Aim: How do we calculate the eccentricity of an ellipse? Do Now: Are there perfect circles in nature?

Where do theses planets belong? Why? I am Planet Y Made of gas Feel really cold 1,430 million km from the sun I am Planet X Made of Rock Feel Super Hot 100 million km from the sun I am: Planet Z Made of Rock Feel Warm 230 million km from the sun 1 2 3

How do we define eccentricity? Eccentricity Many early astronomers believed that planets revolved around the sun in orbits that were thought to be shaped as circles. However, observations of the planets shows that their motions could be explained best if their orbits were not circles, but ellipses. The shape of an orbit is best described by its eccentricity or how elongated the ellipse is. The eccentricity of an orbit is a calculated value that describes the out-of-roundness of an ellipse or how elliptical (oval) it is from being a circle. Eccentricity – out-of-roundness of an ellipse Major axis – longest distance from one end of the ellipse to the other end. Goes through the foci ( 2 focus points) Sun Focus 2 Focus 1 Ellipse – orbit Distance between foci Major axis

How does the shape of each elliptical orbit differ? (a line) Least Eccentric As foci distance increases, the orbit becomes more elliptical Most Eccentric Eccentricity will always be a number between 0 and 1 (decimal) Can NEVER be greater than 1 When Eccentricity equals Zero = shape will be circular The closer the eccentricity is to 0, the least eccentric orbit  When Eccentricity equals One = shape will be a line The closer the eccentricity is to 1, the more eccentric orbit

Identify the planet that has the highest eccentricity Identify the planet that has the highest eccentricity? Lowest eccentricity? Mercury has the highest eccentricity = most elliptical orbit Venus has the lowest eccentricity = most circular orbit

How do we calculate the eccentricity of Planet X’s ellipse? Sun Foci distance = 7.7 cm Eccentricity = 7.7 X 11.2 Major axis = 11.2 cm Eccentricity = 0.6875… Round to the nearest thousandth Eccentricity = 0.688 How is the eccentricity of our planet’s ellipse compared to Neptune's (0.009)? Our planets ellipse is more eccentric than Neptune's orbit. Place an X where our planet will move the fastest on our ellipse. Why will our planet move the fastest when it is next to the sun? Greater gravitational attraction when the planet is closest to the sun

Eccentricity = 1.8 Eccentricity = 0.375 = 4.8 Calculate the Eccentricity of Planet Heckman Round to the nearest thousandth Foci distance = 1.8 cm Major axis = 4.8 cm Eccentricity = 1.8 Eccentricity = 0.375 = 4.8 How is the eccentricity of Planet Heckman compared to Mercury? Mercury is less eccentric than Planet Heckman

How does the shape of each elliptical orbit differ? (a line)

How do we calculate the eccentricity of Planet X’s ellipse? Sun Foci distance = Major axis = Round to the nearest thousandth How is the eccentricity of our planet’s ellipse compared to Neptune's (0.009)? Place an X where our planet will move the fastest on our ellipse. Why will our planet move the fastest when it is next to the sun?

Calculate the Eccentricity of Planet Heckman Round to the nearest thousandth Foci distance = Major axis = How is the eccentricity of Planet Heckman compared to Mercury?

Summary Activity- Exit Card

Extra Questions Earth’s eccentricity of orbit is 0.017 Base your answers to questions 1 through3 on the diagram below, which represents a model of Earth’s orbit. Earth is closest to the Sun at one point in its orbit (perhelion) and farthest from the Sun at another point in its orbit (aphelion). The Sun and point B represent the foci of this orbit. 1) Explain why Earth’s orbit is considered to be elliptical. Earth’s eccentricity of orbit is 0.017 2) Describe the change that takes place in the gravitational attraction between Earth and the Sun as Earth moves from perihelion to aphelion and back to perihelion during one year. The force of gravity decreases, then increases 3) Describe how the shape of Earth’s orbit would differ if the Sun and focus B were farther apart. The orbit would become more eccentric