Eclipses

[raman22feb1988]

An eclipse occurs when three or more objects come in a straight line, (syzygy), when the middle
object partially or completely hides the view of the object at the other end, for a person looking
from one end. For example, a star may hide another star, for an observer from the Earth, or a
planet may hide its moon, or vice versa. In Earth, two types of eclipses are popular: Solar eclipses
and Lunar Eclipses.

Have a note of some of the terms that are used to describe the various parts of shadow of the object
that cause eclipses:
The figure below well describes these terms, as they are drawn by light rays.
Umbra: This is the darkest part of the shadow and a person at the umbra will see a total eclipse,
and the primary body is completely hidden by the secondary body.
Penumbra: A person at the penumbra will see a partial eclipse.
Antumbra: A person at the antumbra will see an annular eclipse, the secondary body is not big
enough to completely hide the primary body, and he can see a ring of the primary body around
the secondary body, which is at the center.


Solar Eclipse:
A solar eclipse occurs when the moon comes between the sun and the earth. The moon's shadow
falls on the earth causing a solar eclipse. A solar eclipse occurs on a New Moon day. There are four
types of solar eclipses: total, partial, annular, hybrid. It occurs during the daytime.


Total Solar Eclipse:
A person standing at the umbra will experience a total solar eclipse. In this case, the sun is completely hidden
by the moon, and the corona and prominences will become visible. A total solar eclipse is a beautiful sight, but
you should never directly look at any solar eclipse.

During a total solar eclipse, the sky becomes dark, though not as dark as during the night time, with strange
shadow effects of scattered light from the edge of the eclipse sites. The horizon will appear brighter, and the
whole landscape takes a strange appearance. Birds go out for roosting, bees stop flying, some of the flowers
will close as if it were night. The following animation demonstrates the stages during a total solar eclipse.


A few minutes before the total solar eclipse, the edges of the sun that are not obscured by the moon emit light,
and is called Diamond Ring. Then the light at the edges become less powerful and are called Baily's beads. Then
it vanishes and the fainter corona and prominences become visible. This is the first instant of the total eclipse.
A total solar eclipse on Earth does not last for more than 6 minutes (maximum), and the moon starts to uncover
the sun and the stages occur back again in reverse.

The moon's umbra does not cover more than 300 kilometers of the Earth's surface, and it occurs only when the
moon is at perigee (close to Earth) and the Earth is at aphelion (furthest from Sun). In some cases, moon will
not be big enough to completely cover the Sun, and an annular Eclipse will occur.

Partial Solar Eclipse:
A person standing in the penumbra will experience a partial solar eclipse. In some cases, the moon's umbra falls
either completely above or below the Earth, and nowhere on Earth, we can see a total solar eclipse. However the
penumbra can fall on the Earth, and we can experience a partial solar eclipse.

Annular Solar Eclipse:
Recall that the orbit of Earth around the Sun is not a perfect circle, it is mildly elliptical. Since the eccentricity of
Earth's orbit is 0.017, it is nearly circular. However the moon's orbit around the Earth is much elliptical with an
eccentricity of 0.05. If the Earth is closer to the Sun at perihelion or the moon is at apogee (furthest from the Earth),
then the moon will not be big enough to entirely cover the Sun. So, the moon's umbra will not be long enough to
reach the Earth, and the people at the antumbra will experience an annular solar eclipse, with a bright ring of the
Sun surrounding the moon.


The following figure shows the motion of moon's penumbra and antumbra during the annular solar eclipse on
15 January 2010.


Hybrid Solar Eclipse:
In this case, the diameter of the moon as seen from the Earth is just big enough to completely cover the Sun.
In this case, the moon's umbra does reach the middle of Earth facing the moon, but not the regions near the
horizon. So, the people near the horizon will start to see an annular solar eclipse, and as the time passes,
the moon's umbra moves to be long enough to reach the Earth, and total solar eclipse becomes visible, and
at the end, the eclipse ends with being annular. In this case, the moon's umbra or antumbra at the Earth is
too small, probably only a few dozens of kilometers within the Earth's surface.

The following figure shows the path of all the total and annular solar eclipses between 2001 and 2020.


The Moon
The moon has no light of its own, and it reflects the light from the Sun. The rotation of the moon around
its axis is synchronized by tidal forces, and it always keeps the same face pointing towards the Earth.
In other words, it is tidally locked. Tidal locking occurs for a smaller moon orbiting around a large planet
over a long period of time, or for a small planet orbiting around the sun. For example, a number of moons
in the solar system are tidally locked to their planets.

Initially, it was thought that Mercury was tidally locked to the Sun, but it is locked in an orbital resonance
of 3:2, that is, it makes 3 rotations for 2 revolutions around the Sun. Sometimes, when the planet and its
moon are comparable in size, both can be tidally locked to each other. For example, Pluto and its moon
Charon which are both tidally locked to each other. Charon orbits around Pluto as if a rod is tied to their
diameters.

The side of the moon that faces the Earth is called the near side of the moon and the side that points away
from the Earth is called the far side of the moon. Since the moon is tidally locked to the Earth, the rotational
period of the moon is exactly the same as the time taken for 1 revolution around the Earth, both being equal
to 27.3 days.

