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# Math in the News: Issue 84

## on Nov 19, 2013

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## Math in the News: Issue 84Presentation Transcript

• Math in the News Issue 84 Comet ISON Approaches In this issue we look at the approaching ISON Comet.
• Comet ISON • 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.
• Scenario 1 • ISON emerges from the sun’s orbit intact (diminished in size) and continues on its journey.
• Scenario 2 • ISON doesn’t survive its encounter with the sun and is vaporized entirely.
• Scenario 3 • ISON fragments and emerges from the sun’s orbit as a scattered collection of small comet fragments.
• Sketching the Path • Let’s assume Scenario 1 and look at the trajectory that the comet might take.
• A Parabolic Path • 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 • At any point on the parabola the distance to the focus is congruent to the vertical distance to the directrix.
• A Parabolic Path • 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 • The perihelion distance can be used to find the equation of the parabola in vertex form.
• A Parabolic Path y = a(x − h) + k 2 • This is the vertex form of the equation for a parabola, where (h, k) define the coordinates of the vertex.
• A Parabolic Path y = ax 2 • If you assume the vertex of the parabola is at the origin, the equation is simplified.
• A Parabolic Path 1 a= 4f • To solve for a, use this equation, where f is the focal distance, or in this case the perihelion distance.
• A Parabolic Path 1 a= 4f • 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 1 AU f = 93,000,000 miles 730,000 miles f ≈ 0.0079 AU 1 a= 4f 1 = 4 • 0.0079 ≈ 31.65 • 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 y = 31.65x 2 • This is the equation of the parabola, and it is scaled for Astronomical Units.
• A Parabolic Path y = 31.65x 2 • 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 y = 31.65x 2 • 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!