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MIT16_07F09_hw08

# MIT16_07F09_hw08 - NAME Massachusetts Institute of...

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NAME : . . . . . . . . . . . . . . . . . . . . . Massachusetts Institute of Technology 16.07 Dynamics Problem Set 8 Out date: Oct 24, 2007 Due date: Oct 31, 2007 Time Spent [minutes] Problem 1 Problem 2 Problem 3 Problem 4 Study Time Turn in each problem on separate sheets so that grading can be done in parallel

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Problem 1 (10 points) A. Determine the locations of the Lagrange points for both the earth-sun system and the earth-moon system relative to the earth. Give dimensions in km. Sketch the relative positions at some instant of time, and show as well the position of Mars. B. Describe 2 space missions that have, will or could use the Lagrange points as key destinations. Describe the mission, and what role the Lagrange point played. If you get stuck, consider the James Webb telescope. There is also the possibility of a mission to the earth-sun L 3 point to look for the alien base. Why might they locate there? Wikipedia will be a big help.
Problem 2 (10 points) 2-1) A spacecraft returns from the moon on the trajectory shown. We wish to place the spacecraft in a circular parking orbit at a radius R o = 3 × R e , where R e is the radius of the earth. Then at a later time, we wish to return the spacecraft to an elliptical orbit that includes a point B on the earth, ignoring the rotation of the earth and atmospheric drag. At the final step, we wish to bring the velocity of the spacecraft to zero and land on a non-rotating earth. The final steps–ignoring the rotation of the earth and atmospheric drag– are quite unrealistic but give a ballpark understanding. This time, do the numbers. The radius of the earth is R e = 6 . 37 × 10 6 ; the mass of the earth is M earth = 5 . 97 × 10 24 ; the universal gravitational constant is G = 6 . 67 × 10 11 . Take c = 4500 m/sec in the rocket equation. 2-1a) The incoming spacecraft trajectory intersects the parking orbit at an angle of 30 degrees with an incoming velocity V i equal in magnitude to the velocity V e required to escape the earth’s gravitational field from a circular orbit radius R o = 3 R e . (hint: What is the velocity required to escape from an orbit of R o = 3 R e ?) What velocity V o will the spacecraft have in the orbit at R o = 3 R e ?. What is the Δ V required change from the initial return trajectory V i to the parking orbit V o ?

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MIT16_07F09_hw08 - NAME Massachusetts Institute of...

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