u/Gereshes

Fundamentals of Astrodynamics by Bate, Muller, and White comes with the perk of being a Dover textbook (Very cheap!)

I go over a bunch of astrodynamics textbooks in a post here

I'm a big fan of Vallado's book, Fundamentals of Astrodynamics and Applications, I just didn't include it as I was trying to limit myself to 5 entries. Vallado is (IMO) a very good reference manual for once you've learned a topic and then need to remind yourself of something specific, like what is the ECEF -> ECI transform, but serves less well for a textbook where you are learning something for the first time. As for the new version, IDK as I haven't read it, but my guess is it's just minor corrections and updates.

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Edit: Added an affiliate link to Vallado's book. Qualifying purchases using that link help fund Gereshes hosting costs.

1) My plans for this subreddit are to make it open so that people can post again. Currently, you must request to post and I'm assuming that no one has been approved to post in the last year as there have been no new posts in the last year.

2) https://www.reddit.com/message/messages/1fod19o

Note: You may have seen this post earlier today. I accidentally deleted that link so here it is re-posted

Thanks!

Thanks!

This doesn't change the point you're trying to convey (that people have unrealistic beliefs about the wage distribution) but your statistics about wages >$120k is an order of magnitude below the true number. According to the social security administration approximately 12.6 million people make more than 120k ( https://www.ssa.gov/cgi-bin/netcomp.cgi?year=2020 )

Because there have been only 3 mission failures in its history there is limited data for that statistic (and in no case of a mission failure do they try recovering the booster). Luckily it doesn't really matter. While writing the post I ran the sim with a 0% prob of the rocket being destroyed and a 100% of the rocket being destroyed if the mission failed and it made no negligible difference because the mission has a 97.8% success rate. The uncertainty in the recovery of starship makes causes a much larger difference in the results, but for the reasons, I mention in the post, there isn't (yet) much better data for starship recovery rates.

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Note: I did not count partial failures because that opens up a whole new can of worms (how does this particular partial failure affect the recovery probability) without IMO providing much predictive power.

Thanks!

Thanks!

TLDR: RL is very poorly suited for Astrodynamics problems and I recommend you pick another topic (Especially if this is a project for an undergrad class due at the end of a semester). If you have your heart set on RL for astrodynamics I would suggest you de-scope to a 2-body (Sun's gravity only) interplanetary transfer from Earth to Mars where you arrive within 1 Mars radius (That should give you an idea of the difficulty of the problem)

Why you should trust me: I'm a PhD student studying astrodynamics who has published papers on using RL for low-thrust trajectory design and Neural Network Optimal Control. Beyond my own publishing record, I know a good chunk of the other people doing "AI in astrodynamics". Here's a sampling of their conference papers Low-Thrust optimal control using RL, Autonomous Guidance for Multi-body Orbit Transfers using RL, Spacecraft Attitude Control Using RL, Designing Impulsive Station-Keeping Maneuvers using RL, Using RL to Uncover a Pareto Front in Multi-Body Trajectory Design.

Why is RL not suited for astrodynamics:

1. Precision: Astrodynamics requires lots of precision. If you want to leave Earth and get to Mars you're gonna need 1e-8 ish numerical precision. RL has a tough time getting below 1e-4, using personal computers, and 1e-6 using supercomputers.
2. Sample inefficiency: RL is ridiculously sample inefficient, and generating large numbers of samples in the CR3BP, especially if you don't know what you're doing, can be very expensive.
3. Reward Shaping: In order to get the RL agent to converge you're gonna need to shape the reward rather heavily. I've seen cases where in order to get the agent to converge, the reward is so far from optimal the agent gets beat by a classical (non-optimal) controller.
4. Classical methods are really good: We know the fundamentals of astrodynamics really well. We can calculate the effects of pluto on spacecraft in Martian orbit (They're negligible). Because of this, we can use traditional techniques (both optimal and classical control) to great effect. Problems that took supercomputers for AI, can be beaten on my laptop using classical methods.

Where might RL be good in Astrodnymaics? : There's some new research on using RLfor spacecraft scheduling that's interesting. Scheduling spacecraft is a good use case as it's fuzzy, avoiding AI's precision problems, and rendering classical methods less useful.

What do I recommend you do? That depends. If you're more into astrodynamics I'd recommend learning some classical techniques (like shooting methods). They are quite powerful, and if wrapped in an optimizer can do basically what you want much better than RL. If you're more into RL I would suggest changing your problem (or changing your topic to make it fuzzier so you're not competing with traditional methods).