Why different phases of the moon?
As we observe at the moon, we see the different phases of the moon everyday. Starting from the New Moon,
it waxes to Crescent, First Quarter, Gibbous and Full Moon, and then wanes back to Gibbous, Last Quarter,
Crescent and New Moon. It takes 29.5 days for transition from one New Moon to the next.

During the New Moon, the moon comes between the Sun and the Earth, and all the sunlight falls on the far
side of the moon, and we cannot see the moon as it rises at sunrise and sets at sunset. Everyday, as the
moon orbits around the Earth from west to east, sunlight begins to fall on the near side of the moon, and we
can see its waxing phases. During the Full Moon, the Earth comes between the Sun and the Moon and all
the sunlight falls on the near side of the moon, and we can see the full moon. It rises at sunset and sets at
sunrise. After that, as the moon begins approaching towards the Sun, the sunlight begins to fall on the far
side of the moon, and the moon wanes back to the New Moon.

Lunar Eclipse:
During a lunar eclipse, the Earth comes between the Sun and the Moon. The Earth's shadow falls on the
moon causing a lunar eclipse. A lunar eclipse occurs on a Full Moon day. There are 3 types of Lunar
Eclipses: total, partial, penumbral. It occurs during the night time.


Total Lunar Eclipse:
Recall that the diameter of the Earth is 4 times the diameter of the moon, so the Earth's umbra is large
enough to completely hide the moon. However, this figure is exaggerated and the Earth's umbra does not
cover a large part of the moon's orbit. Anyway, total lunar eclipses are more frequent than total solar eclipses.
A total lunar eclipse can directly be seen with the naked eye, and is a beautiful sight. Since the Earth's
umbra is bigger, a total lunar eclipse can last for a longer time, usually an hour or two. It is visible from a
large part of the Earth's surface, usually half of the Earth that is facing the moon.

During a total lunar eclipse, the sunlight to the moon is blocked by the Earth. That does not mean the
moon will completely vanish for a while. The Earth's atmosphere reflects the sunlight that can reach the
moon, though no direct sunlight will reach the moon. This is enough to illuminate the moon with orange,
bright copper red, brick red, rust or even nearly black colour, especially at the middle of totality, depending
upon the Earth's atmospheric conditions such as cloud cover or volcanic eruptions, etc.

Partial Lunar Eclipse:
In this case, part of the Earth's umbra falls on the moon and the rest of the moon lies on the Earth's
penumbra. So, the Earth's umbra falling on the moon will cause a partial lunar eclipse, and the rest
of the moon will be dimmer, since it lies on the Earth's penumbra.

Penumbral Lunar Eclipse:
In a penumbral lunar eclipse, the moon passes through the Earth's penumbra without reaching the
Earth's umbra at any time. An observer from the Earth's penumbra falling on the moon will see a
partial solar eclipse, and since some sunlight always falls on the Earth's penumbra, the moon will
always be visible from the Earth in this case, but it goes dimmer. Since, the Earth's penumbra is only
as wide as the moon, most of the penumbral lunar eclipses are partial, and only part of the moon enters
the Earth's penumbra. But, once in a while there will occur total penumbral lunar eclipses, but its
probability of occurrence is only about 1.2%.

Why every New Moon day is not Solar Eclipse and every Full Moon day is not Lunar Eclipse?
If the Earth's orbit around the Sun and the Moon's orbit around the Earth lies on the same plane, then
every New Moon day would be a solar eclipse and every Full Moon day would be a lunar eclipse. Actually,
the orbit of the moon around the earth is tilted to the plane of earth's orbit around the sun (the ecliptic) by
5°. Think of 3D motion of Sun, Moon and the Earth. Compare this with the angular diameter of Sun (0.53°)
and the angular diameter of Moon (0.51°). So, during a Full Moon, usually the Earth's umbra either falls
too above or too below the moon. Similarly during a New Moon, the moon's umbra usually falls either too
North or too South of the Earth.

An eclipse occurs only when the Sun, Moon and the Earth are fairly in the straight line, and it occurs only
when the moon is close to the plane of the ecliptic (earth's orbit). We define two points in the moon's orbit,
the ascending node and the descending node where it crosses the plane of the earth's orbit around the Sun.
A total eclipse can occur only from the position of earth's orbit, where one of the ascending node or the
descending node of the moon coincides with the New Moon or the Full Moon, that is the three objects Sun,
Moon, Earth are in a straight line.


Honestly, this is possible in nearly two opposite points in the Earth's orbit, the conjunction and the opposition,
for any given year. To be frank, for a lunar eclipse, there is a period of 37 days when the moon is closer to either
of the ascending or descending nodes, when the moon can pass through the earth's umbra or penumbra, either its
top or bottom. This is called the eclipse season, when the eclipses are possible. When the Full Moon day coincides
with the middle of the eclipse season, then the Earth's umbra perfectly falls on the Moon and we can experience
a total Lunar Eclipse. Otherwise, it is possible that the Full Moon day coincides with both ends of the eclipse
season, with an interval of 29.5 days, and during both times the moon passes through the Earth's penumbra,
and we can experience a penumbral lunar eclipse during the successive Full Moon days.

