TE Enriched Sample (E)

Summary Key Ideas Kepler’s laws of planetary motion Orbital motion under gravity • Kepler’s third law can be derived from Newton’s law of gravitation . a. For a circular orbit b. For an elliptical orbit, T GM a 4 2 2 3 r = & Gravitational force acting on a planet provides the centripetal force for the circular motion G r Mm r mv T GM r 4 2 2 2 2 3 r = = Ñ v GMm r r 2 planet (mass m ) Sun (mass M ) circular orbit F = elliptical orbit v a planet Sun (mass M ) Orbital Motions under Gravity 3 88 Sun Y X planet Y' X’ 0 0.1 1 10 100 1000 10 000 100 000 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune 100 000 10 000 1000 100 10 1 0.1 T 2 / y 2 a 3 / AU 3 Sun Mercury Venus Earth Mars 1. All planets move in elliptical orbits , with the Sun at one focus. 2. An imaginary line joining the Sun and the planet sweeps out equal areas in equal time intervals. 3. For any planet, the square of its orbital period T is proportional to the cube of the semi-major axis a of its orbit, i.e. T 2 Ä a 3 . DSE Level-up Companion A revision exercise is provided for helping Ss to grip the key points. See Level-up Task 63A . 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.