RL is a super cool technique that can theoretically solve any optimization problem. "Theoretically". In practicality, if your problem can be solved using a traditional method, you're likely better off not using RL

I made this visualization for a blog post, An Introduction to The Bicircular Restricted 4 Body Problem. Starting on a "stable" NRHO orbit in the Earth-Moon system, and varying the Sun's position (relative to the Earth and Moon) show's the unstable manifolds that depart this orbit. The trajectories are calculated using ODE45 in Matlab and visualized in Matlab as well

I made this visualization for a blog post, An Introduction to The Bicircular Restricted 4 Body Problem. Starting on a "stable" NRHO orbit in the Earth-Moon system, and varying the Sun's position (relative to the Earth and Moon) show's the unstable manifolds that depart this orbit. The trajectories are calculated using ODE45 in Matlab and visualized in Matlab as well

I made this visualization for a blog post, An Introduction to The Bicircular Restricted 4 Body Problem. Starting on a "stable" NRHO orbit in the Earth-Moon system, and varying the Sun's position (relative to the Earth and Moon) show's the unstable manifolds that depart this orbit. The trajectories are calculated using ODE45 in Matlab and visualized in Matlab as well

Stephen Strogatz - Nonlinear Dynamics and Chaos is a pretty good mathematical introduction to (as the name implies nonlinear dynamics and then) chaos

I've always gone with

• Submitted to X - It's been submitted to a journal but has not yet been accepted.
• Accepted - The journal has formally accepted it, but it has not yet been published
• Manuscript in preparation - I've been told never to use this one as it could mean anything from you've written an outline to you're editing it. (The norms in your academic field may be different than mine though)

This is just the one that comes to mind first, but the Dawn spacecraft had an MTE 30 days before arrival at ceres. The period before arrival is often the most sensitive to MTE's (because there's so little time to make up for the missed thrust), and I think this was the closest JPL ever got to losing a spacecraft due to a MTE. Currently, most interplanetary spacecraft are high-thrust (which arent super susceptible to MTEs), but as more interplanetary spacecraft adopt low thrust (which has been the trend over the last 20 years), MTE's will become a larger problem. If perseverance was a low-thrust spacecraft, it's safe-mode event about 4 hours into flight may have become a missed thrust event (depending on the con-ops).

Thanks!

Thanks!

1. There are not actually analytical solutions for low-thrust interplanetary trajectories (This fact that the thruster is bounded and the trajectory is mass-optimal basically ensure this). While there are two outcomes (either the spacecraft is fine or it isn't), on long trajectories (>400 days) multiple missed thrust events (MTE) are more likely than 0 or 1 MTE combined. Mission designers also need to figure out "how can we recover the trajectory while saving mission margin for a future MTE"
2. Trusting the black box that is AI, especially with something as expensive as a spacecraft, is a real challenge. NASA is working on building up confidence in AI navigators through tech demonstration missions like CAPSTONE. Now, I'm not on the CAPSTONE team, but the PI on the mission wrote his dissertation on using AI for autonomous trajectory correction (He was dealing with deterministic state errors, not MTEs), so I would be surprised if there was no AI in the mission. Constellations are an interesting test case for AI control, but because they only thrust a small amount of the time, there isn't much MTE potential so I've been staying away.
3. I think there's a lot of potential in both approaches. More generally, RL provides a tool to solve nonlinear stochastic optimal control problems, something that's really hard to do with today's tooling. Additionally, with the rise of deep-space CubeSats, we will either need to massively increase the communications infrastructure to support these new missions, or we'll have to grant them more autonomy. Or maybe I'll take this research a third way. You'll just have to read my future publications to find out ;)

Thanks!

Theoretically yes, but you quickly run into the curse of dimensionality. Unfortunately, as the dimension of the problem grows, so too does the memory requirement (also interpolation has a really bad time in greater than 6 dimensions, and if you also want to measure spacecraft orientation and location you're already up to 10 dimensions). By using a NN, we can push the computationally intensive work from the spacecraft down to Earth, and what's (in my opinion) really neat in this paper, is that the NN learned the local HJB solution well enough to repair the trajectory after multiple stochastic perturbations (missed thrust events), despite not having them in the training dataset.

Sure, (but as you can probably tell from me replying 5 hours late) but I'm swamped with work lately

The training of the neural network is the computationally intensive portion, but that can be done on earth. Running the trained neural network, which is what the spacecraft would do, is computationally cheap. Basically it allows you to move the computation from the spacecraft down to Earth

I made this visualization for a blog post, Nerd Sniping Myself . I was investigating the stability of a dynamical system by numerical integration using Matlab's ODE45 at various radii from the fixed point and ended up with this GIF. (Also visualized using Matlab)

I made this visualization for a blog post, Nerd Sniping Myself . I was investigating the stability of a dynamical system by numerical integration using Matlab's ODE45 at various radii from the fixed point and ended up with this GIF. (Also visualized using Matlab)

I made this visualization for a blog post, Nerd Sniping Myself . I was investigating the stability of a dynamical system by numerical integration using Matlab's ODE45 at various radii from the fixed point and ended up with this GIF. (Also visualized using Matlab)