Physics 197 Lecture 26: Planetary Motion

• School: WUSTL
• Department: Physics
• Course: Physics 197
• Professor: Ferrar

Document Summary

An ellipse"s eccentricity is de ned to be c/a, where 2c is the distance between the two foci. When > 0, the ellipse becomes a circle. When > 1, the ellipse becomes very long and thin. The vertices are the points where the ellipse crosses the axis connecting the foci. For a given focus, the distance to the closes vertex is rc = a(1- ), and the distance to the farthest vertex is rf = a( -1) Hyperbola: the curve comprised of all points p on a plane whose distances r1 and r2 to two given foci f1 and f2 have a difference that is a constant 2a. As r2 grows large, the hyperbola approaches two asymptotes that make the same angle = cos^-1(a/c) with respect to the axis connecting the foci, where 2c is the distance between the two foci. We de ne a hyperbola"s eccentricity to be = c/a: > 1 in the case of a hyperbola.