A Pattern Search Method to Optimize Mars Exploration Trajectories

Round 1

Reviewer 1 Report

Overall, a well written manuscript with relevant references.

Some improvements seem necessary:

1. Detailed formulation of the differential correction process Eq (2) is required to elaborate on how it interfaces the optimization workflow.

2. Drag coefficient of 2.2. is used for both the Earth and Mars atmosphere. Is this assumption realistic?

3. Fig 14 (a): a 2D graph with primary x-axis for departure date and secondary x-axis for arrival date would be easier to read.

4. Could the authors provide details on the initial conditions chosen for the pattern search method? How does the choice ensure the obtained solution is global minimum? Augmenting the tables in Appendix A with the initial conditions that led to the optima would be helpful to replicate the results.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

This work is devoted to optimizing the trajectories to Mars in a promising mission. The authors optimize trajectories using a non-gradient pattern search optimization method. My comments:

1. In the annotation, instead of "object function" please write "objective function".

2. Rows 217-218: it is necessary to clarify what boundary conditions are meant, where they come from. How is it that the inclination of the reference orbit is 80 degrees?

3. In Figure 7, please label the remaining two points: Mars at Arrival, Earth at Departure.

4. Newton's method (2) is used to solve equations. But the target values in Table 4 are not fixed, but represent intervals. How then is Newton's method applied?

5. Mathematical part of section 3.5.1 should be rewritten because nothing is clear. It is not clear what Pk, pk, N, n, p are.

6. Please do not refer to formulas that come after the reference.

7. Rows 83-85: I wouldn't call pattern search a global method. On the contrary, it does nothing to look for the best of the local minima. It's just a local method.

8. The mathematical part of section 3.6 is also of very low quality. The description of the methods needs to be corrected. Nothing is clear at the moment.

9. In figure 10, the number 1e-06 needs to be corrected.

10. It is not clear what is meant in equation 10, why is the vector multiplied by a bracket?

11. In equation 11, exp must be typed in straight letters, as it is a function. The cross is not used to represent multiplication, please use a dot.

12. Row 374: K1 is term rather than coefficient.

The mathematical component of the text should be rewritten. This is essential for understanding the work, since its essence is to describe the application of the pattern search method for optimizing trajectories, and it is this part that is poorly written. I recommend a major revision of the work.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript is written very well and presents an interesting development of the Korean space program. Although it lacks some novelty, this work is definitely worth publishing and presents interest to the readers. I advocate its acceptance, and only would like to see one clarification:

Eq. 8-9. K1 is less than 50, but how exactly K1 is chosen? Is it 0 or zero, or some intermediate values may be chosen? Also, wWhy the value is 50? Why not 5, 500, or 5000?

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I agree with the authors' responses and the modifications to the manuscript. There are a few minor points:

1. Since f(x) is a vector valued function, the equality constraints ceq1 to ceq5 in Eq. 10 (in the revised manuscript) should reference the corresponding components of f(x).

2. Incorporating the explanation of the drag coefficient in the manuscript with the appropriate references would be useful to the readers.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The mathematical component of the article has been rewritten. The methods are now described a little better, but they are still very inaccurate. For example:

1. In line 351 the number of variables is denoted N, and below in line 355 it is denoted as n.

2. It is not clear why the vectors p have dimension 2. In theory, they should have a difference of N or n (the number of variables).

3. In Equation 9, x_k is a vector and x_k+1 is a matrix.

4. In Equation 10, something is indicated first in bold and then in non-bold.

5. In equation 10 there are such things as TOF = x, it is not clear how time can be equal to the vector of optimized variables.

6. In Equation 10, all the functions are denoted as f, although they should all be different functions.

There are other problems with mathematics that can be listed.

Author Response

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Author Response File: Author Response.pdf