The Earth – a Celestial Body
Why does the earth have days and nights?
Does the sun move around the earth, or does
the earth spin about an axis?
Can you justify your answer in terms of
further observations?
Days on the Earth
Why does the earth have days and nights? Does the sun
move around the earth, or does the earth spin about an
axis?
Based on pictures from space, it is easy to see
that the earth is (roughly) a sphere that spins.
We saw from the previous section that the
geocentric view can not explain lots of
observations that the telescope made available,
whereas the heliocentric view can.
Are days always exactly 12 hours long, and if
not, why not?
Days on the Earth
Are days always exactly 12 hours long, and if not, why not?
23½o
The differing length of the days can be
explained by the 23½o tilt of the earth
with respect to the sun. Please note that the sizes
of the earth, sun, and orbit are NOT drawn to scale.
June 21
Dec. 21
The Tilt of the Earth and the Signs of the
Zodiac
(view is looking down above the North Pole; this is opposite of looking up from the
Northern Hemisphere)
Virgo
Leo
Cancer
Libra
Scorpius
Gemini
spring equinox
March 21
June 21
Dec. 21
Taurus
Sagittarius
Aries
Capricornus
Aquarius
Pisces
The Tilt of the Earth
As seen on the previous slide, the sun appears
on the boundary between the constellations
Pisces and Aquarius on the spring equinox
(March 21, when there is 12 hours of day and 12
hours of night everywhere on the earth because the
tilt is pointed sideways to the sun).
The Tilt of the Earth
Due to the sun and the moon trying to “straighten
up” the tilt of the earth, the tilt of the earth
wobbles. We will have a demonstration of this
effect in class. This wobble (actually called a
precession) causes the sun on the spring equinox
to appear to move slowly through the
constellations of the zodiac. The period for one
complete cycle is about 26,000 years. Since there
are 12 constellations of the zodiac, the time the
sun appears in one constellation during the spring
equinox is about 2,000 years. For the past 2,000
years, the sun at the spring equinox has appeared
in the constellation Pisces, but is now starting to
enter Aquarius.
The Tilt of the Earth
Another effect of the precession of the equinoxes
(as it is officially called), is that the signs of the
zodiac as they relate to birthdays shifts about one
sign every 2,000 years. The common dates for the
signs are about 2,000 years old, and so are
approximately one sign out of date. So where the
sun is relative to the constellations of the zodiac is
approximately one sign earlier than what the
common dates would indicate.
The Tilt of the Earth
This precession also changes the astronomical
alignment of objects on the earth, such as
pyramids and the stones of Stonehenge. To
really see such alignments, we must work
backwards to see what the sky looked like
at the time that these works were built.
Seasons on the Earth
What are the seasons on the earth due to?
One possibility is the tilt of the earth, which causes
the northern half of the earth to have longer days
in the spring and summer and shorter days in the
fall and winter, but this is reversed in the southern
half.
farthest
closest
Another possibility is that the earth is going in an
ellipse instead of a circle, and this causes the earth
to be closer to the sun for part of the year and
further from the earth during the other part.
Seasons on the Earth
Since the elliptical motion for the earth is almost
circular, the change due to distance is small. Also,
the elliptical motion would cause both the
northern and southern halves to have the same
seasons at the same time. The tilt would cause the
northern half to have opposite seasons to the
southern half. For the earth, then, the tilt is the
major cause of the seasons. Right now, the time
of closest approach to the sun is in January – not
exactly the hottest time for the northern
hemisphere!
For other planets, though, the situation may be
different.
Astronomical motions and
Ice Ages
There are several things about the earth’s orbit that
may affect the earth’s climate.
1. Since the tilt of the earth precesses, the time of
closest approach moves through the seasons.
This may affect the climate.
2. The tilt of the earth may be oscillating –
becoming a little more than 23½o or a little less.
This type of wobbling may also affect the
seasons and thus the earth’s climate.
