the astronauts) are too small for gravity to effect them.

• Question: Gravity is holding the ISS in orbit. What does Newton’s First Law tell us should happen to the astronauts if gravity isn’t effecting them? Would they be weightless?

If the astronauts are too small for gravity to affect them then this should happen…

Not weightless, pressed against side

The correct answer is…

• The astronauts are falling. The ISS is falling around the Earth and (from Galileo) we know that the astronauts are falling at the same rate as the ISS.

Newton’s big realization

Newton’s Law of Gravity

• F = GMm/r2 Where G is a proportionality constant called the universal gravitational constant. In MKS units it has the value of

G = 6.67 x 10-11 meters3/kg x seconds2

M and m are the masses of the two objects and r is the distance between them.

How light spreads out

• D – circular orbit

• E & F are elliptical orbits.

• The object doesn’t drop fast enough given its speed.

So,

• If your speed is too slow you will fall too rapidly and you will hit the surface of the Earth.

• If your speed is too fast you will move in an elliptical orbit

• If you move at just the right speed (~17,000 MPH) then you will drop at the same rate as the Earth curves around under you. A circular orbit.

What happens if the force of gravity is increased but the amount of gun powder is the same?

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1. The cannon ball will hit the ground sooner.

2. The cannon ball will travel farther.

3. The cannon ball will travel the same distance as before.

What happens if the force of gravity is increased?

What happens if the force of gravity is decreased?

What happens if the force of gravity is decreased?

Is it possible to decrease the force of gravity?

• Sure.

• F = GMm/r2

• The force of gravity drops like the square of the distance

Consider two identical satellites on two different circular orbits.

A

B

Earth

A

B

Which of the following is correct?

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1. Satellite A is traveling faster than satellite B because gravity is stronger for A

2. Satellite B is travelling faster than satellite A because it has farther to go.

3. They are both in orbit so they are traveling at the same speed.

Which is true about the orbital velocity of the two satellites?

Satellite A has a larger velocity than B.

This has to be the case. The force of gravity is stronger on A than on B because A is closer to the Earth.

This means A will drop more quickly than B. So this means that A has to move faster to keep

from impacting the Earth.

Orbital velocity goes down like the square root of r

What about the orbital period?• v goes like 1/√r square both sides• v2 goes like 1/r

• But what is v?• It is the distance divided by time (like miles per hour)

• v = d/t = 2πr/P where 2πr is the circumference of the orbit and P is the orbital

period.• v2 = 4π2r2/P2 this means that • 4π2r2/P2 goes like 1/r or• P2 goes like 4π2r3 Kepler’s 3rd Law

The Mass of the Sun

• Newton’s version of Kepler’s 3rd Law (pg 69 text)

• (M1 + M2)P2 = (4π2/G)r3

• (Msun + Mearth)P2 = (4π2/G)r3 But Msun = 300,00Mearth

• Msun = (4π2r3/GP2)• Where P is the orbital period of the Earth (3.14 x 107 sec) and “r”

is the orbital radius of the Earth (1.5 x 1011 meters)

• Plugging these values in gives Msun = 2 x 1030 kg.

Now back to the Moon

• What is causing the libration (wobble) in the Moon as it orbits the Earth?

• Here is the first hint: The Moon appears to grow and shrink in size as it orbits the Earth.

• What does this tell you about the Moon’s orbit?

• Given what we have learned about orbits, when do you think the Moon’s orbital velocity is the fastest and when is it the slowest?

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1. Fastest when it is closest to the Earth

2. Fastest when it is farthest away

3. Constant throughout it’s orbit

Rotation is constant, orbital speed is not.

• But the Moon’s rotational period is always the same.

• This means that the Moon turns a little too much when it is moving the slowest in its orbit, and it doesn’t turn quite fast enough when it is moving the fastest in its orbit.

• This causes the Moon to appear to wobble as it orbits the Earth. We can actually see 59% of the Moon’s surface instead of 50%.

Lunation and Libration