This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Physics 325 Lecture 10 Planetary Motion in a Central Force Field (cont.) Another consequence of the conservation of angular momentum is Keplers 2 nd law. Consider the area swept out by the radius vector in the time interval dt : The area swept out is 2 1 2 2 r d dA r rd (The picture is greatly exaggerated. The triangle on the right that is adjacent to the trajectory is infinitesimally small (base dr , height rd )). The rate at which the area is swept out is 2 2 1 1 2 2 2 dA d L r r dt dt (10.1) Since L is constant, the area is swept out at a constant rate (Equal areas in equal times). Returning to the equation for the radial velocity we derived in Lecture 9 (Equation 9.13), 2 ( ) eff dr r E U r dt we see that r equals zero, when eff E U . In the case of the inverse square central force, we solved for these turning points in Lecture 8. Generally speaking there are two such turning points, and we call them min r and max r (perigee and apogee, respectively, in Lecture 7). d r(t) r(t+dt) =r+dr rd d r(t) r(t+dt) =r+dr rd We can calculate the angular change in one complete cycle from min r through max r and back to min r : max min 2 2 r...
View
Full
Document
 Spring '08
 Staff
 mechanics, Angular Momentum, Force, Momentum

Click to edit the document details