Problem 4
The orbital elements of the spacecraft have been calculated considering the atmospheric drag
equation provided in equation five. As the atmospheric drag has been introduced in this problem,
the satellite in the orbit should lose some altitude due to the drag and the energy also decreases
followed by the decrease in semi-major axis of the orbit and the z-component of the angular
momentum. The graph of the evolution of orbital elements are shown in figure 4.
Fig 4i: Evolution of energy
Fig 4ii: Evolution of z-component of angular momentum
Fig 4iii: Argument of ascending node
Fig 4iv: Argument of periapsis
Fig 4v: Evolution of semi-major axis
Fig 4vi: Evolution of eccentricity
Fig 4vii: Variation in inclination of spacecraft
Fig 4viii: Evolution of True Anomaly
Problem 5 Solution
The solution for the reference state at problem 5(a) is formulated using ode45 and the x-y plot
for the x and y values of the reference solution is shown in figure 5(i).
Fig 5(i): The xy plot of the reference solution (X*)
Similarly, the actual solution for problem 5(b.i) after considering the perturbations of 𝛿𝛿X is
computed and the x-y plot of the perturbed solution is shown in figure 5(ii).
Fig 5(ii): The x-y plot of the perturbed solution (X)
The computation of STM has been done using the following relation of STM.
= AΦ
The other problems are calculated subsequently in the matlab code Problem5stm.m.