TE Enriched Sample (E)

Energy in orbital motion • Gravitational PE for two point masses U r GMm =- r U / J r / m 0 mass M mass m r 1 U ? − Note: 1. U always takes a negative value. & m and M are always attractive. & Work has to be done to pull them apart. 2. U is larger (less negative) when the separation between m and M becomes larger. 3. When m and M are infinitely far away from each other, U becomes zero. • Conservation of mechanical energy: Without external force, the sum of kinetic energy (KE) and gravitational PE is conserved. a. For an elliptical orbit, mv r GMm mv r GMm 2 1 2 1 1 2 1 2 2 2 - = - r 2 r 1 spacecraft (mass m ) v 2 v 1 Earth (mass M ) GMm PE = − KE = mv 1 2 KE = mv 2 2 1 2 1 2 r 2 GMm PE = − r 1 position 2 position 1 b. For a circular orbit, total mechanical energy E m r GM r GMm r GMm U 2 1 2 2 = - =- = c m Earth r v mass m mass M • Escape speed: initial speed required to escape from the gravity due to a celestial body Earth’s surface cannon infinity mu 2 1 2 − R GMm E = mv 2 1 2 E = & Object reaches a point far away from the body & r tends to infinity; final PE is zero ` E mu R GMm mv u R GM 2 1 2 1 0 2 esc 2 2 $ = - = = & Depends on mass M and radius R of the celestial body Summary 89 Sample © United Prime Educational Publishing (HK) Limited, Pearson Education Asia Limited 2023 All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publishers.