The gravitational force at different places on Earth due

Chapter 6, Problem 6.75

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The gravitational force at different places on Earth due tothe Sun and the Moon depends on each points distancefrom the Sun or Moon, and this variation is what causes thetides. Use the values inside the front cover of this book forthe Earth-Moon distance REM, the Earth-Sun distance RES,the Moons mass Mm , the Suns mass, Ms , and the Earthsradius RE. (a) First consider two small pieces of the Earth,each of mass ra, one on the side of the Earth nearest the Moon,the other on the side farthest from the Moon. Show that theratio of the Moons gravitational forces on these two masses isfiiear \Ffar J= 1.0687.M(b) Next consider two small pieces of the Earth, each ofmass ra, one on the nearest point of Earth to the Sun, theother at the farthest point from the Sun. Show thatthe ratio of the Suns gravitational forces on these twomasses is= 1.000171.Ft:ar /S(c) Show that the ratio of the Suns average gravitationalforce on the Earth compared to that of the Moons is9-^M)/ avg = mNote that the Moons smaller force varies much moreacross the Earths diameter than the Suns larger force.(d) Estimate the resulting force difference (the cause ofthe tides)AF FneaT FfaT Ffs ( Fnear _rV Ffar J F fa r- 1for the Moon and for the Sun. Show that the ratio of thetide-causing force differences due to the Moon compared tothe Sun isA F,MA Fe2.3.Thus the Moons influence on tide production is over twotimes as great as the Suns.

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