Note that it will take 354 days for 12 transitions from a New Moon to the next. So, for the next year, the eclipse
season shifts 11 days earlier. Since the time taken for the moon to move from the ascending node to the descending
node and back to the ascending node is only 27.2 days, so the angle of the moon from the Earth with respect to
the Sun varies every year, and a total lunar eclipse this year can become a partial lunar eclipse next year, and
a penumbral lunar eclipse, the year after. On the other end, a penumbral lunar eclipse will become a partial
lunar eclipse the next year, and a total lunar eclipse after that. Frankly, every 3 years or so, the Full Moon days
coincide near the either of the nodes, and we can see total lunar eclipses twice a year. In the intermediate years,
the Full moon days coincide near the end of the eclipse seasons, and we can have two penumbral lunar eclipses
during the successive Full Moon days, or a partial lunar eclipse alone, or a partial lunar eclipse along with a mild
penumbral lunar eclipse successively.

Note that since the moon moves away from the Earth about 3 cm every year, the apparent diameter of the moon
becomes smaller in the future. By the time, the sun will also grow up in size, as it approaches towards the stage
of the Red Giant. So, in the late future, the moon will never be big enough to completely cover the Sun, even when
the Earth is at aphelion and the moon is at the perigee. So, the total solar eclipse can only last for less than
another 600 million years, based upon a prediction.

Note that the tidal forces of the moon also slow down the rotation of the earth, roughly 1 second in every 500000
years. The moon will not indefinitely move away from the Earth. In the far future, the earth's rotation would have
slowed down further and will keep only one side facing towards the moon (similar to the tidal locking of the moon
from the Earth). Then, the moon will start coming closer towards the Earth. When the moon comes too close
to the Earth, the earth's gravity has enough power to break the moon into millions of fragments that will orbit around
the Earth in the form of rings. Rings of giant planets such as Jupiter and Saturn would have formed in a similar
manner.

By the time, the Sun would have grown into a Red Giant within another 5 billion years or so, and even could have
engulfed the Earth System, which is uncertain, because it would be approximately 250 times its current diameter,
which is the size of the current earth's orbit, and due to tidal forces, the earth's orbit would have increased its radius,
and would be orbiting around the sun in an orbit of radius 1.4 Astronomical Units or so. The Sun would lose its outer
expanding shell, after its Red Giant phase, and the core cools down until it has decayed into a White Dwarf star.

Lunar Months:
For predicting, when the eclipses will occur, we need to understand the different lunar months.

Sidereal Month:
It is the time taken for the moon for one complete revolution around the earth, from due west of the earth, to
the same position again with respect to the earth. It takes 27.321661 days for this process, but as the picture
below shows, when the moon completes one orbit around the Earth, the earth itself has moved around the sun
by about 30° (one twelfth of its orbit), so for the next time the Earth, Moon and the Sun will not be in a straight
line, starting with a New Moon. It will be a waning crescent after that period, so some more time is needed to
be back again in New Moon, and the moon is between the Sun and the Earth.


Synodic Month:
The time taken for transition from one New Moon to the next is called Synodic Month, and it takes about
29.530589 days on the average, which is a little more than the Sidereal Month. Since the orbits of moon
and earth are not perfectly circular, the bodies move faster near the perihelion and so this period is not
fixed and varies between 29.27 days and 29.83 days.

A lunar day is the time taken for an observer on the moon to see the sun from zenith to zenith. This is
same as the Synodic Month and is equal to about 29.530589 days.

Similarly, for an observer on the Earth, the time taken for the Sun to move from zenith to zenith, which is a
solar day, is 24 hours. Since the Earth orbits around the Sun while it is rotating, this is somewhat longer than
the time taken for one rotation of the Earth about its axis, which is equal to only 23 hours, 56 minutes and 4
seconds.

Rotational Period of the Moon:
Since the moon is tidally locked with respect to the Earth, the time taken for one rotation of the moon about
its axis is exactly the same as the time taken for one complete orbit around the earth, and is equal to 27.321661
days. Because of this, the moon keeps always the same side pointing towards the Earth.

Anomalistic Month:
It is the time taken for the moon to move from apogee to perigee and back to apogee and is equal to 27.554549
days. The apogee and perigee of the moon's orbit are not fixed with respect to the Earth, and circle around the
Earth once every 9 years.

Tropical Month:
It is the time taken for the moon to move over from one lunar equinox to the next and is equal to 27.321582 days.

Draconic Month:
It is the time taken for the moon to move from the ascending node to the descending node and back again to the
ascending node, and is equal to 27.212220 days. This is not exactly the same as the time taken for the moon for
one complete orbit around the earth, due to the precession of moon's orbit with respect to the stars. The moon's
orbital plane around the earth and so both the nodes rotate backward around the earth once about every 18.6 years.

The Saros: After what time can we see similar types of eclipses repeating again in a cyclic fashion?
As I have mentioned above, the similar type of eclipse occurs again when the ascending node or the descending
node coincides back with the New Moon day or the Full Moon day. So, we will have to look at the Synodic Months
and the Draconic Months to compare between the similar types of eclipses, when they will occur again.

Clearly, from the above stats, 223 Synodic months correspond to 6585.321 days, and 242 Draconic Months
correspond to 6585.357 days, which is almost the same, and after 6585.3 days, we can have similar types of
Solar Eclipses, belonging to the same Saros series. This corresponds to 18 years, 10 days and one third of a
day, and is known as Saros. Since this is not an integer, the earth has rotated an extra of one third of a rotation,
and so after this time period, the next eclipse falls on different parts of the Earth, which belongs to the same
Saros series, is shifted 120°W, and a bit either north or south. After three such periods, known as the Triple
Saros corresponding to 19756 days (54 years 32 or 33 days), the same part of the Earth will receive the similar
type of eclipse, but in this case, shifted significantly either to the North or to the South.

