# Trajectory Optimization To The Moon (Case Study: Chandrayaan-2)

People always ask this million dollar question of " What is the best path/trajectory to take to reach a certain orbit or point in space".

Chandrayaan-2 had a pretty neat transfer to the moon, it took a while but it got there efficiently. Check this link: https://earthsky.org/space/chandrayaan-2-successful-lunar-transfer-trajectory

I wanted to make a simple analysis (in MATLAB) to find the optimized path to go from a earth orbit to a lunar orbit taking Chandrayaan-2 as a case study.

I guess I should optimize in terms of time and fuel? What theory should be applied to calculate such transfers (keywords or online examples and references)?

• Chandrayaan-2, if I remember correctly, had a rather drawn-out transfer, where the low-thrust engine was fired only at perigee for maximum use of the Oberth Effect. The thrust was designed to be low so the engine did not need to be very heavy. I think keywords you need include “fuel-optimal trans lunar injection”. Dec 21, 2019 at 20:04
• I guess this kind of optimisation wouldn't be applicable for human travel though. Dec 21, 2019 at 22:28
• @CourageousPotato yep! space.stackexchange.com/a/37306/12102
– uhoh
Dec 21, 2019 at 23:12
• @Adham How to best patch my conics?, things tagged patched-conic and 1, 2, 3, and anything about techniques used to plan the grand tour may be helpful
– uhoh
Dec 21, 2019 at 23:26

A study on such transfers requires the knowledge of : Optimal Control Theory and Optimal space trajectories

https://www.elsevier.com/books/optimal-space-trajectories/marec/978-0-444-41812-8

This book would take a lot of time , but enables you with knowledge to do simple study of such missions

Well you should be looking for optimization of fuel as the main criterion for the mission design would be to decrease mass to benefit both the launcher and the economics.

Advice : Fortran is more suitable for such calculations than MATLAB.

• Thanks. Ill check the book out! .... I always had this question of why FORTRAN is considered better for such calculations? Is it because it is faster ? Because as I see it, it is hard to plot and visualize the results in FORTRAN
– John
Dec 23, 2019 at 17:30
• I checked the book, isn't it a little outdated?
– John
Dec 23, 2019 at 17:36
• It may be "old" but it's certainly not outdated. We gain new understanding everyday, but the concepts that guide astromechanics are thankfully fundamental enough to not need significant revision. Why FORTRAN is a different question that could deserve its own answer, but feel free to use MATLAB or a similar modern mathematical software. Dec 24, 2019 at 8:59
• Fortran is built for the purpose of calculations and many satellites, missiles and other trajectory based programs run on Fortran. It has colossal heritage, numerous libraries, very high control and high computation speed Jan 16, 2020 at 0:30