Talk:Beta angle

Question: Mathmatical/Factual Error ?
This line appears in the article:


 * The extreme values of beta angle over a years time for a mission launched at a given orbit inclination, $$i\,$$, varies ± 23.45 degrees. In other words, for a due east launch from the Kennedy Space Center, $$i\,$$=28.5o, and the beta angle will vary from about $$\beta$$ = +52o to $$\beta$$ = -52oover the course of a year

Am I half asleep, or does this math seem to be incorrect? If the beta angle varies ± 23.45o/year, assuming a starting beta angle (to keep the math simple) of 23.45o, then wouldn't $$\beta$$max = 46.9o and $$\beta$$min = 0o? I'm no astrophysicist, and this line is cited, so can anyone clear up my confusion - or am I right? Thanks! Spiral5800 (talk) 18:15, 18 June 2009 (UTC)


 * After re-reading and reconsidering, I realized that the section in question is talking about inclination, $$i\,$$ and currently the article does not have an equation that directly relates $$i\,$$ and $$\beta$$. I will see if I can find such an equation.  Spiral5800 (talk) 12:10, 26 August 2009 (UTC)


 * I've come to think that due to orbital precession effects, any equation describing the relationship between $$i\,$$ and $$\beta$$ would be a very complex differential. I doubt digging one up (or figuring one out) would really contribute to the article anyway.  Spiral5800 (talk) 14:09, 2 December 2009 (UTC)

Copyright violation
As regular editors of this page have not acted on the copyright violations identified above, I've removed the following problem items:
 * First para of 'Determining a beta angle' was almost word for word identical to the third para of the 'Beta angle' section of this page.
 * Both images, although tagged as being released into the public domain by user:Spiral5800, are based on this image, for which the copyright conditions specify educational and non-commercial use (not suitable for Wikipedia) and also request attribution which has not been given. 4u1e (talk) 05:08, 2 August 2010 (UTC)


 * Thanks for the attention to detail. I did construct those images myself on "paint", I believe, and although they were based on images I'd seen elsewhere, they were indeed original material.  As this is an article concerning orbits, and as orbits (though elliptical) in many cases can be approximated by circles, I fail to see how anyone could have defined a beta angle in a diagram without making your alleged copyright violation; I do agree that the images of the sun that were later added to the illustrations for clarity had an unclear copyright status, though I would argue that the article would have best been served by reverting to the older versions of the illustrations that lacked the sun image rather than entirely removing the illustrations.  Besides the sun, which was amended to the illustrations long after their original versions appeared here, the images were composed entirely of the simplest and most common geometric illustrations - specifically a circle and a few line segments - and if circles or circles with line segments intersecting them are somehow copyrighted and off-limits, then wikipedia has far bigger concerns than this article.  Thus, after waiting a year, I am going to re-add the illustrations to this article as the illustrations make the article vastly more accessible to the layperson, among other reasons.  I intend to re-draw them myself from the definitions already outlined in the article so as to avoid any further allegations of copyright violations, though I feel strongly that the removal of the original illustrations was overly haste and insufficiently justified, especially due to their extreme simplicity.  So far as I am aware, one cannot make a copyright claim on a diagram of a circle with one or two lines drawn through it.  If one can, then please let the world know that I hereby copyright the platonic solids and any depiction of them must be removed from wikipedia except where my explicit consent has been given.  Also, although the first couple sentences of the article originally resembled the source from which the information was taken, all wiki editors should know that one of the most important and upheld policies of wikipedia is the NOR - NO ORIGINAL RESEARCH.  I apologize if it was thought that those first sentences were not reworded - thesaurisized - to the extent someone seemed to think appropriate, but the information was clearly cited and there are only so many ways to describe a mathematical concept.  If anyone still perceives a problem, then please head on over to the article on pi - but hold your hands to your head tightly to prevent it from exploding.  If you survive this experience, your detailed explanation of why it is a copyright violation to define pi by saying "pi is defined as the circumference of a circle divided by the diameter of said circle, which is a constant with the approximate value of 3.141592...".  Just because someone else has said something somewhere else on the topic before the article (whether this one or the one about pi) was created does not mean that it's a copyright violation for someone else to say the same thing elsewhere at a later date.  Pi will remain 3.141592... (etc) regardless of how many sources discuss it; the idea that posting "pi is approximately 3.141592 ..." is somehow a violation of someone's copyright is just as inane - and insane - as taking issue with the definition of beta angle as described in this article.  What about E = MC^2?  How would one prefer that to be re-defined or rewritten to conform with such an oddly skewed reading of wikipedia's guidelines?  If the same standards that were applied to this article a year ago were applied to the whole of wikipedia, there would be no wikipedia.  I hope this is as obvious to others as it appears to me.


 * I hope I have properly illustrated how ridiculous this was. I also hope that my waiting a year before returning the diagrams to the article (in the hope that someone besides myself might rectify this issue) is taken as a sign of good faith, patience, and respect for my fellow editors.  A year has gone by and nobody else has taken it upon themselves to add illustrations to this article (illustrations that are desperately needed to clarify the material and make it accessible), so I therefore feel that doing it myself - over again - is more than justified.  I certainly look forward to reading any (hopefully elaborate) explanation if anyone continues to think that my adding a simple diagram that I drew myself in a few minutes with simple "paint" software - featuring only circles and line segments that have been drawn by mathematicians and engineers alike for literally thousands of years - somehow violates any copyright rules, or any other wikipedia rules for that matter.  That said, my sincere respect for editors here leads me to not anticipate any further attempts by editors to tie themselves up in illogical knots of arbitrary "reasoning" in order to decrease the accessibility and value of this article ....  at least, not until they first remove all the diagrams from the sphere article, the circle article, the tesseract article, the angle article - and so on.  Spiral5800 (talk) 01:30, 16 August 2011 (UTC)

"Importance in Spaceflight" section has inadequate explanation
This section doesn't deliver what it promises, an explanation of why beta angle is importance in space flight. It expresses some relationships between what beta angle existed on the ISS and what the Space Shuttle was required to do but offers no clue as to why that's the case. Why does the orbiter go into "rotisserie" mode if the beta angle is great than 60 degress? Why can the orbiter only launch to the ISS during a beta cutout? Does flying in high beta angle turn astronauts into zombies? Does it cause moss to grow in the thruster nozzles? After reading I know beta angle is important but have no idea why. I assume it has something to do with temperature or light? 72.64.98.101 Steevithak (talk) 15:51, 21 December 2014 (UTC)

Improve diagram
The current diagram is not clear; the sun vector appears to be in the orbital plane. —Swpbtalk 19:36, 13 November 2015 (UTC)

Equation
There's an alternative formulation, which can be found in the Spacecraft Thermal Control Handbook, Volume 1, page 40;

They're just different. The formula is STCH is in terms of solar RA and DEC (in the equatorial coordinate system) as opposed to the given formula, which is in solar longitude (in the ecliptic.)

β(t) = arcsin ⁡ ( cos ⁡ ( δS (t) ) · sin ⁡ ( i ) · sin ⁡ ( Ω(t) - ΩS (t) ) + sin ⁡ ( δ S (t) ) · cos ⁡ ( i ) )

δS = solar declination ΩS(t) = solar right ascension

This is simpler in some ways, but they are equivalent.

Pgramsey (talk) 00:17, 10 September 2022 (UTC)