---
# System prepended metadata

title: Comparison of Low Thrust Trajectory and Direct Transfer on Mission Performance

---

# Comparison of Low Thrust Trajectory and Direct Transfer on Mission Performance

## Group 32
* Yung–Jiun Chen, Department of Physics, National Taiwan University
* Wu–An Lin, Department of Physics, National Taiwan University
* Hua Chen, Department of Physics, National Taiwan University
* Bo–Wun Chen, Department of Physics, National Taiwan University

## Abstract
<!-- Give a brief summary of the work you plan to present. The well-written abstract is the single most important part of the proposal. Often, initial proposal review are based on the abstract alone. (Limit:  250 words) -->

In this work, we're aiming to find the optimal propulsion solutions under real world constraint for different mission profile. We will first analyze the trade off between high specific impulse and high thrust for optimizing both minimum time of flight and minimum energy trajectory, then will present real world scenario with discussions about potential propulsion solutions that may achieve such performance.

## Background and Objectives
<!-- Give a short review of the literature and explain why this work is important. Please discuss the scientific or technological impact of this work. If presenting a historic work, give a brief discussion of the historical significance of this work.  You can also include formula
\begin{equation}
H=-t\sum_{\langle ij\rangle} c^\dagger_i c_j + \text{c. c.}
\end{equation} --> 
<!-- You can also include figures, as shown in Fig. 1.
Limit the number of figures to two. 
![](https://i.imgur.com/o1nkQ0G.jpg)
<figcaption>Fig. 1: Average vs year. </figcaption> -->

People once had big dreams about future among the stars. But ever since the national interests in Apollo mission die down and budget for NASA crashed, all these plans to go beyond just foot print and flag fell apart. Nonetheless, studies were conducted, preliminary plans were made. On July 20th, 1989, the 20th anniversary of Apollo 11 Moon landing, a plan under President Bush later known as "Space Exploration Initiative"[^SEI] for human mission to the Moon and Mars was announced. Although the initiatives dissolved as soon as new president took over, some of the most comprehensive study on the mission to Moon and Mars remained, these works continued to become major referential sources of many study and concept of interplanetary missions to this day. </br>One such series of study about the mission architecture trade off is "Space Transfer Concepts and Analysis for Exploration Mission"[^STCAEM], which has one volume dedicated towards examining various types of propulsion system suitable for exploration mission. There's a whole range of points considered from aerobraking and short/long stay trajectory to on orbit assembly timeline, radiation, and even abort scenario, but among all, we are most interested in the part about optimized trajectory for each of the different propulsion system. One interesting point being brought up is that, for both low energy and low time of flight trajectories, a hybrid of high thrust during planetary maneuver and high efficiency low thrust during orbit raising can provide better performance than alternatives, we hope these results can also be obtained by our own analysis. </br>

## Methods, Steps and Progress
<!-- Describe the methods, the time frame and the division of labor among group members in this work. -->

### Methods
<!-- Discuss the methods that are required to perform the studies introduced in this work, including the experimental setup/ theoretical tools and procedures. -->

One of the more readily available approach for optimization of spacecraft trajectory is to use GMAT[^GMAT], a trajectory modeling software developed by NASA Goddard Space Center. We're expecting to use this software to compile our numerical result.

### Timetable
<!-- Give a weekly timetable from the week starting from 11/15. The timetable should show your progress toward making a oral presentation and a poster. -->
<!-- Or you can include a Gantt chart. -->

|Week|Task|
|----|----|
|Nov 15 - 21|Materials reading and discussion.|
|Nov 22 - 28|Materials reading and discussion.|
|Nov 29 - Dec 05|Analysis (Equation deriving).|
|Dec 06 - 12|Analysis (Equation deriving).|
|Dec 13 - 19|Numerical modeling.|
|Dec 20 - 26|Numerical modeling.|
|Dec 27 - Jan 02 2022|Designing poster layout.|
|Jan 03 - 09|Poster presentation demoing.|
|Jan 10|Poster presentation.|

### Responsibilities
<!-- Please address what each member's role in the project will be. -->

|Name|Task|
|----|----|
|Yung–Jiun Chen|Poster design|
|Wu–An Lin|Proposal|
|Hua Chen|Materials reading|
|Bo–Wun Chen|Materials reading|
|Shared Task|Analysis (Equation deriving), Numerical modeling|

## Expected Difficulties and Solutions
<!-- Describe briefly what is the expected difficulties in this work and your possible solutions. -->

Because there's only a broad constraint on the propulsion characteristic, we need to find a way to streamline the process of evaluating different propulsion system. This would be hard, because the difference between low thrust and high thrust solution are so drastic that, at most practical cases, solving them warrants two different categories of methods.
Thankfully, there's already off-the-shelve software that can do analysis on high thrust impulse and, maybe within a few tweaks, impulse approximated low thrust trajectory that allows streamlining of the evaluation.

## Results and Evaluation
<!-- Describe briefly what you expect to learn and produce from this work. Please give concrete goals and how you can evaluate if these goals are reached. -->
<!-- Finally, give proper citations[^ex] of work you referenced in your proposal[^mcco02]. Limit this section to two pages, including figures. -->

We will present analytical evaluation qualitatively to explain the characteristic of different trajectory. And the numerical result should be presented as a chart of different propulsion system versus:
* least time: time of flight (with fixed payload, constrained mass ratio)
* lowest energy: mass ratio (with fixed payload)

As for goals, if we can get both direct transfer and low thrust model done, it's a success.

## References
<!-- [^ex]:See for example: G. H. Cross, Nature **374**, 307  (1995); M. Key *et al.*, Phys. Rev. Lett.  **84**, 1371 (2000). 
[^mcco02]: L. McComb, J. Dept. Phys. **75**, 234 (2002). -->

[^SEI]:[Space Exploration Initiative, wiki](https://en.wikipedia.org/wiki/Space_Exploration_Initiative#Ending)
[^STCAEM]:[STCAEM paper on NASA Technical Reports Server](https://ntrs.nasa.gov/citations/19930013159)
[^GMAT]:[NASA GMAT](https://software.nasa.gov/software/GSC-17177-1)