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Future research on navigation: pilotage is the navigation by the use of manmade landmarks like buoys
and lighthouses. Waypoint navigation: is navigation by the use of machines like radars and satellites.
Pilotage involves map making and plotting out set land markers so that navigators can calculate their
position off of their surroundings. Waypoint uses satellites other electronic devices like radars to
automatically determine the navigators location and their relative distance from other features.
http://academickids.com/encyclopedia/index.php/Navigation is
In the sixteenth century, most people believed in the ideas of the ancient astronomer Ptolemy,
that the planets, Moon, and Sun all orbited around the Earth. Then in 1543, Nicolaus Copernicus
proposed the idea that the planets and the Earth orbited around the Sun. However, Copernicus'
new theory was no better at predicting the positions of the planets in the sky than the olderEarthcentered theory. There was still something missing.....
Half a century later, Johannes Kepler sought to refine the Copernican system and truly
understand how the planets move around the Sun. He studied observations of Mars recorded by
his mentor, Tycho Brahe. Rather than trying to force the data to support a pre-determined view
of the Universe, Kepler used Tycho's observations to guide the creation of his theories. This was
a radical departure from the thought processes of his era, and it is a signal of the beginning of our
modern scientific age.
In 1609, Kepler published his first and second laws of planetary motion, The Law of Ellipses and
The Equal-Areas Law. Ten years later he published a third law, The Harmonic Law. He had
succeeded in using a scientific method to create a simple, elegant, and accurate model to
describe the motion of planets around the Sun,
Previous theories of the Solar System, including those of Ptolemy and Copernicus, believed that
the orbits of the planets were perfect circles. Kepler was unable, however, to fit Tycho's
observations with circular orbits. He rejected the ancient idea of circular orbits had discovered
that:
The orbits of the planets are ellipses with the Sun at one of the foci.
This is now called Kepler's First Law or The Law of Ellipses.
What is an ellipse? Glad you asked. An ellipse is a closed, curved shape that is defined by two
foci. An ellipse is a like a flattened circle. In fact, if both of the foci of an ellipse are at the same
point, an ellipse becomes a circle! If you think about it, the relationship between an ellipse and a
circle is similar to the relationship between a rectangle and a square.
An ellipse has two axes. The long one is called the major axis, and the short one is called the
minor axis. Astronomers will often use the term "semimajor axis". That's just half the length of
the major axis!
The shape of an ellipse is measured by its eccentricity. The "flatter" the ellipse, the greate the
eccentricity. A circle, for example, has an eccentricity of zero since both foci are at the center.
As the ellipse becomes flatter and flatter, the foci get farther from the center, and the eccentricity
will approach, but never equal, one.
Now, you can experiment with elliptical orbits with the Ellipse-O-Tron below. Try entering
various values for the eccentricity. Look at the shape of the orbit. Watch how the distance from
the planet to the Sun changes.
In addition to determining that the orbits of the planets around the Sun were ellipses, Kepler also
noticed that their speeds varied throughout their journies Kepler noted that the planets seemed to
move fastest when they were at their closest point to the Sun (called perihelion) and slowest
when they were at their farthest point from the Sun (called aphelion). Using some rather brilliant
insights of geometry, Kepler discovered that:
The line that connects the planet to the Sun sweeps out equal areas in equal times.
This is now known as Kepler's Second Law or The Equal Areas Law.
The motion this law describes also tells us that the average distance from a planet to the Sun is
equal to the length of the semimajor axis. That's why astronomers love the term so much!
You can watch this law in effect with the Orbit-Area-O-Tron 2000. Simply enter in an
eccentricity and watch as three areas are swept out from the orbit. Where is the planet moving
fastest, when it is close to the Sun or far from the Sun? When is it moving slowest?
After determining his first two Laws of Planetary Motion, Kepler continued to study the orbits of
the planets. Ten years later, he discovered a relation between the time of a planet's orbit nad its
distance from the Sun:
The squares of the orbital periods of the planets around the Sun are proportional to the
cubes of the orbital semimajor axes.
What does this mean? This means that if you know either how much time a planet's orbit around
the Sun takes you can easily know it's average distance from the Sun, or vice-versa! Now you
will often see Kepler's Third Law written like this:
P2=a3
Where P is the orbital period in Earth years and a is the length of the semimajor axis (average
distance from the Sun) in Astronomical Units.
Now, you can try out Kepler's Third Law using the Kepler-Calc-O-Tron 2000. Just type in either
the orbital period or the average distance from the Sun, press the appropriate button, and
*presto* you'll have your answer! Try looking up the values for some of the planets in your
textbook and try them out!
http://projects.astro.illinois.edu/data/KeplersLaws/
The practice of navigating by the stars is as old as antiquity. In the modern age, light pollution has
reduced the night sky to only a few constellations. Fortunately, when hiking in the wilderness, we often
find ourselves miles from any electric light source. Here we can appreciate the innumerable stars, watch
the movements of the planets, and navigate by the constellations. A rudimentary knowledge of the stars
can help you find your way, even in places like New York City
Read more at Trails.com: How to Navigate by the Stars | Trails.com
http://www.trails.com/how_925_navigate-stars.html#ixzz1MbweVLnb
The Drake equation states that:
where:
N = the number of civilizations in our galaxy with which communication might be possible;
and
R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fℓ = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their
existence into space
L = the length of time for which such civilizations release detectable signals into space.[3]
[edit] Alternative expression
The number of stars in the galaxy now, N*, is related to the star formation rate R* by
where Tg = the age of the galaxy. Assuming for simplicity that R* is constant, then
and the Drake equation can be rewritten into an alternate form phrased in terms
of the more easily observable value, N*.[4]
[edit] http://en.wikipedia.org/wiki/Drake_equationR factor
mber of civilizations should bArticle:
Navigating by the Stars
by Joe Rao, SPACE.com Skywatching Columnist
Date: 19 September 2008 Time: 07:00 AM ET
This classic star trail image shows how stars move in our sky as Earth rotates. More than 150
individual one-minute digital images were stacked in Photoshop. A first-quarter moon
illuminated the surrounding landscape for the duration of the exposures.
CREDIT: Peter Michaud, Gemini Observatory
View full size image
Astronomy is the oldest of the sciences, and quite possibly the oldest use of astronomy is navigating by
the stars. This craft dates from prehistoric times among humans, and is even practiced by certain
animals.
For example, during the 1960s, a study undertaken by New York's Cornell Lab of Ornithology
demonstrated through use of planetarium simulations that the indigo bunting, a brilliantly blue bird of old
fields and roadsides, migrates at night using the stars for guidance. It learns its orientation to the night sky
from its experience as a young bird observing the stars.
Some primitive tribes accomplished amazing feats of pathfinding using only the sky as their guide. The
Māori came to New Zealand from eastern Polynesia, probably in several waves between the years 1280
to 1300. With no instruments or tables to consult, they very carefully observed the night sky as well local
weather patterns and ocean currents.
e prhttp://www.space.com/5849-navigating-stars.htmloportional to the star formation rate,
though this makes technical sense. (The product of all the terms except L tells how many new
communicating civilizations are born each year. Then you multiply by the lifetime to get the
expected number. For example, if an average of 0.01 new civilizations are born each year, and
they each last 500 years on the average, then on the average 5 will exist at any time.) The
original Drake Equation can be extended to a more realistic model, where the equation uses not
the number of stars that are forming now, but those that were forming several billion years ago.
The alternate formulation, in terms of the number of stars in the galaxy, is easier to explain and
understand, but implicitly assumes the star formation rate is constant over the life of the galaxy.