Eclipses on other planets:
Eclipses are also possible on other planets, for example, for a Solar Eclipse on Mars to occur, neither of its
moons, Phobos or Deimos are big enough to completely cover the sun, though they are much nearer to
Mars than the moon is to the Earth, they are too small in size, they are irregularly shaped objects, probably
captured asteroids with a diameter of hardly 10 kilometers. The following animation shows Phobos transiting
the Sun as one can see from the surface of Mars.


It is also possible for one moon to eclipse another moon belonging to the same planet system. Pluto's moon
Charon, which is about half the size of Pluto, is also the site of many eclipses, of either the Sun or the other
moons within the same planet system.

Transit of Mercury:
It is also possible to view Mercury transiting the Sun from the Earth. It occurs during the first half of May or
November, not every year, and is not visible all over the globe, but only from the side of the Earth that is facing
the Sun. Since Mercury is very small in diameter and very far away from the Earth, Mercury will appear only
as a small black dot that is transiting the Sun. The transit of Mercury on May 7, 2003 lasted for about 6 hours.
The November transits occur over a period of 7, 13 or 33 years. The May transits occur only over a period of
13 or 33 years. The transits of Mercury across the Sun during the 21st Century are as follows:
May Transits: 2003, 2016, 2049, 2062, 2095, 2108
November Transits: 1999, 2006, 2019, 2032, 2039, 2052, 2065, 2078, 2085, 2098

Transit of Venus:
It is also possible to view Venus transiting the Sun from the Earth, but the occurrence of this incident is very
rare. Since Venus is larger in size and closer to the Earth than Mercury is, Venus should appear larger in
size while it is transiting the Sun. Transition of Venus occurs four times every 243 years, following in a regular
pattern. To be precise, it occurs twice with a time gap of about 8 years, followed by 121.5 years or 105.5 years
alternatively. Transition of Venus last occurred on June 8, 2004, and then the next such transition will occur
on June 6, 2012. Before these two events, the previous transition of Venus across the Sun occurred in December
1874 and December 1882. After 2012, thus, finally, the next transitions of Venus across the Sun will only be in
December 2117 and December 2125.

[raman22feb1988]

The axial tilt of the different planets are given below:
Mercury: 0.01°
Venus: -2.6°
Earth: 23.439281°
Mars: 25.19°
Jupiter: 3.13°
Saturn: 26.73°
Uranus: -82.23°
Neptune: 28.32°
Pluto: -60.39°
Moon: 1.5424°

The axis of Earth's rotation is tilted by an angle of 23.44° to the ecliptic (plane of Earth's orbit around the Sun).


The effects of the axial tilt are the occurrences of various seasons felt over the Earth: Spring, Summer, Autumn (Fall),
Winter. The seasons are experienced much effectively over the temperate and frigid zones. In the tropical areas, it
is generally warm throughout the year, so seasons are less effective, although the tropical regions will have wet and
dry seasons, usually.

In the Northern Hemisphere, summer is from June to August, autumn is from September to November, winter is from
December to February, spring is from March to May. This is opposite in the case of Southern Hemisphere. Actually
these are true for the areas beyond the tropics. Summers are warmer, when sun is at maximum altitude in the sky
at noon, and sun is above horizon for a longer time. Winters are cooler, when sun is at minimum altitude in the sky
at noon, and sun is above horizon only for a shorter period of time.

June 21 is the longest day in the Northern Hemisphere, when the sun reaches the maximum elevation in the sky at
noon (beyond the Tropic of Cancer and Tropic of Capricorn), and stays above the horizon for a long time. This is
called the summer solstice for the Northern Hemisphere. And it will be the winter solstice for the Southern Hemisphere.
Note that this may not be the warmest day, since it will take some time for the Earth to heat up - and so the warmest
days will be around mid July. Similarly, December 21 is the shortest day in the Northern Hemisphere, and it is the
winter solstice for the Northern Hemisphere, and it will be the summer solstice for the Southern Hemisphere.

March 20 and September 22 are equinoxes, when the sun is above the equator, and all the places will receive 12
hours of day and night. On June 21, the Sun is above the Tropic of Cancer and moves slowly over the Tropic of
Capricorn on December 21. Spring is the time before summer, when it becomes warmer after winter, and plants
begin to grow their leaves, and flowers become to bloom. After summer, the autumn is the time when it becomes
cooler, and plants begin to shed their leaves.



Places in the equator receive 12 hours of day and 12 hours of night throughout the year. However on 23½° latitude,
during the summer solstice, we receive 13½ hours of daylight and 10½ hours of darkness. During the winter solstice,
there is 13½ hours of darkness, and only 10½ hours of daylight. At 50° latitude, during the summer solstice, the
sun is above the horizon for 16 hours, and only 8 hours of night. At the Arctic and Antarctic Circle, during the summer
solstice, the sun is on or above the horizon for 24 hours, and during the winter solstice, the sun is on or below the
horizon for 24 hours. At the poles, during the summer solstice, the sun seems to circle in the sky at 23½° latitude,
without going down the horizon, and during the winter, the sun is below the horizon for 6 months. Any place within
the Arctic Circle or the Antarctic Circle, will receive one day during summer when the Sun does not set, and one
day during winter when the Sun does not rise. These places are called the land of midnight sun, or the land of
mid day darkness.

