Lesson 6:

Applications of Conics

By Carly Coffman

Comet & Planet Orbits

Of the 610 comets identified prior to 1970,

Ø     245 have elliptical orbits

Ø     295 have parabolic orbits

Ø     70 have hyperbolic orbits

(Algebra and Trigonometry,  Larson & Hostetler 2001)

As you will see in the following pictures, planets also have elliptical orbits.

One example of an elliptical orbit is the famous Halley’s Comet.

It takes a period of 76 years to complete it’s orbit.

A recent comet named “Linear” has a parabolic orbit.

1)    Why would the path of comets be of any interest to you and me?

 Planet Period (yr) Mercury 0.241 Venus 0.615 Earth 1 Mars 1.88 Jupiter 11.8 Saturn 29.5 Uranus 84 Neptune 165 Pluto 248

Here is a table for the period (length of time for a planet to complete one orbit around the sun) of each planet.  (The mathematics behind planetary orbit can be found at http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l4a.html)

Eccentricity

*You may work the problems on this application page on notebook paper.  Make sure that you show your work and that you write neatly.

The eccentricity determines the shape of the object path.  Here is a table for eccentricity values:

The eccentricity of a planet with an elliptical orbit is defined by e = c/a where e is the eccentricity, a is half of the minor axis, and c is found by c^2 = a^2 – b^2 (where b is the length of half of the minor axis and c is the distance from the center to each focus).

2)    The planet Pluto moves in an elliptical orbit with the sun at one of the foci.  The length of half of the major axis, a, is 3.666 x 10^9 miles and the eccentricity is 0.248.  Find the smallest distance and the greatest distance of Pluto from the center of the sun.  (Draw a diagram)

*From Algebra and Trigonometry , Larson & Hostetler, 2001