The Flat Earth Society

Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: spherical on May 09, 2019, 05:54:23 PM

Title: Angle and Length of a pole's shadow
Post by: spherical on May 09, 2019, 05:54:23 PM
I am trying to crunch numbers for two shadows, but for some reason it became complex:

What: A vertical pole 10 meters high with an arrow on top
Location: Close to Quito Equador (Lat: 0°, Long: 78°W), very good flat ground.
Date: March 20 2019 or 2020 (Equinox)
Shadow Time (#1): 09:00h (9am) local time, no Daylight Savings Time in Quito after 1993.
Shadow Time (#2): 16:00h (4pm) local time.

Based on FE map, I am interested to calculate the pole's shadows (#1 and #2) length on
the ground and the angle of arrow projection from the North Pole in degrees.

I'm having some difficulties with this math.

Some volunteers please? One decimal digit will be enough.
Tom Bishop's numbers would be nicely welcome.

Answer #1:  Length _____m,  Angle _____°
Answer #2:  Length _____m,  Angle _____°
Title: Re: Angle and Length of a pole's shadow
Post by: spherical on May 11, 2019, 04:41:16 PM
A modest contribution to help Tom Bishop, I made the drawing below, based on a FE map.
I am almost able to calculate the angles, just waiting Tom numbers for confirmation.
The shadow lengths on the ground are more difficult, due FE perspective and vanishing points.

(http://www.guidetrack.com/FE/shadow916.jpg)
Title: Re: Angle and Length of a pole's shadow
Post by: Tom Bishop on May 11, 2019, 07:27:22 PM
Read about the equinox here: https://wiki.tfes.org/Equinox
Title: Re: Angle and Length of a pole's shadow
Post by: spherical on May 12, 2019, 02:52:04 PM
Read about the equinox here: https://wiki.tfes.org/Equinox

Sorry Tom, found no answer on the link to help me calculate the angles requested.

No matter very tinny refraction of the sun's light on the atmosphere, an observer in Quito will see the 9am Sun on Mar20/21 pretty close to altitude 45° at azimute 90° (totally East).

Can you pretty please dedicate few minutes and calculate the angles and shadows sizes for me?

Oh, I just realize the 9am shadow length, because the Sun is at 45° it forms an isosceles right triangle, and the shadow will be exactly the same as the height of the pole, 10m.   Am I correct Tom?

(http://www.guidetrack.com/FE/quitopoleshadow.jpg)
Title: Re: Angle and Length of a pole's shadow
Post by: Rounder on May 13, 2019, 03:09:50 PM
I am trying to crunch numbers for two shadows, but for some reason it became complex:

What: A vertical pole 10 meters high with an arrow on top

I assume you refer to this monument?
(https://traveltime.com.ec/wp-content/uploads/2014/09/ciudad-mitad-del-mundo.jpg)


Shadow Time (#2): 16:00h (4pm) local time.
Curious as to why you chose 4pm instead of 3pm?  3pm would have a 45° elevation angle just like 9am does, but 4pm will not.
Title: Re: Angle and Length of a pole's shadow
Post by: spherical on May 13, 2019, 03:54:33 PM
Curious as to why you chose 4pm instead of 3pm?  3pm would have a 45° elevation angle just like 9am does, but 4pm will not.

45° is already there at 9pm, why repeat?
Now, 4pm was chosen exactly for the little offset on the shadow and angle, as a "control experience" and being high enough in the sky to suffer minuscule refraction on the atmosphere.

I wonder if Tom Bishop would have time to help with the numbers.
Title: Re: Angle and Length of a pole's shadow
Post by: spherical on May 29, 2019, 05:27:29 PM
Still waiting the numbers from Tom Bishop.
Title: Re: Angle and Length of a pole's shadow
Post by: junker on May 29, 2019, 06:18:11 PM
Still waiting the numbers from Tom Bishop.

There is absolutely no reason to bump this thread, especially if you have nothing to add to it. You are acting like Tom owes you something, I can assure you he does not. Have a warning for low-content, and since you are already on three warnings go ahead and have a few days off to review the rules.