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 EarthWhy 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?

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

23½o

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)

Pisces

Aries

Taurus

Gemini

CancerLeoVirgo

Libra

Scorpius

Sagittarius

Capricornus

Aquarius

spring equinox

March 21

Dec. 21June 21

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 EarthDue 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 EarthWhat 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.

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.

closestfarthest

Seasons on the EarthSince 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 TimeTo 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

Sunrise and star rise

Star rise comes before sunrise

Earth rotates counterclockwise as viewed from above North pole

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 MoonThe 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

1

midnight noon

sunrise

sunset

New Moon

1st quarter

3rd quarter

Full Moon

Sizes are NOT drawn to scale!

View is looking down from above the North

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 SiderialSizes 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).

noonmidnight

evening

morning New

1st quarterFull

3rd quarter

Original Position of the sun

Position of sun one moonth later.

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”

1

midnight noon

sunrise

sunset

New Moon: mountain at midnight

1st quarter: mountain at sunrise

3rd quarter: moutain at sunset

Full Moon: mountain at noon

Sizes are NOT drawn to scale!

View is looking down from above the North

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 MoonSince 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)

HT

LT

LT

HT

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 objects5. Rilles – cracks in the maria from collapsed lava

tunnels.

Surface of the Moon

• Earth facing side of moon:

http://photojournal.jpl.nasa.gov/jpegMod/PIA00405_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. AlignmentsSizes are NOT drawn to scale

View is looking down from above the North Pole

noonmidnight

evening

morningNew

1st quarter

Full

3rd quarter

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.

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.

umbra

Shadows: Umbra and Penumbra

The penumbra is the area of partial shadow.

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.

penumbra

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 MoonSizes are NOT drawn to scale

View is looking down from above the North Pole

noonmidnight

evening

morningNew

1st quarter

Full

3rd quarter

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.