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Pupil
Karma Points: 50
Respect (86%):
Date Posted: 7/23/2008 3:33:07 PM  Status: Live
please help me
Course Textbook Chapter Problem
N/A N/A N/A N/A
Question Details:
At a certain instant, the earth, the moon, and a stationary 1350 {\rm kg} spacecraft lie at the vertices of an equilateral triangle whose sides are 3.84 \times 10^{5}\:{\rm km} in length.
 
the magnitude of the net gravitational force exerted on the spacecraft by the earth and moon.
  F  =
  {\rm N}
 
Find the direction of the net gravitational force exerted on the spacecraft by the earth and moon. State the direction as an angle measured from a line connecting the earth and the spacecraft.
  ^\circ
What is the minimum amount of work that you would have to do to move the spacecraft to a point far from the earth and moon? You can ignore any gravitational effects due to the other planets or the sun.
  W  =
  {\rm J}
 
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Answers:

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Sage
Karma Points: 5,630
Date Posted: 7/24/2008 6:22:49 AM  Status: Live
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Response:
The force exerted by the earth on the stationary spacecraft is
F1 = (GMeMs/r2)
Here,G = 6.67 * 10-11Nm2/kg2,Me is the mass of the earth, Ms is the mass of the spacecraft and is equal to 1350 kg and r = 3.84 * 105km = 3.84 * 108 m.
The force exerted by the moon on the stationary spacecraft is
F2 = (GMmMs/r2)
Here,Mm is the mass of the moon.
The magnitude of the net gravitational force exerted on the spacecraft by the earth and moon is
Fnet = F1 + F2
The direction of the net gravitational force exerted on the spacecraft by the earth and moon is towards the earth.The spacecraft is attracted towards the earth at an angle of 45o.
The minimum amount of work to move the spacecraft to a point far from the earth and moon is
W = Fnet * r,where r is the length of the vertice of the equilateral triangle.
 



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