I have a friend in high school AP Algebra 2 and he needs to write a report on Circular Conic Sections. He has to use the internet as a reference. He is particulary interested in their use in Aerospace and Physics and how that may apply. Can anyone point us to an online reference that may describe how they are used in this context?

Yes we are using google, but he would like a selectionj of references to choose from.

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Eagle Eye Observatory

one word.

Orbits. All orbits are conical sections.

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Apollo: The History and the Hoax
Enter the World of Athran

yea, but his report is specifically on circles, Orbits are elipses, no?

So far he has tagged some info on particle accelerators, Circular vs Linear, so that should clear up the Physics section, still looking for some info on aerospace

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They can be circular, elliptical, parabolic, or hyperbolic. In practice, you aren't likely to find an orbit that is truly circular, but some come very close. For an assignment, don't overthink the problem.

By the way, why is this in ATM?

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The Leif Ericson Cruiser

A lot of orbits are very close to circles. Even the orbit of the Earth, which is 5 million km closer to the sun in January than in July, is very close to a circle--it deviates from a circle by only 10 thousand kilometers, less than the diameter of the earth.

Moved, from the ATM section, to the Q&A one.

I don't want to divert you from the purpose of the thread, but
what is the difference between a "circular conic section" and a
plain old "circle"? As a guess, were different students assigned
different conic sections to study, and he got circles?

-- Jeff, in Minneapolis

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"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Earth's orbit is a very close approximation of a circle, but it is
essentially an ellipse, and doesn't need to be circular.
Things which rotate often need to be circular. If they aren't
circular they don't work well. Turbines, pistons in cylinders,
pumps, wheels and axles, flywheels, gyroscopes, motors and
generators, transmission shafts, and the like generally need
to have circular cross-sections in order to function.

Spheres and ellipsoids (which have circular cross-sections)
are efficient containers. For example, fuel tanks and eggs.
Cylinders are also useful as containers. Have your friend
look in his kitchen cupboards and refrigerator. Screw tops
depend on circular cross-sections.

When I look around the room, I see lots and lots of things
with circular cross-section. Somewhat annoyingly, they are
all manmade. I think I'd have to look outside at the Sun or
Moon to see something naturally circular. (The Sun is out.
It looks round, but it's hard to tell for sure, it's so bright.)

-- Jeff, in Minneapolis

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http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

Go to google and type in:

conic section circles

You'll get a list of websites about this.

http://mathworld.wolfram.com/ConicSection.html

http://www.algebralab.org/lessons/le...ics_circle.xml

http://xahlee.org/SpecialPlaneCurves...cSections.html

http://math2.org/math/algebra/conics.htm

http://mathforum.org/library/drmath/...d_circles.html

http://mathforum.org/dr.math/faq/for...aq.circle.html

http://math.about.com/library/blconic.htm

http://en.wikipedia.org/wiki/Conic_section

Sam5's mathworld and wikipedia links are ones that I would recommend off the bat (even though they can discuss higher levels of math). I would also suggest this page for circles in physics/astronomy: http://en.wikipedia.org/wiki/List_of_circle_topics. It has links to a decent number of use of circles in physics.

The Honda NR500 racing motorcycle had oval pistons! They wanted to use a V8, but the rules only allowed a maximum of four cylinders, so they used oval pistons with two connecting rods and eight valves per cylinder. Very complex, very expensive, very high revving (20,000+ rpm), but not very successful!

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T. Anderson

yea, but his report is specifically on circles, Orbits are elipses, no?

Circles are elipses, they are just a special case were both foci are at the same position within the elipse, just as a square is a special case of rectangle where all sides are equal.

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It must be fun to lead a life completely unburdened by reality. --- JayUtah

You can't reason an irrational person out of an irrational belief. --- Noclevername

Apollo: The History and the Hoax
Enter the World of Athran

Thats exactly right. His paper is specifically on perfect circles.

One thing he wound up using is that a circle is a shape that encompases the largest are with the least amount of perimiter (circumference). Regarding natural shapes, bubbles naturally take on sperical shapes because it holds the most inner area with the least surface area of the membrane.

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