Uploaded October 2021 | Updated September 2026, 3 weeks ago
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!)
✵✵✵✵✵ 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
We hope you will post your answers to the Challenge problem on social media. Be sure to tag Socratica so we can come say hi!
✷ Facebook: facebook.com/SocraticaStudios
✷ Instagram: instagram.com/SocraticaStudios
✷ Twitter: twitter.com/Socratica
✵✵✵✵✵ THANKS TO OUR SOCRATICA FRIENDS
This video was made possible by the generous support of our VIP Patrons on Patreon. We hope they know how much we appreciate them!!
Philip Rice, Colin Negrych, Israel Scott Grogin, Christopher Kemsley, ERIC ECCLESTON, Michael Shebanow, maltev, Antoine, Sravana Karnati, Jeffrey A. Smith, David Brumley, Vishal Dalal, Robert Collins, David Robb, Ryan Richardson, Claudio Corbetta, cmumulle, lars, Terry Wang, Matt Jordan, James, Rusty Newton, William Rassieur, Massimiliano Pala, Rob Neal, Saneesh Joseph,Scott Dreblow, Nunya Beezwax, Justin Fritz, Chris Kunstt, Marcos Silveira, Jeremy Shimanek, Kavon Johnson, Nikita Lesnikov, Charles Southerland, Alvin Khaled, Kevin B, Deeptanshu Malik, John Krawiec, Umar Khan, Steppenturtle, MdeG, Carlos Araujo, and the unstoppable amazing Tracy Karin Prell!
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:
✷ launchpadworkshop.org
✷ socratica.com/the-socratica-method/launchies
Mike writes hard sci-fi! Read his book Star Dragon:
✷ amzn.to/3GsKaYd
Christian generously reviewed this script and offered advice. Be sure to check out his channel “Launchpad Astronomy” where your friendly neighborhood astronomer keeps you up to date on all the latest in the astro world.
✷ youtube.com/c/ChristianReady/videos
✵✵✵✵✵ SUPPORT SOCRATICA
You can support our channel by making purchases using our affiliate links. These are books and other resources we have used ourselves, and can personally recommend. A small percent of your purchase (usually 1-2%) will be shared with Socratica by the vendor.
We highly recommend the Astronomy textbook “Universe” by Roger Freedman et al:
✷ 9th Edition amzn.to/2so6Ums
✷ 10th Edition amzn.to/2tfBjUe
✷ 11th Edition amzn.to/3mhxqvv
Moon Globe with explorations
✷ amzn.to/3me3kZM
Celestron 6-inch computerized telescope
✷ amzn.to/3mhdysk
Our STUDY TIPS BOOK is now available!
How To Be a Great Student
✷ e-book: amzn.to/2Lh3XSP
✷ Paperback: amzn.to/3t5jeH3
Or read for free when you sign up for Kindle Unlimited:
✷ amzn.to/3atr8TJ
Shop Amazon Used Textbooks - Save up to 90%
✷ amzn.to/2pllk4B
✵✵✵✵✵ MORE WAYS TO SUPPORT SOCRATICA
JOIN this channel for cute owl badges:
✷ bit.ly/SocraticaBadges
SUBSCRIBE to Socratica:
✷ bit.ly/SocraticaSubscribe
SUPPORT Socratica on Patreon:
✷ patreon.com/socratica
DONATE with Paypal:
✷ paypal.me/socratica
GIFT CRYPTO with Bitcoin:
✷ Our address is bc1qda47tgfyk67lxa7yqn8y5m02hjcglghsd5c58n
✵✵✵✵✵ CREDITS
Presented by Liliana De Castro
Written by Kimberly Hatch Harrison
Produced by Kimberly Hatch Harrison & Michael Harrison
Pukka 9RTTEFFWIARIH5IJ
Sunkiss ANKYFOP1U1ZYTLGB
#Astronomy #Supermoon #SmallAngle
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!)
✵✵✵✵✵ 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
We hope you will post your answers to the Challenge problem on social media. Be sure to tag Socratica so we can come say hi!
✷ Facebook: facebook.com/SocraticaStudios
✷ Instagram: instagram.com/SocraticaStudios
✷ Twitter: twitter.com/Socratica
✵✵✵✵✵ THANKS TO OUR SOCRATICA FRIENDS
This video was made possible by the generous support of our VIP Patrons on Patreon. We hope they know how much we appreciate them!!
Philip Rice, Colin Negrych, Israel Scott Grogin, Christopher Kemsley, ERIC ECCLESTON, Michael Shebanow, maltev, Antoine, Sravana Karnati, Jeffrey A. Smith, David Brumley, Vishal Dalal, Robert Collins, David Robb, Ryan Richardson, Claudio Corbetta, cmumulle, lars, Terry Wang, Matt Jordan, James, Rusty Newton, William Rassieur, Massimiliano Pala, Rob Neal, Saneesh Joseph,Scott Dreblow, Nunya Beezwax, Justin Fritz, Chris Kunstt, Marcos Silveira, Jeremy Shimanek, Kavon Johnson, Nikita Lesnikov, Charles Southerland, Alvin Khaled, Kevin B, Deeptanshu Malik, John Krawiec, Umar Khan, Steppenturtle, MdeG, Carlos Araujo, and the unstoppable amazing Tracy Karin Prell!
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:
✷ launchpadworkshop.org
✷ socratica.com/the-socratica-method/launchies
Mike writes hard sci-fi! Read his book Star Dragon:
✷ amzn.to/3GsKaYd
Christian generously reviewed this script and offered advice. Be sure to check out his channel “Launchpad Astronomy” where your friendly neighborhood astronomer keeps you up to date on all the latest in the astro world.
✷ youtube.com/c/ChristianReady/videos
✵✵✵✵✵ SUPPORT SOCRATICA
You can support our channel by making purchases using our affiliate links. These are books and other resources we have used ourselves, and can personally recommend. A small percent of your purchase (usually 1-2%) will be shared with Socratica by the vendor.
We highly recommend the Astronomy textbook “Universe” by Roger Freedman et al:
✷ 9th Edition amzn.to/2so6Ums
✷ 10th Edition amzn.to/2tfBjUe
✷ 11th Edition amzn.to/3mhxqvv
Moon Globe with explorations
✷ amzn.to/3me3kZM
Celestron 6-inch computerized telescope
✷ amzn.to/3mhdysk
Our STUDY TIPS BOOK is now available!
How To Be a Great Student
✷ e-book: amzn.to/2Lh3XSP
✷ Paperback: amzn.to/3t5jeH3
Or read for free when you sign up for Kindle Unlimited:
✷ amzn.to/3atr8TJ
Shop Amazon Used Textbooks - Save up to 90%
✷ amzn.to/2pllk4B
✵✵✵✵✵ MORE WAYS TO SUPPORT SOCRATICA
JOIN this channel for cute owl badges:
✷ bit.ly/SocraticaBadges
SUBSCRIBE to Socratica:
✷ bit.ly/SocraticaSubscribe
SUPPORT Socratica on Patreon:
✷ patreon.com/socratica
DONATE with Paypal:
✷ paypal.me/socratica
GIFT CRYPTO with Bitcoin:
✷ Our address is bc1qda47tgfyk67lxa7yqn8y5m02hjcglghsd5c58n
✵✵✵✵✵ CREDITS
Presented by Liliana De Castro
Written by Kimberly Hatch Harrison
Produced by Kimberly Hatch Harrison & Michael Harrison
Pukka 9RTTEFFWIARIH5IJ
Sunkiss ANKYFOP1U1ZYTLGB
#Astronomy #Supermoon #SmallAngle
