ch13-p004 - 4. The gravitational force between you and the...

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(a) The ratio of the moon’s gravitational pulls at the two different positions is 2 2 2 86 1 28 6 0 /( ) 3.82 10 m 6.37 10 m 1.06898. /( ) mM E E ME E E E M E E GM m R R FR R FG M m R R R R §· + × == = = ¨¸ +− × × ©¹ Therefore, the increase is 0.06898, or approximately, 6.9%. (b) The change of the gravitational pull may be approximated as 10 22 2 2 3 4 12 . () mm m m m E EE ME E ME E ME ME ME ME ME GM m GM m GM m GM m GM mR RR FF R R R R R −= + = −+ On the other hand, your weight, as measured on a scale on Earth is 2 E gE E GM m Fm g R . Since the moon pulls you “up,” the percentage decrease of weight is 3 3 22 6 75 24 8 7.36 10 kg 6.37 10 m 4 4 2.27 10 (2.3 10 )%. 5.98 10 kg 3.82 10 m m E M E M R FM R −− § · ×× = × × ¨ ¸ © ¹ 4. The gravitational force between you and the moon at its initial position (directly
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