3. The power output of the sun may vary somewhat
over the ages. We’ll consider this more in Part
Four where we consider the life cycle of stars.
Time (of day)
How do we measure time?
Obviously, we have 24 hours in a day, 60 minutes in
an hour, and 60 seconds in a minute.
Is there an absolute definition of a second, or is it
defined just as above – relative to a day. Could
the earth’s spin be slowing down or speeding up,
so that a day would be slightly longer or shorter?
Has a day always been exactly one day long?
Time
Since the time from dawn to dusk varies
across the seasons (and across the latitudes),
how do we mark how long one day is? We
can do it from noon to the next noon – when
the sun casts the shortest shadow. But noon
happens at different times for different
longitudes. Does everyplace then have its
own noon?
Time
To be practical, we can’t have everyplace
have its own time. But we can’t have
everyplace in the world have noon at the
same time. What do we do?
Standard Time
To balance between standardization and reality, we
have created 24 time zones. Each location in a
time zone will have a standardized time. But since
there are 24 of them, the true local noon will only
be about a half hour off at most.
Daylight Savings Time is another political decision –
it moves accepted noon one hour earlier than real
noon so that there will be one more hour of
daylight in the afternoon and one less hour in the
morning to give people more time to do outside
activities after work during the longer summer
days.
Solar versus Siderial Time
Since the sun rises a little later each day
according to the stars (or the stars rise a
little earlier each day than the sun), there are
actually 366 siderial days a year instead of
365 solar days. So how many times does
the earth actually spin around in one year,
365 or 366?
Rotation about the Sun
Earth rotates counterclockwise as viewed from above North pole
Sunrise and star rise
Star rise comes before sunrise
Time
As the previous slide indicates, the earth needs to spin 366
times a year in order to have 365 days a year – since the
spinning of the earth and the rotation of the earth are both
in the counterclockwise direction as seen from above the
north pole.
If the earth did not spin at all (relative to the stars), there
would still be one day in a year, but the sun would rise in
the West instead of the East. If the earth did spin around
once a year in the counter-clockwise direction, there
would be no days at all – the same place would be facing
the sun all the time. This relationship between spin and
orbit provides the explanation for the difference between
the 365 and 366 days in the synodic versus siderial days.
Time – leap years
Every four years (with a few exceptions) we have
leap years? Why?
Time
It turns out that the earth takes approximately
365 days to cycle through the seasons, or to
have the sun move through the twelve
constellations of the zodiac.
A more precise number is: 365.2422 days a
year.
How do we handle the fractional day?
Leap Years
Julius Caesar created a calendar that added Feb. 29
every four years (leap year), but this accounted for
365.25 days a year – very close to 365.2422 but
not quite right – a slight bit longer than the real
year. This Julian calendar produced an error of
about 10 days by the year 1582 when Pope
Gregory XIII decreed that Oct. 5 would become
Oct. 15 to catch up. Think of the repercussions –
what about your monthly rent or car payment?
Leap Years
To reduce the slight error in the Julian
calendar, Pope Gregory created a calendar
that would delete the leap year at the turn of
the century unless that century was divisible
by 400. Thus, 1900 was NOT a leap year,
whereas 2000 WAS a leap year. This
correction resulted in an average Gregorian
calendar year of 365.2425 – much closer to
the actual 365.2422 value.
Hunt for Red October
Tom Clancy wrote a novel entitled “The Hunt
for Red October”. The name of his Soviet
submarine was meant to celebrate the
Russian (communist) revolution that was
dated in November of 1917. However, the
Russians did not accept the Gregorian
calendar, and so were about 12 days
“earlier” in their Julian calendar and so their
date for this event was October of 1917.
The Moon
The closest celestial object
to the earth is the Moon.
Let’s now consider it.
How does it move?
How far away is it?
(How do we know that?)
How big and massive is it?
What about its surface?
Does it have an
atmosphere?
