TE Enriched Sample (E)

64 In Force and Motion , we learnt that Newton discovered the law of universal gravitation . Accordingly, an object attracts another object by the force of gravity. For two point masses or two spherical mass distributions (e.g. the Sun and planets), the gravitational force between them is F G r m m 2 1 2 = Orbital motion under gravity 3.2 Fig. 3.10 Attraction between two spherical mass distributions F F r m 2 m 1 Note that the force is proportional to the masses m 1 and m 2 , and inversely proportional to the square of the separation r . The constant G = 6.67 × 10 −11 N m 2 kg −2 is the universal gravitational constant, which connects mass to gravity. Newton’s law of universal gravitation tells us about the gravitational force between the celestial bodies, while Newton’s second law of motion tells us how the bodies move under the force. In principle , we can combine the two laws to calculate the motion of any celestial body moving under gravity very accurately. Although Newton’s laws allow us to calculate any motion under gravity in principle, practical calculations for more than two bodies interacting by gravity (e.g. Sun, Moon and Earth) could be very complicated and require the use of a modern computer. Enrichment Empirical laws versus physical laws Both Kepler’s laws and Newton’s laws can describe the motion of celestial bodies. What are their differences? Kepler discovered the three laws of planetary motion based on Tycho’s observation data. The laws describe how the planets move based on the observation data gathered in the past, but do not explain why they move in this way. Such laws are called empirical laws . In contrast, Newton’s law of universal gravitation and his second law of motion explain why the planets move based on physics concepts, including the force of gravity and acceleration. Such laws are called physical laws . Physical laws are universal, i.e. they do not apply only to planets, but to any objects in the universe, such as an apple, a spacecraft, a planet, a star, or a galaxy. In fact, Kepler’s laws of planetary motion can be derived mathematically from Newton’s laws, and they are just an application of Newton’s laws to a specific situation. law of universal gravitation 萬有引力定律 Teaching notes ‘Uniform circular motion’ and ‘Gravitation’ are introduced in the compulsory part: ‘Force and Motion’. Teaching notes Solving problems involving the motions of planets, moons and satellites is required in the HKDSE. 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.