TE Enriched Sample (E)

Kepler’s laws of planetary motion 63 3.1 1. Ceres is a dwarf planet in the solar system. Its orbital period is 4.6 years. Find the semi-major axis of its orbit. Applying T T a a E E 2 3 = d n c m , the semi-major axis can be found by a 3 = & a = 2. True or false: (a) Kepler’s third law relates the orbital periods of the planets to the semi-major axes of the orbits. (b) Kepler’s third law does not apply to circular orbits. (c) Kepler’s third law is valid only when the time is expressed in years. Checkpoint 2 3. The graph that relates orbital period T to semi-major axis a is shown. 1 a 3 / AU 3 T 2 / y 2 1 Earth True or false: (a) The data for the Moon lie on the same straight line. (b) The straight line passes through the origin. (c) Data for more massive planets are on the right of the Earth on the graph. Exercise 1. The dwarf planet Pluto has an orbit of semi-major axis 39.5 AU. What is its orbital period? A. 39.5 3/2 y B. 39.5 2/3 y C. 39.5 −3/2 y D. 39.5 −2/3 y 2. The orbital period of the Earth is one year and its orbital semi-major axis is 1 AU. Which of the following may represent the orbital period T and the semi-major axis a of an imaginary planet which orbits the Sun? T a A. 2.83 y 2 AU B. 2.83 y 4 AU C. 4 y 2 AU D. 4 y 4 AU 3. Two planets, X and Y , move in nearly circular orbits around a star. Y is twice as far away from the star as X . (a) A student claims that the orbital period of Y is twice that of X . Explain why he is incorrect. (b) Find the ratio of the orbital period of X to that of Y . 4. The orbit of Mars is quite elliptical. Its perihelion and aphelion distances from the Sun are 1.38 AU and 1.67 AU, respectively. 1.67 AU 1.38 AU Sun Mars (a) Find the semi-major axis of its orbit. (b) Find its orbital period in years. 5. Comet Encke is a short-period comet. Its closest distance to the Sun is 0.33 AU and its orbital period is 3.3 years. (a) Find the semi-major axis of the orbit of Comet Encke. (b) Find the aphelion distance of Comet Encke. (c) Jupiter orbits the Sun with a semi-major axis of 5.2 AU. (i) Does the orbit of Comet Encke lie inside that of Jupiter? Why? (ii) Do you think that the orbital period of Jupiter is longer than that of Comet Encke? Why? F F T 2.77 AU T 2 = 4.6 2 T T F 1 : 0.354 A A yes yes 4.10 AU 2.22 AU 1.88 y 1.53 AU (3.1) 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.