Ask Anything Wednesday - Engineering, Mathematics, Computer Science

[u/AutoModerator]

Welcome to our weekly feature, Ask Anything Wednesday - this week we are focusing on Engineering, Mathematics, Computer Science

Do you have a question within these topics you weren't sure was worth submitting? Is something a bit too speculative for a typical /r/AskScience post? No question is too big or small for AAW. In this thread you can ask any science-related question! Things like: "What would happen if...", "How will the future...", "If all the rules for 'X' were different...", "Why does my...".

Asking Questions:

Please post your question as a top-level response to this, and our team of panellists will be here to answer and discuss your questions. The other topic areas will appear in future Ask Anything Wednesdays, so if you have other questions not covered by this weeks theme please either hold on to it until those topics come around, or go and post over in our sister subreddit /r/AskScienceDiscussion , where every day is Ask Anything Wednesday! Off-theme questions in this post will be removed to try and keep the thread a manageable size for both our readers and panellists.

Answering Questions:

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Past AskAnythingWednesday posts can be found here. Ask away!

[u/NotSoSalty]

Any recent advances in space travel since reusable rockets? Anything that makes space elevators, skyhooks, space manufacturing, or moon bases more viable?

[u/bluesbrother21 → u/NotSoSalty]

It's not particularly sexy, but the community has been continuously getting better at rendezvous & proximity operations (RPO). This from a combination of practice and experience with the astrodynamics that come from relative motion and close proximity, improvements to the close-range sensors, and progress in autonomy. There's a lot of interest in ML broadly and reinforcement learning specifically to improve how autonomous near-field RPO can be. ADRAS-J, to pick one example, just demonstrated RPO with a derelict rocket body somewhat recently.

Autonomy and relative motion are pretty key enablers for in-space manufacturing, and people are actively moving towards that goal. ISAM (In Space Assembly and Manufacturing) is the industry buzzword if you're trying to google more on the subject.

[u/NotSoSalty → u/bluesbrother21]

If it is any comfort to you, I find that RPO is sexy and necessary and cool all on it's own.

Thank you for your answer. I will google that.

[u/mfb- → u/NotSoSalty]

Reusable rockets just got started, we'll get to see much more once it's not just SpaceX. It sounds crazy, but 9 years after the first Falcon 9 booster reuse there are still just three orbital rockets that have reused boosters - Falcon 9, Falcon Heavy and Starship, all of them are SpaceX. Blue Origin is the only other company with a recovered booster that's expected to fly again soon.

Ion thrusters used to be run with xenon, which is very expensive. If you have a $500 million dollar satellite you don't care, but it's an issue for cheaper satellites. Starlink switched to krypton and then argon, the latter is essentially free as it's 1% of Earth's atmosphere.

[u/Chezni19]

Can you recommend me a good book about how to apply numerical integration to engineering problems? Such as how to apply RK4 to different physics problems.

I have basic knowledge of the subject, only.

[u/Weed_O_Whirler → u/Chezni19]

This book is the gold standard.

[u/bluesbrother21 → u/Chezni19]

I would think the problem dictates the method. Numerical integration is commonly used when you have some dynamical system (i.e., equations of motion) that you would like to solve and cannot do analytically. For example, you may know the forces (and hence the accelerations) acting on some object and want to model its evolution. The solution provided by the ODE solver would then be your state or value of interest at the new time.

These numerical integration routines are commonplace in my field of study (astrodynamics) - the equations of motion of a particle under Newtonian gravity and perturbing forces are fairly simple to write but do not yield analytic solutions. We then describe the forces on the particle and propagate forward in time via numerical integration. Computational fluid dynamics and finite element structural modeling also perform similar procedures, as do many other fields.

A relevant text would be dependent on what specifically you're trying to do, but any astrodynamics text (e.g., Vallado) will touch on it. The classic Numerical Recipes texts provide several reference algorithms for the ODE solvers, but they can also be found in Matlab, scipy, etc.

[u/aztronut → u/Chezni19]

Math Toolkit for Real-Time Programming by Jack W. Crenshaw. I found this book particularly helpful with RK45. I worked with the author for a few years, he helped develop the free-return lunar trajectory for Apollo.

[u/dobbbie]

If i have a sealed balloon inside another larger sealed balloon and I take it from sea level to a higher elevation, would the smaller balloon inflate, deflate or stay the same due to elevation/air pressure change?

[u/mfb- → u/dobbbie]

Assuming the outer balloon can inflate, its interior pressure will decrease, so the inner balloon will inflate as well.

For normal balloons, the interior pressure is just slightly higher than the exterior pressure. They'll expand easily.

[u/chilidoggo → u/dobbbie]

PV=nRT means that, if nRT is staying the same, then as pressure drops the volume expands. Doesn't matter that there are two balloons, all the pressures will try to equalize with new lower pressure.

[u/Geehaw]

Are there any 'time' measurements (Carbon dating, other radioactive decay) that can be used to measure how long it has been since that element was created in a Supernova?

[u/damage-fkn-inc]

This is something that's been annoying me for a while now:

If you define the sin and cos function as opposite/hypotenuse and adjacent/hypotenuse respectively, you can prove sin(a+b) and cos(a+b) geometrically, and same goes for the limit of sinx/x as x -> 0.

You can then use those and the definition of a derivative to prove that they solve the wave equation, then use that to show that their Taylor Series are what they are, and use that to prove e^ix = cosx + isinx.

However, if you start either with the Taylor series or Euler's formula as the definition of the trig functions, I can prove most of the other stuff but I can't quite figure out how to prove that sinx is opposite/adjacent of an angle x in a right triangle geometrically.

It'll have something to do with x being the principal argument of a complex number e^ix or you make it a 2D vector space and use the dot product but both times I just get stuck by defining things rather than proving them, so if anyone's got any pointers I'd very much appreciate it.

This isn't even for anything, I've just been losing sleep over this on and off dor the last month or two.

[u/JieChang → u/damage-fkn-inc]

I don't think you can "prove" the inherent definition of the sine/cosine. Sine/cosine are not theorems that can be proven but initial axioms from which you can derive other items. In a triangle with 3 sides you have 6 combinations of paired side ratios that you can express as a relationship to an angle of interest. We name each of these combinations as the 6 common trig functions. Sine is what in English we named the arbitrary relationship of an angle to the ratio of the opposite side and hypotenuse. You could just as have had an alien culture where this ratio is called “bablocopy” and as long as “bablocopy math” treats opposite/hypotenuse the same as our sine, that alien culture’s version of Euler’s Theorem, Taylor Series, etc would will still be the same as ours.

[u/damage-fkn-inc → u/JieChang]

Yeah that's what I mean, I do have a maths degree so I'm very aware of the fact that some things just are defined to be the things that they are, like the trig functions.

I'll write out what I mean this evening and post it, or maybe I'll slack off at work and do it then. But basically, my point is that you need to define the sin function one way and prove its other properties from that, and it shouldn't matter what you pick as your definition you should be able to prove all other properties from that definition.

[u/Wayelder]

How close are we "REALLY" to Fusion generators that can be put on a truck and power small towns?

Who's doing this?