TE Enriched Sample (E)

Orbital Motions under Gravity 3 Example 3.2 Halley’s Comet 62 Halley’s Comet orbits the Sun in an elliptical orbit. The perihelion and aphelion distances are 0.586 AU and 35.1 AU, respectively. Sun Halley’s Comet 35.1 AU 0.586 AU aphelion perihelion (a) Find the semi-major axis of the orbit in AU. (b) Find the orbital period of Halley’s Comet in years. Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) The semi-major axis a of the orbit is given by . . . a 17.8 AU 2 0 586 35 1 17 843 . = + = (b) The orbital period is T = a 3/2 = 17.843 3/2 ≈ 75.4 y . Snapshot Nature Comets Comets are small icy bodies that orbits the Sun. They move in elongated elliptical orbits. Short-period comets have periods less than 200 years. From the equation T 2 = a 3 , we know that their orbital semi-major axes are less than 200 2/3 ≈ 34 AU, which is just beyond the solar system. Long-period comets may have periods over 1000000 years, and orbits extending over 10000 AU! The small icy solid part of a comet is called the nucleus . When it comes close to the Sun, the icy materials vaporize, forming a giant gaseous cloud called a coma . Solar radiation ‘blows’ on the gas and creates a beautiful tail which extends in the opposite direction from the Sun. The gaseous coma and tail reflect sunlight and allow the comet to be seen from the Earth. Long-period comets move in very elongated orbits. This means that they may come very close to the Sun. The so-called sungrazing comets may approach the Sun to within a few thousand kilometres above the solar surface. Some of them do not survive under the intense radiation of the Sun. Comet ISON, for instance, disintegrated when it passed the perihelion in November 2013. Structure of a comet tail nucleus coma radiation from the Sun Disintegration of Comet ISON near the Sun Sun ISON Halley’s Comet ( 哈雷彗星 ) Teaching notes This example shows the direct application of T 2 = a 3 .Ts should remind Ss that this is because the orbital motion in this example is around the Sun and T is in year while a is in AU. Teaching notes At distances very far away from the Sun, the orbital speeds of comets are very low and therefore they take an extremely long time to revolve around the Sun (Kepler’s second law). Extra information An excellent introduction to comets can be found at the following NASA webpage: http://solarsystem.nasa.gov/ planets/comets 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.