Can we predict eclipses?
The Galileo spacecraft sent back this image of the Moon as
it headed into the outer solar system. The distinct bright ray
crater at the bottom of the image is the Tycho impact basin.
Motions of the Moon
We should all be familiar with the phases of
the moon: from New Moon to 1st Quarter to
Full Moon to 3rd Quarter back to New
Moon. This takes about a moonth – I mean
month. Actually, it takes about 29.5 days to
go through this cycle.
The phases of the Moon are related to the time
of rising of the Moon. We will see a
diagram on the next slide.
Phases of the Moon
Sizes are NOT drawn to scale!
1
View is looking down from above the North
1st quarter
sunset
Full Moon
midnight
noon
sunrise
3rd quarter
New Moon
Phases and Rising Times
of the Moon
New Moon rises at _____ and sets at ____ .
1st Quarter rises at _____ and sets at ____ .
Full Moon rises at _____ and sets at ____ .
3rd Quarter rises at _____ and sets at ____ .
Phases and Rising Times
of the Moon
New Moon rises at sunrise and sets at sunset.
1st Quarter rises at noon and sets at midnight.
Full Moon rises at sunset and sets at sunrise.
3rd Quarter rises at midnight and sets at noon.
Synodic and Siderial Periods
We have left out one of the motions in our diagram.
The earth is moving around the sun. In one
moonth (I mean month), the earth has moved
about 1/12th of its orbit around the sun. You can
see that the alignments of the moon with the sun
will be off about 1/12, so there will be a difference
of 1/12 of 29.5 days = about 2 days. The actual
moonth is 29.5 days – from full moon to full
moon. This is called the synodic period. The
actual orbit of the moon around the earth only
takes 27.3 days. This is called the siderial period.
Synodic versus Siderial
Sizes are NOT drawn to scale.
View is looking down from above the North.
Earth is really moving down (counterclockwise),
but it appears that the sun moves up (clockwise).
Position of sun
one moonth later.
Full
1st quarter
evening
midnight
noon
morning
New
Original
Position of
the sun
3rd quarter
A Moon “Day”
Does the Moon spin? If we lived on the
Moon, would there be night and day?
Would we see the earth in the night sky – as
we see the Moon in the night sky from the
earth?
Observation: we only see one side of the
moon – we never see the “back” side of the
moon. On the diagram in the next slide, we
mark the position (with a line) of one of the
famous mountains on the moon.
A Moon “Day”
Sizes are NOT drawn to scale!
1
View is looking down from above the North
1st quarter: mountain at sunrise
Full Moon:
mountain at
noon
sunset
midnight
noon
sunrise
New Moon: mountain
at midnight
3rd quarter: moutain at sunset
The “front” and “back”
of the Moon
In order to keep that same mountain facing towards
the earth, the Moon must spin so that its day is the
same length as its period around the earth – its
month.
That means a “day” on the Moon would last 29.5
earth days.
That also means the the earth would be in the sky
only for that half of the moon that faces the earth
(the half with the “mountain”). The “back” side of
the Moon would never have the earth in its sky.
“Earthlight” on the Moon
Since the earth has a diameter 4 times that of the
Moon (info on this is coming up later in this section), the earth
in the Moon’s sky would appear to be 4 times
bigger than the Moon appears in the earth’s sky!
Also, a “full earth” would cause much more light
at night on the Moon than the light from a full
Moon on the night earth. Since the earth’s
atmosphere reflects a lot of light, the Earth will
not only be four times bigger but also about 4
times brighter per area – making it about 16 times
brighter than the full Moon on the earth!
Remember that there would be no clouds on the
Moon to block the light from the full earth.
“Earthlight” on the Moon
And since the earth spins with a period
of 24 hours instead of 29.5 days, you
could eventually see all places on the
earth from the Moon – as long as you
were on the “front” side of the Moon.
