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The output argument of the program, orbit, must be a matrix of the format t 0 E 0 u 0 r 0 x 0 y
The output argument of the program, orbit, must be a matrix of the format
t E
u r x y
t E
u r x y
tn En
u n rn xn yn
where ti iT n Ei is the solution to Kepler Equation,
u i is the true anomaly corresponding to ti ri is the
distance between the satellite and the earth at ti and xi yi are the cartesian coordinates.
Each function must be in a different m file, with the same name as the function.
Summary
You are required to submit to Project in Canvas the following files:
The source files bismnwtmbisnwtmtanomm described above
A pdf file with a brief report of the project. The report should include the following sections:
Implementation:
Describe the tests that you have done to validate your code, what you have discovered, the problems
encountered, and their respective solutions. You must include at least the following test
T e n
and tolerances tolbe tolne in bisnwtm
Derive a formula for x in terms of E and then decide the value for toln if we want the error in the
xcoordinates of the orbit to be smaller than
Intuitively, rootfinding solvers find a scalar root x in R and thus, the points in the orbit can be
found one by one, applying Algorithm and the transformations described in Section for each
time of the period. A slight change, though, would allow us to work with a vector x in Rn and
find all the points of the orbit at once. Show your modified implementation and discuss about the
differences between the two approaches.
Assume the orbit eccentricity e Reformulate so that fixedpoint iteration method can be
applied with convergence, and then estimate the number of iterations needed in fixedpoint iteration
to solve with accuracy
Solutions: Plot the orbits that you have obtained with your selected initial data and parameters.
You also need to submit a Matlab script demom which calls tanom and displays the orbits.
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