Orbital Mechanics Guides

Introduction

Here are some links to orbital mechanics stuff and dynamics in general.

Links

Three Degree of Freedom (Orbital)

https://orbital-mechanics.space/the-n-body-problem/circular-restricted-three-body-problem.html

Six Degree of Freedom (Attitude)

https://en.wikipedia.org/wiki/Tennis_racket_theorem

Mechanical Concepts

Every so often, I get into these Wikipedia binges where I start looking up random things. A little while back, I got into reading on various on mechanical devices. Maybe one day I will build one of these.

Hoberman Sphere

A Hoberman sphere is an isokinetic structure patented by Chuck Hoberman that resembles a geodesic dome, but is capable of folding down to a fraction of its normal size by the scissor-like action of its joints. Colorful plastic versions have become popular as children's toys: several toy sizes exist, with the original design capable of expanding from 5.9 inches (15 cm) in diameter to 30 inches (76 cm).

A Hoberman sphere typically consists of six great circles corresponding to the edges of an icosidodecahedron. The Hoberman sphere can be unfolded by allowing certain members to spread apart. The operation of each joint is linked to all the others in a scissors mechanism like those used to mount pantograph mirrors, or how a folding chair operates. In larger models, this can be accomplished by feeding out a string or cable instead.


Kinematic Synthesis
Kinematic synthesis, also known as mechanism synthesis, determines the size and configuration of mechanisms that shape the flow of power through a mechanical system, or machine, to achieve a desired performance.

Hartenberg and Denavit describe kinematic synthesis as

...it is design, the creation of something new. Kinematically, it is the conversion of a motion idea into hardware.

The earliest machines were designed to amplify human and animal effort. Later, gear trains and linkage systems captured wind and flowing water to rotate millstones and pumps. Now machines use chemical and electric power to manufacture, transport, and process items of all types. Kinematic synthesis is the collection of techniques for designing those elements of these machines that achieve required output forces and movement for a given input.

Wenkel Engine

The Wankel engine is a type of internal combustion engine using an eccentric rotary design to convert pressure into rotating motion.

All parts of a rotary engine rotate in one direction. This is opposed to the common reciprocating piston engine, which has pistons instantly and rapidly changing direction 180 degrees. In contrast to the reciprocating piston designs, the Wankel engine delivers advantages of simplicity, smoothness, compactness, high revolutions per minute, and a high power-to-weight ratio.

[Astronomy] Superhabitable Worlds

Introduction

And when it comes to Earth, life has thrived, finding its way into every possible ecological niche, adapting itself through evolution to handle bitter cold, intense heat, the intense pressures at the bottom of the oceans, even cities, living right next to human beings. But could Earth be better? Could there be planets which are super habitable?

In a 2016 paper called Superhabitable Worlds accepted by the journal Astrobiology, two physics professors, Rene Heller and John Armstrong, run through the conditions that might make the most habitable possible planet. They propose that stars with less mass than the Sun, classified as K stars, are probably the best candidates for diversity since they’re long-lived and relatively stable. A K-type star will have a lifetime of 20-70 billion years without those pesky red dwarf megaflares.

You would want other planets in the star system, capable of redirecting asteroids and comets with their gravity to deliver water and other chemicals needed for life. Thanks for that, Jupiter.
And ideally, you want multiple habitable planets in the same system, capable of sending life back and forth. A process known as panspermia.

Planet Simulator Tool

Just for giggles and fun, NASA actually has an online software called ROCKE-3D general circulation model (GCM) which can study different points in the history of our own planet and other Solar System terrestrial planets, as well as exoplanets. Check it out!

https://data.giss.nasa.gov/rocke3d/maps/

Literature: On a Blue Day

Note: Just another exercise in dramatic writing. Just to let you know that I'm honest and will never go anywhere I shouldn't be, I never did any of this. All imagined in my mind and expelled henceforth from it!

I'm not in the library for its books or its "esteemed" educational value. I'm here for it offers me an expansive solitude that I can find little of elsewhere. This was the feeling I had even before I found a key to the roof top. I was in the elevator going up.

Second floor. The only person beside me in the elevator was a short girl with a large backpack. We were in a pseudo-comfortable silence. The backpack was pink. I glanced at her shoes. They were also pink. I turned away and silently counted in my head waiting for this pink monstrosity to leave.

Fourth floor. The door opened and the eyesore thankfully departed. I quickly punched the button to close the door before anyone could get in. Not that I could see anyone waiting in front of the elevator but you could never be too careful ensuring zero disturbance.

My current mood was an unstable system and the slightest perturbation may cause it to fall into the more stable mood best described as handling reality. Rare moods have to be preserved in a state of unstable equilibrium for as long as possible. It's like taking psychedelics once in a while to connect with the universe but doing that too much will seriously impair with handling reality. But regardless these rare moods must be preserved for how else could you experience the spectrum of your mind?

Sixth floor. Philosophical musings shoved aside, my mind returned to the practicality at hand. Leaving the elevator, I surveyed the area next to the stairs. No one in sight. Climb? Yes! My internal voice had to shout.

I went up and saw a door with a keyhole. Glanced back again and saw no one. I turned the key and walked out into the sun. The roof top was empty as expected.

I chose a boring day to be up here. No clouds. Just an aimless infinite blue. No wind. Just flocks of crows or ravens flying aimlessly. A slight breeze? Probably the downwash from their wings or more likely my imagination.

I sighed and walked towards the edge. Funny how there's no guard rails. If someone falls off though, they'll be all over it with regulations and whatnot. That's the funny thing about this country. One person's carelessness instantly means everyone else has suddenly irrevocably turned stupid.

I walked along the edge. If I fall off, there may be some interesting consequences. Quick images flashed through my mind like a film fast forwarded X16. I lose my footing on my next step and I topple over the side with a yelp. Good that I already have numbers prepared in my head in case something like this happens. Every floor is ~3 meters tall. There's approximately 7 floors making it 21 meters tall. Terminal velocity for a skydiver of around my weight is about 50 m/s. Obviously, I won't reach terminal velocity but how many seconds will I have? Every second my body is gaining velocity of ~10 m/s. This means I have about two seconds to think of anything in my last moments. This approximation isn't good enough, some part of me wanted to say.

I told it to shut up. Am I really going to squander my last moments trying to resolve the time of flight before I can no longer model myself as a rigid body or point mass? That's somehow comically absurd.

Third floor. Time does slow down in your last moments. Somehow I was able to think all that and I'm still just half-way there. The windows are rushing by at an accelerated pace. No one has noticed me yet. I hear the wind howling by. Maybe I'll suddenly sprout wings and fly. Will they be a mechanical contraption or magical? I spared a moment to ponder on which one I preferred. I decided that I'll go with both for redundancy. Saving myself should be a system with no single point of failure.

First floor. Sadly, daydreaming really doesn't help with developing powers in reality. The grey ground flew towards me mercilessly. I saw two people glowing white standing close to where I was soon to land with a crunching splat. They were smiling. Are they angels?

Odd, I almost did think I saw two glowing entities down there. I blinked. There were just two students there talking. I stopped my daydreaming on the edge of the roof. I stepped back and turned around. Either I have briefly entered the twilight zone or I really needed some sleep. Either way my mood was gone and this short venture was done. I went back inside and closed the door quietly behind me.