Distance to the Moon
Given that earth is the blue circle, where is the
moon?
a
b
c
d
off the screen
Distance to the Moon
The earth-moon distance is roughly 250,000
miles. Since the circumference of the earth
is roughly 25,000 miles, that puts the moon
at a distance equivalent to 10 times around
the earth, or at a distance of about 30 times
the diameter of the earth. This is roughly
drawn to scale below:
earth
moon
How do we know this?
By using Newton’s Laws of Gravity and
Newton’s Laws of Motion, and observing
the period of its motion about the earth (full
moon to full moon), we can calculate the
moon’s distance from the earth. Today we
have laser range finders, and we can figure
it out that way.
Elliptical Orbit
The Moon actually goes in an elliptical orbit,
with the closest approach being about
221,000 miles (perigee) and the furthest
distance being about 253,000 miles
(apogee). These distances will be important
when we consider eclipses.
Size of the Moon
The angle the moon makes with the eye at the earth’s
surface is about 0.5o . Since we know the distance
to the moon, we can then figure out that the moon
has a diameter of about 2160 miles which is about
27% (roughly 1/4th) of the earth’s diameter.
To go completely around the moon (circumference)
you would have to go about 6,800 miles –
compared to the earth’s 25,000 miles.
Mass of the Moon
To find the mass of a celestial object, we either have
to weigh something on its surface or we have to
have something orbit it. Since the Moon doesn’t
have any moon’s of its own, we had to put a
satellite in orbit around it. From that, we find that
the mass of the Moon is about 1.23% that of the
earth. Since the diameter of the Moon is 27% that
of the earth, we would have expected its mass to
be (.27)3 = .0197 or about 1.97% that of the earth.
This means that the Moon is on average less dense
than the earth. It’s density is more like that of the
earth’s crust than the earth’s core.
Gravity on the Moon
Since the Moon is smaller and less dense than
the earth, it should not be surprising that it’s
surface gravity is smaller than the earth’s. It
is about 1/6th that of the earth’s. That
means that a 120 pound weight on the earth
would weigh about 20 pounds on the Moon.
Gravity of the Moon
The earth’s gravity pulls the moon and keeps
it in orbit. (Without its motion, the moon would
fall down to the earth. Without the earth’s gravity,
the Moon’s motion would cause it to leave the
earth.)
Does the Moon’s gravity pull on the earth?
Are there any effects that we can see if the
Moon does in fact pull on the earth?
Gravity of the Moon – Tides
What are tides, and what causes tides?
What is the length of time between low and high
tide?
Are some tides bigger than others?
Is it in any way related to either the sun or the
Moon?
We will try to answer the first question AFTER we answer the
other three.
Tides
What is the length of time between low and
high tide?
Tides do NOT occur at the same time every
day. The high tide comes about 6 hours and
12 minutes after low tide. This means that
there are two high tides and two low tides
almost every day, but they do not happen at
the same time every day.
Tides
Are some tides bigger than others?
Some tides are bigger than others. The
biggest tides are called spring tides (not the
spring season, but because they spring up), and
the lowest tides are called neap tides. The
time between spring tides and neap tides is
about a week.
Tides
Is it in any way related to either the sun or
the Moon?
We notice that high tide occurs close to the
time that the Moon is either overhead or
“underneath”.
We notice that spring tides occur near full
moon and new moon, and the neap tides
occur near 1st and 3rd quarters.
Tides
What causes tides?
From the previous data, and from Newton’s
Laws of Gravity, we can understand that
gravity – both from the sun and from the
Moon – cause the tides. Looking down
from above the North pole, we see:
(diagram is NOT drawn to scale)
LT
HT
HT
LT
Tides
It is easy to see that the water closest to the
moon should be pulled more than the earth’s
center, and so should be at high tide.
But why is there a high tide on the side away
from the moon? There the water on the far
side of the earth is pulled LESS than the
center of the earth, and so “floats” away
from the earth – causing a high tide there.
