Math in the News: Issue 84
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Transcript of Math in the News: Issue 84
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Math in the NewsIssue 84
Comet ISON Approaches
In this issue we look at the approaching ISON Comet.
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Learn more about Comet ISON from this video.
http://youtu.be/A1yH_DuC88M
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• As ISON approaches the sun, it will lose mass.
• As it emerges from around the sun, there are three possible outcomes for the comet’s trajectory.
Comet ISON
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• ISON emerges from the sun’s orbit intact (diminished in size) and continues on its journey.
Scenario 1
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• ISON doesn’t survive its encounter with the sun and is vaporized entirely.
Scenario 2
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• ISON fragments and emerges from the sun’s orbit as a scattered collection of small comet fragments.
Scenario 3
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• Let’s assume Scenario 1 and look at the trajectory that the comet might take.
Sketching the Path
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• The path of Comet ISON can be approximated with a parabola.
• A parabola is the locus of points equidistant from the focus and a segment perpendicular to the directrix.
A Parabolic Path
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• At any point on the parabola the distance to the focus is congruent to the vertical distance to the directrix.
A Parabolic Path
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• The path of the comet is approximated by the shape of the parabola, and the sun is at the focus of this parabola.
A Parabolic Path
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• The perihelion distance can be used to find the equation of the parabola in vertex form.
A Parabolic Path
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• This is the vertex form of the equation for a parabola, where (h, k) define the coordinates of the vertex.
A Parabolic Path
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• If you assume the vertex of the parabola is at the origin, the equation is simplified.
A Parabolic Path
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• To solve for a, use this equation, where f is the focal distance, or in this case the perihelion distance.
A Parabolic Path
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• NASA estimates Comet ISON will come within 730,000 miles from the sun. Let’s express this distance in Astronomical Units (AU). (1 AU is the distance from Earth to the sun.)
A Parabolic Path
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• NASA estimates Comet ISON will come within 730,000 miles from the sun. Let’s express this distance in Astronomical Units (AU).
A Parabolic Path
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• This is the equation of the parabola, and it is scaled for Astronomical Units.
A Parabolic Path
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• The graph of the parabola shows where it intersects the Earth’s orbit (y = 1 AU) as it leaves the sun’s orbit.
A Parabolic Path
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• NASA estimates that Comet ISON may come as close as 0.5 AU to Earth on its way away from the sun. Assuming it does, it should be a dramatic event in the night sky!
A Parabolic Path