During the equinox, the sun is above the equator. The sun as a sphere, rather than a single source of light, will
take 32 hours to cross the equator. Only in the places within the tropics (23.44°N to 23.44°S), it is possible to
have the Sun at noon to be at zenith (overhead), when there are virtually no shadows at all, at noon. At the equator,
during noon, the sun rises to a maximum altitude of 66.56° north or south, during the June or December solstice.
At 23.44° latitude, the sun is at zenith during the noon, on the summer solstice, and rises only to an angle of
43.12° at noon during the winter solstice. At 50° latitude, the sun rises to an angle of 63.44° during the summer
solstice, and only 16.56° during the winter solstice. At the poles (90° latitude), the Sun never rises above 23.44°
above the horizon, at any part of the year, and during the equinoxes, the Sun is at horizon throughout the day.

Besides the normal day and night, twilight is experienced when the Sun is below the horizon upto 18°. Dust particles
high in the atmosphere scatter light to the night side of the planet. Dawn and dusk are periods of twilight experienced
before sunrise and sunset. Twilight can be classified as civil, nautical, astronomical twilight depending upon its
intensity and the elevation of sun below the horizon, as 6°, 12°, 18° respectively. For example, at 20° latitude,
the path of sun below the horizon is steep, at 70°, during the equinox, so the twilight is shorter, probably only
one hour before sunrise and one hour after sunset. At 50° latitude, during the summer solstice, the twilight
exists for nearly 4 hours before sunrise and 4 hours after sunset, in addition to 16 hours of daylight. In fact,
there is barely any night at all. Note that the sun is only 16.56° below the horizon, during the midnight, so there
will be still astronomical twilight present. This will be the phenomenon of gray nights - when it doesn't get dark
enough for the astronomers to do their observations in the sky. Twilight will exist in other planets too, for example
in Mars, twilight exist for nearly 2 hours before sunrise and 2 hours after sunset, due to the presence of dust
particles very high in the atmosphere.

Perihelion is the point in the Earth's orbit, when it is closest to the Sun and it occurs around January 5. Aphelion
is the point in the Earth's orbit, when it is furthest from the Sun and it occurs around July 5. Note that since the
Earth's orbit is elliptical, although only slightly - with an eccentricity of 0.017, with Sun as one of its focus, the
Earth moves faster at the perihelion than at aphelion. As a result, the southern hemisphere summers are shorter,
only for a period of 89 days, when compared to the northern hemisphere summers which last for a period of 92
days. Also since the perihelion coincides with the southern hemisphere summer, this causes the solar insolation
to be 6.8% more at perihelion, than at aphelion - the southern hemisphere summers are warmer and at aphelion,
the southern hemisphere will have a cooler winter. On the other hand, the northern hemisphere summers are
cooler and the winters are warmer. So, the seasons in the southern hemisphere are somewhat more extreme
than that in the northern hemisphere. However, as a whole, the Earth is warmer at the aphelion, than at the perihelion,
because the northern hemisphere has more land than the southern hemisphere, and the land heats up more quickly
as well as releases up the heat away more quickly than the sea. At the equator, January will be warmer, because the
Earth is closer to the Sun than July. At a little north of the equator, these effects will be compensated up.

The Earth takes 23 hours 56 minutes 4 seconds to complete one rotation about its axis. But, as the Earth moves
around the Sun while it is rotating, the time taken for the Sun between two noons is slightly longer, which is equal
to 24 hours. The Earth takes 365 days 5 hours 48 minutes 46 seconds to complete one orbit around the Sun. The
rotation and revolution period for the various planets are as follows:

Planet Rotation Period Revolution Period
Mercury 58.646 days 87.969 days
Venus 243 days 224.7 days
Earth 23 h 56 min 365.242 days
Mars 24 h 37 min 686.971 days
Jupiter 9 h 55 min 11.87 years
Saturn 10 h 38 min 29.45 years
Uranus 17 h 14 min 84.07 years
Neptune 16 h 6 min 164.9 years
Pluto 6 days 9 hours 248.1 years
Moon 27.321661 days 27.321661 days

Milankovitch cycles
The axial tilt of the Earth, which is currently at 23.44° is not fixed, but varies over time.
Over the past 100000 years, the axial tilt has varied between 22.1° and 24.5°. This forms
a cycle of maximum and minimum around every 41000 years. The axial tilt currently at
23.44° is decreasing, and will reach its minimum value around the year 10000 AD.

The eccentricity of the Earth's orbit also varies over time, varying between 0 (nearly circular)
to 0.05 (mildly elliptical). The eccentricity is currently 0.017, and is currently decreasing.
The variations in Earth's orbit are mainly due to the gravitational force exerted by the giant
planets such as Jupiter and Saturn. So, in another 10000 years, we could have the perihelion
near the end of July.

The plane of the Earth's orbit also changes, and forms a cycle around 70000 years. In
addition, we have cycles in the precession of the Earth's axis every 26000 years. Precession
is the direction in which the North Pole or the South Pole points to, say during the equinoxes,
with respect to the fixed stars, and to the plane of the Earth's orbit. The direction in which
the North Pole points to, during the equinoxes, completes a circle once every 26000 years.
Due to this phenomenon, in another 13000 years or so, the Northern Hemisphere summer
will occur in December, and winter in June, and after 26000 years or so, we could have
back the summer again in June and the winter in December.