Tides
Just like the hottest time of the year (mid July) is a
few weeks AFTER the longest day of the year
(June 21), the highest tide comes a little AFTER
the direct alignment with the moon.
This effect causes the earth to pull the moon a bit in
its orbit, and this causes the moon to speed up a
bit, and this causes the moon to orbit a little
farther out – about 4 cm a year. The
corresponding pull of the Moon slows the earth
down a bit – causing the days to become a little
longer over time.
Gravity
Working backwards, it appears that when the earth
first formed, the period for its spin (the day) was
only about 5 or 6 hours long – instead of the 24
hours now.
Again working backwards, it appears the Moon was
first only about ½ - and maybe as close as 1/10th of its present distance. That would have caused
the tides to be much, much higher than they are
today.
Tides – Sun and Moon
The fact that the tides are correlated with the
Moon more than the sun indicates that the
Moon has the biggest effect. But the tides
are correlated somewhat with the sun – the
spring tides occur when the Sun and Moon
line up – at New Moon (or anti-align at Full
Moon), and neap tides occur when the Sun
and Moon are at right angles – at 1st and 3rd
quarters.
Atmosphere of the Moon
Does the Moon have an atmosphere?
Not really. About half of the present atmosphere of
the Moon is from the exhaust of the Apollo Moon
Missions!
Therefore, there is no weather on the moon.
No atmosphere means that wings (airplanes,
helicopters, etc.) and parachutes won’t work.
It also means that there is essentially no protection
from x-rays and micrometeorites on the Moon’s
surface as there is on the earth.
Surface of the Moon
The major features of the Moon’s surface are:
1. Craters - they come in all sizes. There are more
on the “far” side of the moon.
2. Marias - smooth plains, probably from molten
lava flows in the past.
3. Mountains around the rims of the maria are
probably the result of huge collisions that caused
the maria.
4. Rays – probably from ejected material from the
impacts of colliding objects
5. Rilles – cracks in the maria from collapsed lava
tunnels.
Surface of the Moon
• Earth facing
side of moon:
http://photojournal.jpl.n
asa.gov/jpegMod/PI
A00405_modest.jpg
Surface of the Moon
• Far side of
moon:
http://photojournal.jpl
.nasa.gov/jpegMod/
PIA00304_modest.
jpg
Eclipses - shadows
There will be four main elements to consider
for understanding eclipses:
1. Alignments (new moon and full moon)
2. Length of shadows (umbra and penumbra)
3. Elliptical orbit of moon (apogee and
perigee)
4. Tilt of moon’s orbit with the ecliptic
1. Alignments
Sizes are NOT drawn to scale
View is looking down from above the North Pole
1st quarter
evening
Full
midnight
noon
morning
3rd quarter
New
Alignments
As you can see from the previous slide, the
Moon’s shadow will reach the earth only at
or near New Moon. This shadow will block
the sun and results in a Solar Eclipse.
The earth’s shadow will reach the Moon only
at or near Full Moon. This shadow will
block the sun from reaching the Moon and
results in a Lunar Eclipse.
2. Shadows:
Umbra and Penumbra
The umbra is the area of total shadow.
umbra
If (part of) the Moon goes through the umbra of the
earth, we will have a (partial) total lunar eclipse.
If a part of the earth goes through the Moon’s umbra,
we will have a total eclipse of the Sun at that part
of the earth.
Shadows: Umbra and Penumbra
The penumbra is the area of partial shadow.
penumbra
If the earth goes through the penumbra of the Moon,
we will have a partial eclipse of the sun.
If the Moon goes through the penumbra of the earth,
we will only see a slight dimming of the moon –
nothing particularly striking.
3. Elliptical Orbit:
Length of Shadows
The length of the shadow (umbra) of the Moon is
232,000 miles.
The distance from the Moon to the earth varies: at
perigee it is 221,000 miles – close enough for the
umbra to reach the earth; at apogee it is 253,000
miles – too far for the umbra to reach the earth.
