Orbits and Eccentricity More with Ellipses in Sec

Orbits and Eccentricity More with Ellipses in Sec. 8. 2 b

Orbits and Eccentricity Many moons ago, it was discovered that many celestial bodies (for example, those orbiting the sun) followed elliptical paths… Perihelion – point closest to the sun in such an orbit Aphelion – point farthest from the sun in such an orbit The shape of an ellipse (including these orbital paths) is related to its eccentricity…

Orbits and Eccentricity a–c a+c Sun at focus Orbiting Object Center Semimajor Axis

Definition: Eccentricity of an Ellipse The eccentricity of an ellipse is where a is the semimajor axis, b is the semiminor axis, and c is the distance from the center of the ellipse to either focus. What is the range of possible “e” values for an ellipse? What happens when “e” is zero? A CIRCLE!!!

Practice Problems The Earth’s orbit has a semimajor axis and an eccentricity of. Calculate and interpret b and c. Semiminor Axis The semiminor axis is only 0. 014% shorter than the semimajor axis…

Practice Problems The Earth’s orbit has a semimajor axis and an eccentricity of. Calculate and interpret b and c. Aphelion of Earth: Perihelion of Earth: The Earth’s orbit is nearly a perfect circle, but the eccentricity as a percentage is 1. 67%; this measures how far off-center the Sun is…

Other Types of Practice Problems Prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. Put into standard form:

Other Types of Practice Problems Prove that the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. Standard Form: Vertices: Foci: Eccentricity:

Other Types of Practice Problems Write an equation for the given ellipse. (– 4, 5) Center: C(– 4, 2) (0, 2) Standard Form: Semimajor, semiminor axes: