How to Use Small Angle Formula + SUPERMOON & MICROMOON (Astronomy)
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- Опубліковано 2 лип 2024
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✵✵✵✵✵ How to Use Small Angle Formula
SUPERMOON & MICROMOON (Astronomy)
Have you been surprised by all the headlines about SUPERMOONS lately? What IS a Supermoon, and is it really all that big? How do astronomers describe the visual size, or APPARENT SIZE, of objects in the night sky?
One of the essential tools astronomers use is the SMALL ANGLE FORMULA. This is a way to quantify this relationship: for a given diameter, the ANGULAR SIZE of an object decreases the farther away it is.
Today we’ll explain this formula, and work an example problem using the phenomena of SUPERMOONS and MICROMOONS. A Supermoon is a full moon at the closest point in the moon’s orbit (PERIGEE) whereas a Micromoon is a full moon at the point in its orbit farthest from Earth (APOGEE).
Supermoons aren't actually any bigger. The moon's diameter, or linear size, does not change. But its apparent size, or ANGULAR SIZE, does change! And that’s what we are quantifying when we use the SMALL ANGLE FORMULA. It involves a little Trigonometry.
✵✵✵✵✵ CHAPTERS
You can jump to chapters in the video here:
0:00 Introduction
0:43 Angular Size
1:19 Setting up the Trigonometry problem
2:03 Small Angle Formula
2:39 Explaining units, arc-seconds
3:42 Calculation: Supermoon vs Micromoon
5:24 Challenge Problem: The Sun at Perihelion vs Aphelion
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Special Thanks go out to @LaunchPadAstronomy! Liliana and Kimberly attended the annual Launchpad Astronomy Workshop for writers, led by astronomy professors Mike Brotherton and Christian Ready. Read more about our experience here:
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Presented by Liliana De Castro
Written by Kimberly Hatch Harrison
Produced by Kimberly Hatch Harrison & Michael Harrison
Pukka 9RTTEFFWIARIH5IJ
Sunkiss ANKYFOP1U1ZYTLGB
#Astronomy #Supermoon #SmallAngle
After watching this lesson on the Small Angle Formula, try solving the Challenge Problem: What is the difference in Apparent Size (aka Angular Size) of the Sun when it's at PERIHELION (closest point to the Earth) versus APHELION (farthest point from the Earth)? We solve this problem on our website so you can check your work here: www.socratica.com/lesson/small-angle-formula-problem
Os seus conteúdos são sem igual, em qualquer idioma, porém por obséquio, volte a fazer vídeos em português. Estamos sentindo muito a sua faaaallta....
Bem vinda de volta, estávamos com saudades.
I think this is the most underrated channel in youtube...... btw love your content....i have seen your whole series of abstract algebra...❤️
Thank you for your kind words! We're so glad you're watching!! 💜🦉
Astronomy!! Yeah!
Let's go Let's go!! 💜🦉
Happy to see this series return.
Glad to see you're making more videos.
Our Socratica Astronomy series is back! Bookmark the playlist here:
✷ socratica.link/Astro_Playlist
We also ask you join our STELLAR email list so we can notify you when new videos go live:
✷ snu.socratica.com/astronomy
(Don’t rely on the YT algorithm to show you what you’re really interested in!)
Hi Socratica... thank you for come back!!!
Amo tanto seus vídeos!!!♥♥
I watched your abstract algebra videos, that was very amazing and helpful to me, so thank you so much...🧡
We're so glad to hear you enjoyed Abstract Algebra! We had so much fun making those videos!! 💜🦉
Yeah. It was the same for me. High quality compact videos👍
Would love and devour any further abstract algebra videos! (I doubt I'm alone in saying that.)
@@Socratica can you please do more videos like the Abstract Algebra one? For example Algebraic Geometry, Algebraic Topology, Differential Geometry, Functional Analysis etc.? That would be amazing!
A charming and intelligent presentation. Who could ask for more?
Simply the best!
Thanks you have the clearest expinations. I have subscribed. Thank you very much.
I love the smallangle formula, and thanks for how is is derived, saves so much time scratching your head.
My favourite youtuber since 2017
Wow, amazing way of teaching ❤ Thank you 🤩
Thanks for your excellent presentation
Excellent presentation. Very clear and no nonsense
Thank you for your kind message! This is our biggest goal, to help people understand more. 💜🦉
your video's are just awesome, , .... keep 'em coming. Off topic but would love to see a Galois application video form you guys.
Love your videos 👍
thanks for the video i stood up all night anticipating this video thats why im the first like and view and comment lol
Premiere Party checking in!! 💜🦉
now watching socratica when im not doing anything becomes now a habit, thanks to liliana
The production quality of this channel is HUGE, I can't even imagine how much work went into it. You motivated the topic very well (nice intro!) and you covered the topic superbly. Keep it up!
Thank you so much for your kind comments! After peeking at your channel, we know you understand how much work goes into making videos. Happy to learn about your channel, and happy to connect! 💜🦉
@@Socratica Wonderful, I just sent you an email.
saudade socratica portugues
Very cool
Nice...
How come this video only has 37k views?! I love all your videos!
It always takes our videos a while to be discovered! Thanks for your kind comment-we love making these videos!! 💜🦉
Thanks!
Thank you so much for your kind support, Socratica Friend! 💜🦉
Wow! The small angle formula makes so much sense given that the derivative of tan(theta) when theta is close to 0 is approximately 1.
I noticed that because the small angle formula is theta = d/D, then if we just want to know the relative ratio between the angular sizes of the moon at perigee and apogee, we can just simplify it to the ratio between the distances from Earth at apogee and perigee (notice that apogee and perigee get swapped in the numerator and denominator), so that we don't have to calculate the arc-seconds if we don't want to. Distance at apogee divided by distance at perigee is 405 million km divided by 360 million km is 1.125.
So for the sun, the ratio between the angular sizes of the moon at perigee and apogee is 152 / 147 = 1.034
¡Gracias!
Thank you for your kind support!! 💜🦉
Wow! Liliana - give me that wicked look (@3:41) and I'll follow you anywhere. 😉 Thanks for making this presentation fun.
Love from India this channel is jem
I love this channel. Saludos desde México.
Hello to our Socratica Friends in México!! 💜🦉
YOU R IN NETFLIX!!!. AMO ESTE CANAL. LASTIMA Q YA NO ESTE EN CASTELLANO. ( The mind explained-focus )
Atriz inteligente, se vira em qualquer trabalho.
Your videos are awesome I saw that you have an array of python videos
However I was wondering and I think it would actually be great if you can actually make a python 3 crash course
Your videos are clear and concise and that is why I’m so looking forward to the python 3 crash course
Thanks for your encouragement! Love the idea of a quick "Jump into Python 3" mini-course.
Wow man
YOOOOOOOOOOO, I stumbled upon some gold !!!!!
Meu Deus eu tô chocado com tua dicção em inglês e português, esperamos atenciosamente pela volta do canal em português
It's kinda similar to a parallax thing I've studied a little before, can you cover that up too?
Moon is good but you are also good
#Please make videos on Vector Space, Riemann Internal !
I've seen the Moon so much, i can tell the difference at a glance now.
Hi , I have a question ,I have one list :
country = [ Australia , america , England , Spain]
If i want to choose 2 of them random for (List A) and choose 2 of them random for (List B ) and values of two lists arent same (not equal to gether)
Can You say which code should i write🥺
Ok, now I want more.
More astronomy videos on the way! 💜🦉
Make a video on choosing career!
This is a great idea for our study tips series! We did make one about choosing your college major: bit.ly/CollegeMajor
I have a question looking at beatleguice I get .04188 arc seconds google says something li .047 anyway I'm told we cannot perceive less than 1 arc second. and yet we can see this star normal vision. Any answers appreciated...wonder what would be a minimum for normal vision??
Jyotish Sastra (astronomical science), Sulbha Sastra (geometry), Ganit Sastra (mathematics) are some Vedic Literature from thousands of year old knowledge.
What's the calculation for Nibiru?
May I ask a question?
Volta pra gente
I tried looking directly at the sun once and I started seeing things in a purple perspective
Does 12% difference is apparent size mean that the diameter appears to be 12% bigger for a supermoon compared to a micromoon?
In this case, the supermoon covers 25% more space in the sky than the micromoon because from earth, it appears to be a 2D object.
Am I right?
You'd better use "spatial angle" as a measure for such a comparison
There are earth's atmospheric effect that occasionally affect the moon's apparent size.
¿Cuántos idiomas hablas y cuál es la que aprendiste en la infancia?
OK, let me ☆first come and say "hey"
But ☆after that I should say it's the earth atmosphere that causes big moon because of bigger deflection angle while it approaches the horizon level.
At the end ☆ I wish I could show this video to my TA to convince him Arctan(D/d) ~D/d for such tiny angles and the answers they get from their calculators are sort of computational errors.
caralho essas equações vão ser ótimas pra me distrair futuramente.
infelizmente minha matemática és bem pobre no momento não tenho conhecimentos necessários pra essas equações
Porque vcs não fazem mais vídeos traduzidos no português é uma pena fazem falta 😢😭
Não Seria melhor você aprender Inglês de una vez?
BRASIL
Kepler’s laws are mass and force free. Newton gummed up physics: downhill since then. Galilean relative motion has the earth approaching the released object. D=1/2at^2 part of the Atomic Expansion Equation. Indeed the moon ( and all atoms/ atomic objects) double in’size’ every 19 minutes.
Liliana S2
Cuando en castellano?. No te olvides de NOSOTROS. Saluditos
The Sun would be cool!
Volte a fazer vídeos para gente
There's also the effect - it's an illusion - that the moon appears larger at the horizon.
We love watching that happen when the moon rises!
405/360 =>12.5% and 152/147 => 3.4% , why use that formula to compare positions of the same heavenly object?
Very good presentation. But why is it necessary to teach trig to adults? Is it because they regret not having paid attention when they were being taught at age 14?
If you flip this around, we hope that people will find it reassuring that you can actually cover a lot of science without requiring much advanced math.
The other thing we learned while teaching is that most education is heavily "siloed"-so a student will learn how to graph an exponential equation in math class, but they look blankly at it in a science class. They almost have to start from scratch to understand how to apply math in a scientific context.
@@Socratica
Fair point, but again it comes down to bad teaching.
I tried to explain this to my 9-year old son ho was skeptical at first until I had him watch this video.
Hooray!! Thanks for sharing, how cool is that that your son is learning this now.
if library of alexandria was a person it'd be Socratica
Thanks, Liliana! Now, can you mathematically explain why werewolves get triggered by the full moon?
Esta moça e do Brasil.
*Equador
Got to b an easier (better) way
Trigonometry, my arch nemesis. Or maybe that title belongs to calculus.
We'll win you over to the mathy side yet. 💜🦉
@@Socratica If they only knew that trigonometry is embedded in linear equations... Yup the tangent is hiding in y=x.
So, ladies, you who state and tend to show that your estimation of distances is horrible but also are used to admiring and hyping that 12% of change -- please choose your real side.
…damn …. That moon sure knows when to speed up or slow down so we can only see the same “face”… Ohh, and the gravity that makes that happen is not in the slightest effected by the Big Bang expansion….. hmmmm…. I smell a rat or a dead cat…. not sure which but that’s Quantum theory for you…. You never know until you look!
Can't stop laughing 🤣 big D over little D
Big D means Dallas in the US
It’s cheese. Fake news
Hero(Achilles)
Philosopher King(Virtuous Soul) 1.) atoms are orderly, motion is chaotic
2.) aether is real
"Gold for the Bronze 3.) Eratosthenes was right!
~ 4.) circle square triangle
Bronze for the Gold" 5.) pentagram is alpha
The elite shall have no Gold
and create no soul ensuring Bronze (*) < 0
always turns to Gold & Gold to Bronze...
Dr. Gord aka Carl ATHF
p.s. I hope your having a nice roygbiv
the problem with the world today is there'-s too much pop'n and not enough shine+
Bicycle 5-2 4/4 do re mi fa so la ti do
Dodecahedron its the shape of the universe ua-cam.com/users/shortsBidsCu9jWpk