The length of the shadow of the earth (furthest
extent of the umbra) is 860,000 miles. Thus it
always extends far enough to reach the Moon if
the Moon is directly behind the earth.
Motions of the Moon
Sizes are NOT drawn to scale
View is looking down from above the North Pole
1st quarter
evening
Full
midnight
noon
morning
3rd quarter
New
4. Tilt of the Moon’s orbit
The Moon orbits the earth on a slightly tilted
plane relative to the plane the earth moves
in as it orbits the sun (the ecliptic). The
Moon’s orbit plane is tilted 5.5o relative to
the earth’s plane.
5.5o
Tilt of the Moon’s plane
The diagram in the preceding slide would
indicate that we would NOT have an
eclipse, even if the Moon were at full Moon
or new Moon. However, there is a “line”
where the two planes (the ecliptic and the Moon’s
orbital plane) cross. If the Moon happens to be
on or close to this line, called the line of
nodes, we have the possibility of an eclipse.
Line of Nodes
This situation, the Moon being on the line of nodes,
happens twice each year as the earth orbits the
sun. Therefore, it appears that there should be two
eclipse seasons per year.
The line of nodes itself moves slightly each year, so
the actual time between eclipse seasons is a little
bit different from 6 months – it is actually once
every 5.8 months.
Length of Eclipse Seasons
The length of time that the Moon is close enough to
the line of nodes for its shadow to line up with the
earth is 31 days. This means that there will be at
least one and possibly two solar eclipses each
season. However, these solar eclipses may only
be partial or annular. A total eclipse will occur
only if the Moon is near perigee in its orbit.
Although partial solar eclipses are common, total
eclipses happen only for a small area on the
earth (that moves as the earth rotates and the
moon continues in its orbit). That makes these
types rare.
Length of Eclipse Seasons
The length of time that the Moon moves through the
earth’s umbra is 24 days – smaller than the 31
days for the earth to move through the Moon’s
umbra because the earth’s umbra narrows down as
it extends back behind the earth. This means that
at most there will be only one lunar eclipse each
season, and sometimes there will not be any.
Unlike solar eclipses, though, a lunar eclipse should
be able to be seen anywhere on the earth that
has nighttime at the time of the eclipse (and
clear weather).
Where did the Moon come from?
There are three main theories about the origin
of the moon:
1. It formed at the same time as the earth.
2. The earth captured it as it passed by.
3. An object smashed into the earth and the
resulting “splatter” was thrown into orbit
and eventually by gravity formed into the
moon.
Where did the Moon come from?
Data: the age of the moon rocks brought back by the
Apollo missions show them to be roughly 4.4
billion years old. Recall that the earth is
estimated to be 4.5 billion years old, but the
surface rocks of the earth are much younger due
to weathering and plate techtonics (earthquakes
and volcanoes).
Data: the density of the moon is about the same as
the crust of the earth.
Where did the Moon come from?
Data: to “capture” a body and have it orbit, the
captured body must lose speed. The two
mechanisms to lose speed are drag through an
atmosphere and collisions with other bodies.
Data: we’ll see in a bit that the terrestrial type
planets Mercury and Venus do not have any
moons, and Mars only has two very tiny rocks
(captured asteriods?) as moons. The giant planets
of Jupiter, Saturn, Uranus, and Neptune, however,
have lots of moons.
Where did the Moon come from?
The best guess presently is that a large
planetoid crashed into the hot earth very
soon after the earth formed, and the splash
of the collision orbited the earth and
eventually by gravity formed the moon.
The Moon and life on earth
There is speculation today that the Moon is very
important to the existence of life on earth.
1. The gravitational linkage between the earth and
moon does not allow the tilt of the earth to vary
much which keeps the climate more stable.
2. The tides on the earth caused by the pull of the
moon also appear to be important to the
development of life.