TE Enriched Sample (E)

Kepler’s laws of planetary motion 59 3.1 B Kepler’s second law: Equal area in equal time Kepler’s second law states that ( MC: DSE 2012 Q1.5, 2016 Q1.4, 2022 Q1.4) Sun planet Y 1 X 1 Y 2 X 2 Fig. 3.7 Kepler’s second law Checkpoint 1 1. True or false: (a) Kepler’s first law states that the Sun is at the centre of the elliptical orbit of a planet. (b) Kepler’s second law states that the radius vector of a planet sweeps out equal areas in equal time intervals. (c) According to Kepler’s second law, a planet moves faster when it is nearer the Sun and slower when it is farther away. 2. A planet orbits around the Sun as shown. The major axis of the elliptical orbit is 3.05 AU long. The focus is 0.145 AU from the centre of the orbit. (a) Label the perihelion and the aphelion on the figure. (b) Calculate the perihelion distance and the aphelion distance. planet Sun (c) At which point, perihelion or aphelion, does the planet travel the fastest? 3. The figure below shows the area swept out by the radius vector of a planet in six time intervals. All the areas shown are equal. X Z Y X ′ Y ′ Z ′ Sun True or false: (a) The orbital period of the planet is six times the time taken for it to travel from X to X ′. (b) The planet takes equal time to travel from X to X ′ and from X ′ to Y . (c) The planet has the highest average speed when it travels from Z to Z ′ among the six intervals shown. Fig. 3.7 shows the motion of a planet in two equal time intervals. The planet takes time t to move from X 1 to X 2 , and the same time t to move from Y 1 to Y 2 . According to Kepler’s second law, the areas swept out by its radius vector (shaded areas) are equal. The speed of a planet is related to its distance from the Sun. In Fig. 3.7, the planet moves faster when it is closer to the Sun, and slower when it is farther from the Sun. Both the distance and speed of the planet change in an elliptical orbit. An imaginary line, called the radius vector, joining the Sun and the planet sweeps out equal areas in equal time intervals. Teaching notes Remind Ss that, in an elliptical orbit, (a) the speed of the plant is not constant, and (b) in general, the instantaneous velocity of the planet is not perpendicular to the Sun's gravitational force. (See DSE 2012 Q1.5, 2016 Q1.4) perihelion aphelion perihelion: 1.38 AU aphelion: 1.67 AU T T F F T T perihelion Teaching notes Remind Ss that, for equal time intervals, the planet's successive positions are widely spaced if it moves fast, and closely spaced if slow. (See Checkpoint 1 Q3 and DSE 2016 Q1.4) Teaching notes Angular momentum of orbital motion is not required in 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.