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### BedSt1_30

Course: MAE 212, Fall 2008
School: ASU
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Word Count: 246

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1.30 Problem At a point between the earth and the moon, the magnitude of the force exerted on an object by the earth's gravity equals the magnitude of the force exerted on the object by the moon's gravity. What is the distance from the center of the earth to that point to three significant digits? The distance from the center of the earth to the center of the moon is 383,000 km, and the radius of the earth is 6370...

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1.30 Problem At a point between the earth and the moon, the magnitude of the force exerted on an object by the earth's gravity equals the magnitude of the force exerted on the object by the moon's gravity. What is the distance from the center of the earth to that point to three significant digits? The distance from the center of the earth to the center of the moon is 383,000 km, and the radius of the earth is 6370 km. The radius of the moon is 1738 km, and the acceleration due to gravity at its surface is 1.62 m/s2 . Solution: Let rEp be the distance from the Earth to the point where the gravitational accelerations are the same and let rMp be the distance from the Moon to that point. Then, C rEp rMp D rEM D 383,000 km. The fact that the gravitational attractions by the Earth and the Moon at this point are equal leads to the equation RE rEp 2 gE D gM RM rMp 2 , where rEM D 383,000 km. Substituting the correct numerical values leads to the equation m s2 6370 km rEp 2 9.81 D 1.62 m s2 1738 km rEM rEp 2 , where rEp is the only unknown. Solving, we get rEp D 344,770 km D 345,000 km. c 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 1
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