Dear high school/college students, Here's an application of hyperbolas that you never learned

Save
2 years ago
51

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/ZachStar/ . The first 200 of you will get 20% off Brilliant's annual premium subscription.
Floating Globe: https://stemerch.com/collections/science-toys/products/led-magnetic-levitation-globe
QED shirt: https://stemerch.com/collections/qed
STEMerch Store: https://stemerch.com/

â–ºFollow me
Odysee: https://odysee.com/@ZachStar:0
Instagram: https://www.instagram.com/zachstar/
Twitter: https://twitter.com/ImZachStar

â–ºFull answer (spoilers)
The path traced out by the tip of the shadow can be...
1) A circle (if you are on one of the poles during their summer)
2) An ellipse (if you are in the Arctic or Antarctic circle, but not on either pole, during a day where the sun doesn't set)
3) A line (this happens if you are anywhere on Earth besides the poles, during either the Spring or Autumn equinox)
4) A parabola (this happens if you are in/on the Arctic or Antarctic circle during a day where the sun BARELY sets, meaning it sets and rises in the exact same location. This happens twice a year for any point in those circles. If you are ON one of the circles, then it will happen during the Summer or Winter solstice for the Arctic and Antarctic circles respectively).
5) A hyperbola (If you aren't in one of the places listed above on those specific days, then you'll get this shape. This is what happens at most places on Earth throughout most of the year).

â–ºResources
Interactive tool: https://www.geogebra.org/m/AHEgBVUd
Video showing linear path on Equinox: https://www.youtube.com/watch?v=Wz-nXJYUDhI&t=1s

Support the Channel: https://www.patreon.com/zachstar
PayPal(one time donation): https://www.paypal.me/ZachStarYT

Join this channel to get access to perks:
https://www.youtube.com/channel/UCpCSAcbqs-sjEVfk_hMfY9w/join

2D Graphing Software: https://www.desmos.com/calculator

Animations: Arkam Khan (For contact info go to https://www.arqum333.com/)

Check out my Spanish channel here: https://www.youtube.com/channel/UCnkNu2xQBLASpj6cKC8vtpA

â–ºMy Setup:
Camera: https://amzn.to/2RivYu5
Mic: https://amzn.to/35bKiri
Tripod: https://amzn.to/2RgMTNL

â–ºCheck out my Amazon Store: https://www.amazon.com/shop/zachstar

Loading comments...