math in the news: issue 84

Math in the NewsIssue 84

Comet ISON Approaches

In this issue we look at the approaching ISON Comet.

Learn more about Comet ISON from this video.

http://youtu.be/A1yH_DuC88M

• 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

• ISON emerges from the sun’s orbit intact (diminished in size) and continues on its journey.

Scenario 1

• ISON doesn’t survive its encounter with the sun and is vaporized entirely.

Scenario 2

• ISON fragments and emerges from the sun’s orbit as a scattered collection of small comet fragments.

Scenario 3

• Let’s assume Scenario 1 and look at the trajectory that the comet might take.

Sketching the 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

• This is the vertex form of the equation for a parabola, where (h, k) define the coordinates of the vertex.

A Parabolic Path

• If you assume the vertex of the parabola is at the origin, the equation is simplified.

A Parabolic Path

• To solve for a, use this equation, where f is the focal distance, or in this case the perihelion distance.

A Parabolic Path

• 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

• 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

• This is the equation of the parabola, and it is scaled for Astronomical Units.

A Parabolic Path

• 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

• 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