A walker's guide to science in general and physics in particular

[hamiltonianflow]

Hello everyone. I've started a small series with popularising science using KSP in mind. The goal is to explain physics concepts which are used in KSP in a way accessible to people w/out maths or physics background (so the stuff interesting for those people won't start until some very late instatements). The best case scenario is that at the end reader will be able to use the formulae showing up all the time on the forum, and use computer programmes to make their very own pork-chop plots, aerodynamics curves etc. (but this is still long way ahead).

At the moment the series has following instalments:

1. So what’s the deal with orbital motion anyway?
   
2. Kinematics of orbital motion continued, i.e. talk about periods and velocities
   
3. Vectors, vectors, vectors… and derivatives!
   
4. The change of velocity, i.e. acceleration, and CASes
   
5. Basic gravitation, i.e. force of gravity between two bodies and barycentres
   
6. Gravity field around a planet, i.e. how to do some science in KSP
   
7. Orbital mechanics resources
   
8. On the equations of motion, i.e. the essence of dynamics, and something about rockets
   
9. Orbital period and Kepler’s 3rd law, i.e. prepare your (non-atomic) watches
   
10. Kepler’s 3rd law in our solar system and KSP (the first attempt)
    
11. Orbital velocity for a circular orbits
    
12. How to get off this rock, i.e. pervaya kosmicheskaya skorost’
    
13. Orbital trajectories and solving equations of motion in a spreadsheet
    
14. What is that shape? - Equations of motion and elliptic trajectories
    
15. ΚÉνικά. i.e. the ugly shadow of algebraic geometry
    
16. A few words about the foci
    
17. Some more properties of ellipses: area and integration
    
18. Even more properties of ellipses: circumference and special function
    
19. Ellipses, circles, parabolas and moduli space of conics
    
20. Eccentric anomaly ̉ۡ, true anomaly ̉ۢ and a pile of non-intuitive jargon
    
21. The equations of motion around gravitating body: from Cartesian to polar coordinates
    
22. Intermission: Kabbalah with Titius-Bode law
    
23. Intermission: Setting sail for space (part 1): Ideal solar sail
    
24. Angular momentum conservation and Kepler’s 2nd law
    

If anyone has any comments, please share. Thanks for feedback.

Edited September 25, 2015 by hamiltonianflow

[Rosco P. Coltrane]

I like it, I like it. Kudos!

Too bad I simply don't have the time to seriously dive into this stuff, but I'll check it none the less.

[Starwhip]

Very well done, great use of KSP images.

[Specialist290]

I'll have to give this a more thorough overlook when I get the time, but at a glance this looks like it could be prime Drawing Board material

[hamiltonianflow]

Updated with part 15

ΚÉνικά. i.e. the ugly shadow of algebraic geometry

which starts the treatment of elliptic orbits.

[hamiltonianflow]

Updated with part 16

A few words about the foci

which is all about focal points.

[hamiltonianflow]

Updated with part 17

Some more properties of ellipses: area and integration

which is about computing the area of an ellipse with a short digression about Riemann integrals (which you can avoid using the internet, but do you want to?).

[Rosco P. Coltrane]

Ah, integrals... my nemesis. A young boy headed for college. TV put many crazy ideas on his head, ideas of fun times, learn a couple of life lessons maybe, and then the very first day, Monday 8 am, he got his brain all messed up in this class called Mathematical Analysis I... Worst part, it's "I", which means there's gonna be a II and III and who knows!

But, it's interesting how something you just hated when you had to do it under obligation can be fun when you're doing it just because.

[hamiltonianflow]

Updated with part 18

Even more properties of ellipses: circumference and special function

which is about computing the circumference of an ellipse.

[hamiltonianflow]

Updated with part 19

Ellipses, circles, parabolas and moduli space of conics

which is about getting a parabola out of an ellipse, and how the topology of the space of conics even looks like.

[peachoftree]

what visual pack do you use to get kerbin to look so good?

[hamiltonianflow]

what visual pack do you use to get kerbin to look so good?

Clouds from EnvironmentalVisualEnhancements; also TextureReplacer with KSPRC - Renaissance Compilation; and parts of some Astronomer's Visual pack, though I don't remember which one (for sure not the newest one).

[hamiltonianflow]

Updated with part 20

Eccentric anomaly ̉ۡ, true anomaly ̉ۢ and a pile of non-intuitive jargon

which is about the eccentric anomaly, the true anomaly and complains how broken the astronomical nomenclature is.

[Tweety]

Don't know if it bothers you but a couple of times the word launches/launch has been replaced with lunches/lunch. I like to think that kerbals are always thinking of their stomachs (if that's what they have). Brilliant reading though. I like reading stuff like this so have some cookies.

Tweety

[hamiltonianflow]

Thanks. That was embarrassingly many meals. Hope that they're all gone though.

[hamiltonianflow]

Updated with part 21

The equations of motion around gravitating body: from Cartesian to polar coordinates

which is about rewriting the Newton's equations from Cartesian coordinates into the polar ones, with addition of some complaining that it would be so much easier in Lagrangian formulation.

[hamiltonianflow]

Updated with part 22

Intermission: Kabbalah with Titius-Bode law

which is about some planetary numerology, as something for people who didn't appreciate boring manipulations from last time.

[hamiltonianflow]

Updated with part 23

Intermission: Setting sail for space (part 1): Ideal solar sail

which is about solar sails, that is spacecrafts that use the radiation from the sun to propel themselves (though they are absent from the stock game, there are mods (like SolarSailNavigator or KSP Interstellar Extended) which give you those functionalities).

[bigcalm]

This is really good! Could you do something that shows how to calculate more precisely the delta-v required to lift off a body -- I had a go myself here - https://docs.google.com/spreadsheets/d/1WaJEZKcyvqzXa0oAx1tEmOYDgXKqiiwEDDSF4xuW-3k/edit?usp=sharing - but ended up concluding that my maths simply wasn't good enough!

[hamiltonianflow]

This is really good! Could you do something that shows how to calculate more precisely the delta-v required to lift off a body -- I had a go myself here - https://docs.google.com/spreadsheets/d/1WaJEZKcyvqzXa0oAx1tEmOYDgXKqiiwEDDSF4xuW-3k/edit?usp=sharing - but ended up concluding that my maths simply wasn't good enough!

Because I took as a starting point orbital mechanics and not spacecraft design, there will be some time before I'll write anything about ÃŽâ€v etc. - I definitely want to do that, but it'll take some time. Also, when I'll start writing about it, I will make all the usual assumptions like instantaneous burns etc., so it won't be an engineering-like treatment (more like theoretical physics-like), so if you would use those formulae instead of some numerical integrators and apply them to KSP, you will get some discrepancies.

[hamiltonianflow]

Updated with part 24

Angular momentum conservation and Kepler’s 2nd law

which is about an angular momentum and how to derive Kepler's second law from the Newton's equations of motion.