When all the factors are considered up together, then we will have around 100000 year cycle
after which we can see similar patterns of ice ages. This is called Milankovitch cycles.

Over the past 500 million years, the Earth has changed its climate from hot house, like the
age of dinosaurs to an ice house, like it is today. The variations of the Earth's climate over the
past 500 million years is given below:


We are currently in an ice age, because the Greenland and Antarctic Ice sheets still exist.
During a hot house period, there will be no ice caps at the poles at all. During an Ice Age,
we have glaciation and inter-glaciation periods, and these are caused due to the Milankovitch
cycles. The last glacial period ended about 10000 years ago, and we are in an inter-glacial
period. The last glacial maximum occurred about 18000 years ago, which is the coldest
period of the glacial periods. The ice sheets expand during the glacial periods and contract
during the inter-glacial periods.


Such variations also occur in the other planets too, within the Solar System. For example,
in Mars, the axial tilt is supposed to vary between 15° and 35°. Mars has two very small,
irregular shaped moons, Phobos and Deimos, with diameter extending only upto tens of
kilometers. They are probably suspected to be thought as captured asteroids.

The moon plays an important role in keeping the variation of the axial tilt of the Earth
relatively stable, precisely between 22.1° and 24.5°. But, it will not remain so at all, for ever,
after a long time. The moon moves away from the Earth at the rate of about 3 cm every year.
The moon is now currently at a distance of about 60 Earth radii from the Earth. In about
1.5 billion years or so, when the moon moves away to a distance of about 66 Earth radii,
the forces and the torques that are being exerted by the jovial planets such as Jupiter and
Saturn will follow so, and the axial tilt will vary between about 22° and 38°. In around another
2 billion years or so, when the moon goes to a distance of about 68 Earth radii, from the Earth,
another resonance will occur so, and then the axial tilt will thus finally oscillate between 27°
and 60°. These factors will have severe and extreme effects on the Earth's climate.

[ThreeHeadedMonkey]

Well, that's very interesting, but this is a website about Classic DOS Games. You might be better off writing for wikipedia if you want to share your scientific knowledge with the world.

[raman22feb1988]

Well, that's very interesting, but this is a website about Classic DOS Games. You might be better off writing for wikipedia if you want to share your scientific knowledge with the world.

In the beginning, the people within the forum were interested in reading about
the scientific facts, mathematics and distributed computing projects. So that
I come and post occasionally some stuff within this forum, whenever I collect
something about them up.

Chat is a section within this forum, to discuss about anything that is not at all
related to the Classic DOS Games. So, we can discuss about these interesting
things over here.

Wikipedia has already everything in detail, with respect to mathematics, science,
engineering, medicine or even geology. So, there is not much to contribute to the
Wikipedia for now. But, most of the things that I posted over here, are those items
that I gathered only from the Wikipedia itself, besides the other related web sites
for these types of the articles.

[DOSGuy]

Actually, I find astronomy very interesting. Most of the math problems that raman posts are way over my head, but this is the sort of thing that I usually go to Wikipedia to read up on. I used to buy astronomy books to get all of the data tables for the planets and moons. I'm fascinated by everything from their size to the length of their days and years.

To me, the New Horizons mission (currently in progress) is one of the most important in history, and certainly the most interesting since the Voyager missions. Galileo and Cassini taught us a lot about Jupiter and Saturn, but we had already been there. We have never sent anything to Pluto, and there's a chance that it will visit another Kuiper Built Object after it passes by. The is the first mission to explore Trans-Neptunian Objects.

The other thing that makes the mission special for me is the fact that we aren't able to photograph Pluto from Earth. We can "explore" the other planets from here, but Pluto remains a mystery to us. The highest resolution images that Hubble has ever taken of Pluto create an approximately real color mosaic that shows the planet to be brown, and that's about it. New Horizons will finally show us what Pluto and its moons look like.

Anyway, this part of the forum is here so that people can chat about anything they want. I assumed that it would fill with posts about popular media, but science and technology is fine by me.

[raman22feb1988]

1) Find the value of k such that y=x is a tangent to y=k^x.
(a) 1.44 (b) 13/9 (c) e^(1/e) (d) 1.45

2) Find the value of k for which the elliptic curve
y^2 = x^3 - kx + 1
has a self-intersection on the X-axis
(e) 1.86 (f) 1.87 (g) 1.88 (h) 1.89

3) The curve y = -x^4-2x^3+2x^2+3x+1 is symmetric about
(i) x = -0.5 (j) x = 0.5 (k) y = -0.5 (l) y = 0.5

4) The value of k for which the curve y = -x^4-2x^3+2x^2+3x+k
has a local minima at the X-axis is...
(m) 0.875 (n) 0.825 (o) 0.8175 (p) 0.8125

5) Given that 2 nCr = 3 nC(r-1) = 6 nC(r-2). Find out the value of n.
(q) 20 (r) 17 (s) 14 (t) 11

