
DYNAMICS  CASE STUDY



Introduction

Problem Diagram


After docking with the Soyuz, the Apollo must reenter the earth's atmosphere from perigee (the closest point of the orbital path to the earth). If the Apollo is traveling too fast, it will burn up during reentry.
What is known:
 The mass of the Apollo is m_{A} = 18.0 Mg.
 At apogee (the furthest point of the orbital path from the earth), the speed of the Apollo is v_{A} = 4,373 m/s.
 At apogee, the Apollo's distance from the center of the earth is r_{A} = 16,000 km.
 The radius of the earth is R_{E} = 6,370 km.




Question


At perigee, what is the Apollo's angular momentum, distance from the center of the earth, and speed?





Approach



 Use the equations of angular momentum to determine the angular momentum at apogee, then at perigee.
 Use equations involving the distance from the center of the earth and the transverse velocity (derived from angular momentum) to find the velocity at perigee.




