Subject Code : AE313
Assignment Task:

Task:

Problem 1 (15 pts)
Briefly answer the following questions.

a) (2 pts.) Consider an elliptical orbit: at what point(s) are the velocity vector and the radius vector perpendicular to each other?

b) (2 pts.) For a spacecraft orbiting a gravitational source with gravitational parameter μ in a circular orbit of radius r, what is the ratio of the escape velocity to the spacecraft’s circular orbit velocity?

c) (2 pts.) Consider an elliptical orbit: what is the range of values of true anomaly where r? ⋅ v? < 0?

d) (2 pts.) In words, briefly explain the utility of using the Lagrange coefficients f, g, ? , ?

e) (3 pts.) What are the six Classical Orbital Elements (COEs)? Which ones are constant?

f) (2 pts.) Between Kepler’s Time Equation, Barker’s Equation, and Hyperbolic Kepler’s Time Equation, which one has an analytic solution for the angular variable as a function of time?

g) (2 pts.) In deriving Kepler’s Time Equation, there is an expression for one of the constants of orbital motion that allows us to relate true anomaly to time. What is such expression? (We used it many times during lectures)

 

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  • Uploaded By : Pearl
  • Posted on : October 29th, 2018

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