[raman22feb1988]

http://earthquake.usgs.gov/
This website shows the places where earthquakes have occurred during the past 7 days.
Most earthquakes occur at the plate boundaries, though earthquakes do occur within plates
also. The following link shows the plate boundaries within the world.
http://en.wikipedia.org/wiki/File:Plates_tect2_en.svg
There are 3 types of plate boundaries: Convergent, where the plates subduct under another
plate and are destroyed as they melt inside the mantle. Divergent, where plates move away
from each other creating new crust. Volcanoes are common across divergent boundaries, like
the mid-atlantic ridge. Trenches are usually formed across ocean convergent boundaries, like
the Mariana Trench, the deepest trench in the world, and when an ocean plate or continental
plate subduct under another continental plate, we have mountain ranges like the Andes or the
Himalayas. Conservative boundaries, where plates slide over each other, neither creating nor
destroying the crust, such as the St. Andreas Fault of California. Since the volume of Earth
remains the same, rate of subduction should be equal to the rate of sea-floor spreading. The
ocean floor is continuously regenerated, so the ocean floors are less than 300 million years
old, while the continental crust can be as much as 4 billion years old.

See the weather across different places
http://weather.yahoo.com/
http://news.bbc.co.uk/weather/
The coldest places will be at the poles, and across the equator, the weather will be fairly be
stable all round the year. The hottest places will be across the deserts in the Tropics, during
the summer, where the climate is extremely dry, and so the temperature variations will be
very high between summer and winter, and even during day and night. Around the equator,
the climate is wet all round the year, and the sky will always be cloudy. Antarctica is the
coldest, driest and windiest continent.
See also the sunrise and sunset timings all round the year. Places north of the Arctic Circle
and places south of the Antarctic Circle will always experience midnight sun one day during
the summer, and another day during the winter when the sun does not rise above the horizon.
Also see the durations of civil twilight, nautical twilight and astronomical twilight.

http://www.scotese.com/
See the Earth History, Climate History and the Continental Drift, how the continents drifted
over the past 750 million years to predictions 250 million years into the future. Super continents
break apart and form again in cycles. Rodinia broke apart 750 million years ago, and assembled
into Pangea 200 million years ago. Pangea broke apart into the continents that we know today,
and will assemble into Pangea Ultima about 250 million years into the future. Also, see the climate
history - we are currently in an Ice House world. There has been times when the earth has been in
an Ice House climate mode (now, Late Carboniferous (300 million years ago), Late Ordovician
(450 million years ago), Cryogenian (750 million years ago), Early Proterozoic (2400 - 2100 million
years ago)). Within the Ice House, there exist interglacial periods - the last glacial period ended
about 10000 years ago, and now we are in an interglacial period. The Ice Age expands and contracts
due to variations in the Earth's orbit - eccentricity and axial tilt - probably due to the gravitational
interactions with Jupiter and Saturn. These are called Milankovitch cycles. Also see the evidence
of Snowball Earth during the Late Proterozoic (Cryogenian period), when the ice caps would have
covered the whole world, extended upto the Equator.

Eclipses
http://eclipse.gsfc.nasa.gov/eclipse.html
http://www.hermit.org/Eclipse/
Solar eclipses occur during a New Moon day and Lunar eclipses occur during a Full Moon day. Not
all New moon days are Solar eclipses and not all Full moon days are Lunar eclipses, because since
the moon's orbit around the earth is tilted to the plane of earth's orbit around the sun (the ecliptic) by
5 degrees, the sun, moon and earth will always not be in a straight line. There exist a period of 37 days,
the eclipse season, during which the moon will be near the ecliptic, crosses the plane of the ecliptic
at the middle and the eclipse is possible. The moon will be either at the ascending node (moving upwards)
or the descending node (moving downwards) from the plane of the ecliptic.
Solar eclipses are of 4 types: Partial, Total, Annular and Hybrid.
When the moon is near the apogee, the moon will appear smaller than the sun, and will not completely
cover the Sun during the maximum solar eclipse. So, we see an annular solar eclipse or a ring (or annulus)
of Sun around the eclipsed Sun by the moon. When the moon is near the perigee, we can expect a total
solar eclipse. During the annular solar eclipse, the moon's umbra (from where the total solar eclipse is
seen) does not reach the Earth. And then during a total solar eclipse, the moon's umbra does not cover
more than 300 kilometers of the Earth's surface and can last for maximum case only for upto 6 minutes,
in time. An annular solar eclipse can last upto 12 minutes, in duration. A hybrid solar eclipse is just in the
edge of the total solar eclipse, and the annular solar eclipse, when the central places will see a total solar
eclipse, and then the other places will simply see an annular solar eclipse. In this case, the moon's umbra
will be extremely small, only typically covering a few dozen miles.
Lunar eclipses are of 4 types: Penumbral (when the moon passes through the Earth's penumbra, without
touching the umbra at all, in this case, the moon gets dimmer, as the time passes on by), partial, total. Since the Earth's umbral shadow is bigger than the moon's umbral
shadow, a total lunar eclipse can cover the entire moon, and can last upto an hour and half. And then all
the places facing the moon can see it up.
Note that after a period of 6585 1/3 days, the sun, moon, earth will be in line again, and we can view similar
type of eclipse, of the same size and duration. This is the Saros period, and such eclipses are named with
the same Saros number. Since it is 1/3 days, the earth would have rotated 1/3 rotations extra and we can
view the similar type of eclipse across the different parts of the world. After three such periods, called the
Triple Saros, the same type of eclipse will be again visible in the same part of the world, but shifted significantly
north or south. This is approximately equal to 54 years and 1 month. Saros = 18 years 10 or 11 days.
Also see the transits of Mercury and Venus across the Sun, when they occur so, on the same website or on
the Wikipedia.
The moon is tidally locked to the Earth, and always keeps the same face pointing towards us. From the moon,
the Earth will be always at the same position, but the phase keeps changing. From the far side of the moon, we
cannot view the Earth at all. During the new moon, the moon is between sun and earth, and sunlit side of moon
is the far side of the moon, but during the full moon, the earth is between sun and moon, and sunlit side of moon
is the near side of the moon. New moon rises during sunrise and sets during sunset, and then the full moon rises
during sunset and sets during the sunrise time. In other words, the night side of the Earth will only always see the
full moon, and new moon faces only always the day side of the Earth.

