Download Question

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?
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
.
0%
1
0%
2
0%
3
• Volume = (4/3)πR3
•
•
•
•
•
RE = 4RM
VE/VM = (RE3)/(RM3)
VE/VM = (43RM3)/(RM3)
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?
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
0%
1
.
0%
2
0%
3
Time to discuss gravity and orbits.
The International Space Station (ISS)
Why are the astronauts in the ISS, weightless?
1. There is no gravity in outer space
2. There is no gravity in a vacuum.
3. The ISS is to far away for Earth
gravity to effect it
4. The astronauts are too small to be
effected
5. The astronauts are falling
0%
1
0%
0%
2
3
0%
0%
4
5
• 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...
1. The hammer
2. The feather
3. They hit at the same
time.
0%
1
0%
2
0%
3
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?
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.
.
0%
1
0%
2
0%
3
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.
B
B
A
A
Earth
Which of the following is correct?
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.
0%
1
0%
2
0%
3
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
• v2 goes like 1/r
square both sides
• 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?
1. Fastest when it is closest
to the Earth
2. Fastest when it is
farthest away
3. Constant throughout it’s
orbit
.
0%
1
0%
2
0%
3
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