View of earth from moon and sun - side of earth facing the moon and then the sun
http://www.smeter.net/propagation/views ... m-moon.php
http://www.smeter.net/propagation/views ... om-sun.php
During Full moon, the earth will not be lit from the moon, and then during the new moon days, the earth will be
fully lit by the sun from the moon.

Current position of sun and moon from the earth: Inclination, azimuth
http://timeanddate.com/worldclock/sunearth.html
During the June Solstice (that occurs around June 21st), the Northern Hemisphere will be tilted towards the Sun,
and it will be summer for the Northern Hemisphere. Winter for the southern hemisphere. The sun will be above the
tropic of cancer (23 1/2 degrees north), with warmer and longer days for the northern hemisphere, and shorter and
cooler days for the southern hemisphere. During the December solstice, (December 21st), the southern hemisphere
will be tilted towards the Sun, and summer for the southern hemisphere, and winter for the northern hemisphere.
The sun will be above the tropic of capricorn (23 1/2 degrees south latitude). Equinoxes will occur around March 20,
and September 22, when sun is above the equator, and all places receive 12 hours of day and night. Places at the
equator receive everyday equal to 12 hours 7 minutes of day and night only. Follow up with the seasons: Spring
(March, April, May), Summer (June, July, August), Fall or Autumn (September, October, November), Winter
(December, January, February) within the Northern Hemisphere, and then vice-versa from the side of the Southern
Hemisphere.

Calendars
http://timeanddate.com/calendar/?year=2009&country=1
The earth takes 365 days 24 hours 48 minutes 46 seconds to complete up one orbit around the Sun. This is equal
to 365.2422 days. Before AD 44, all years had exactly 365 days. After that Julian Calendar was followed, in which
the fourth year was introduced as a leap year. This is equal to 365.25 days. The Gregorian Calendar was adopted
in Italy, Spain, Poland and Portugal on October 15, 1582 by dropping 10 days from the Calendar. This new rule
stated that century years were leap years only if they were multiples of 400. So, we have 365.2425 days on an
average. United Kingdom, United States and other countries did not adopt the Gregorian Calendar until the year
September 14, 1752, when they synchronized by dropping 11 days from their calendar. Sweden and Finland, which
were following up with the Julian Calendar until the year 1700, dropped the day February 29, in the year 1700,
according to Gregorian calendar, and so they were out of phase with both the Julian Calendar and then also the
Gregorian calendar too. They synchronized with the Julian calendar in the year 1712, by having a double leap year,
namely February 30, 1712. They switched over to the Gregorian calendar on March 1, 1753, by dropping out 11
days after February 17, 1753.

http://timeanddate.com/worldclock/astronomy.html?n=553
Here, see the timings for sunrise, sunset, moonrise, moonset, moon phase, duration of civil twilight, nautical twilight,
astronomical twilight all round the year.

http://jove.geol.niu.edu/faculty/stodda ... arium.html
Simulation of solar system, comets, sky view from any point within the world, position of sun, moon, earth, moon phase,
distance from the earth, position, declination, azimuth.

[raman22feb1988]

You may have a look at my latest prepared powerpoint presentation file on Astro Science.
Some points not included within the slides:
We have 8 planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune) and 3 dwarf planets (Ceres, Pluto, Eris) within our solar system, discovered so far, till now.
Ceres is the largest asteroid, and it was considered as a planet when it was being discovered; but due to the discovery of the other asteroids between the orbits of Mars and Jupiter, it lost its status as a planet. Today, it is considered as a dwarf planet.
Ceres is of magnitude 6.7 at opposition; Uranus 5.5 and Neptune 7.7; Pluto around 11.7. The largest magnitude star visible with the naked eye is 6. A magnitude difference of 1 makes a star fifth root of 100 times brighter. Note that with urban street lights, you cannot even easily see a star of magnitude 2 in the sky.
Betelguese is a red giant, whose radius will be comparable to the orbit of some asteroid between Mars and Jupiter. It is near the end of its life. Someday, it will end up in a supernova explosion. Only 200 light years away from the Earth, can that supernova explosion cause harm to the Earth's climate, atmosphere, etc.?

astronomy.zip

I have removed all the pictures that were there, from this file because of the 1 MB file size limit for the attachments. The original file size was 4 MB, and that the pictures were captured from different websites from the internet, mainly with the aid of Google Images, Wikipedia only.

Thus, the original astronomy.ppt file is always being available up so, at the following website link page:
http://balu.akila.googlepages.com/astronomy.ppt