Macarios

Solar noon Sun altitude tool, to help with Zetetic approach
« on: January 22, 2018, 07:35:17 PM »
I was told that Zeteticism explores by inquiry; it is investigative method.
Correct me if I'm wrong.

Here is some tool for those who would like to investigate Sun's behavior, or use Sun itself for measurements on ground.
(This is not about Flat or Globe model, we won't create any model here.
This is purely about observations and measurements in reality around us.)

Once you verify it, SunCalc have all data about Sun for your inquiries.
Also, timeanddate.org, if you need more.
(If you don't have time to verify, people live there, they would expose errors by now.)

This is how:

Mark latitude of your location, measure Sun altitude for solar noon.
One way to measure is to poke or find straight stick/pole vertically in the ground and then measure both, stick and shadow.
When the shadow is shortest (Sun highest), it is solar noon.
Sun altitude is ARCTAN(STICK / SHADOW).

Compare with formula marked as (1) below.
For Equinox (March 21, or September 22) compare with formula marked as (2).
(Sun for Equinox is directly above Equator and declination is zero.)

Compare measured values with values from https://www.suncalc.org/.
If they match, you can ask trustworthy people on other latitudes to do measurements for you.
Compare their measurements with SunCalc.org
If they match too, you can confidently use the site for any Sun data you might need.
(Set solar noon by moving slider on top of the window to the middle of the day segment,
until you get azimuth of the Sun as close as possible to 180 degrees, or to 0 if location is south.)

Ofcourse, if you want to know Sun altitude for Equinox, you can just read latitude of desired place and subtract from 90.
Declination for Equinox is zero and this is faster than opening SunCalc for Sun altitude.


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Formula for solar noon Sun altitude

Sun's daily apparent trajectory over the sky has its highest point.
Moment when Sun is at that point is called solar noon.
It is around 12pm, plus or minus several minutes, depending on observer's longitude within the time zone.
During Daylight saving it is around 1pm, plus or minus mentioned several minutes.

Sun altitude for solar noon depends on latitude, and on season.
For Equinox, Sun is directly over the Equator and has altitude of 90 degrees there.
At the same moment, at 45 degrees north or south has altitude of 45 degrees, at 30 degrees has altitude of 60 degrees and at 60 degrees has 30 degrees.
People noted that.

People also noted that with seasons those angles change.
At Equator for northern summer Sun altitude is moved north, and for winter south, taking summer there.
People this deviation named Sun's declination.
Declination is changing between 23.44 degrees north for summer solstice and 23.44 degrees south for winter solstice.

So, they come up with formula for solar noon Sun altitude:

A = 90 - L +/- D    ...... (1)

where A is Altitude, L is observer's latitude, and D is declination.

It is obvious that for Equinox declination is zero, and altitude is

A = 90 - L          ...... (2)

Here is how to calculate Sun altitude for any solar noon anywhere:


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Re: Solar noon Sun altitude tool, to help with Zetetic approach
« Reply #1 on: January 24, 2018, 02:24:39 AM »
One of my "someday if I have time" project ideas is to compile a list of webcams at various latitudes pointed at tall objects of known height.  Traffic cameras are where I started looking, since they often have vertical objects like streetlights, signs, etc in the image.  Ideal would be to find a bunch of them along the same longitude so they all have solar noon at the same time (give or take a little bit).  It shouldn't be difficult to figure out the shadow length within a reasonable margin of error.  Then an individual could check the sun angles at a wide range of latitude for oneself, without relying on anyone else for data.

Someday, if I have time.
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Macarios

Re: Solar noon Sun altitude tool, to help with Zetetic approach
« Reply #2 on: January 24, 2018, 03:55:03 PM »
Basic distance tool:

If you verified your Sun tool (I use suncalc.org), you can now use it to find subsolar point at any time.
Simply enter the date and time, and read the Sun altitude A.
Then move location south by 90-A (or north if you are at south side of Earth).
If you are 30 degrees north and have A=50 degrees, then go 90-50=40 degrees south and you will find subsolar point at 10 degrees south.
When you set location, check if A is 90. If not, adjust location.

Mark latitude and longitude, then find location at same latitude to the east where subsolar point was some time ago.
Mark time and new longitude.
You will see that difference of longitudes always confirms that Sun, and subsolar point, travel 1 degree every 4 minutes.
If longitude difference between two locations is 10 degrees, then the time difference is 40 minutes.

When subsolar point is at one location, all locations on the same meridian, north and south of it, have solar noon at the same moment.
So, if we investigate locations that are not between two Tropics, we can use speed of solar noon.
Actually it is enough to use solar noon in or out of said area, as long as we use same latitude.

I used solar noon at Equator, between four cities there, in Africa.
Jilib Somalia - 42.78 degrees east
Kampala Uganda - 32.57 degrees east
Mbandaka Congo - 18.29 degrees east
Libreville Gabon - 9.47 degrees east
all four of them within narrow band of 0.5 degrees at Equator.

I also used distancecalculator.net for distances between them:
1. Jilib to Kampala - 1135 km - longitude difference 10.21 degrees - solar noon speed 1135 / 10.21 * 15 = 1667.5 km/h
2. Kampala to Mbandaka - 1591 km - longitude difference 14.28 degrees - solar noon speed 1591 / 14.28 * 15 = 1671.2 km/h
3. Mbandaka to Libreville - 984 km - longitude difference 8.82 degrees - solar noon speed 984 / 8.82 * 15 = 1673.46 km/h

All models, Flat or Globe, have same circumference of Equator (CE) to be 40070 km.
Form 1. we have CE = 1667.5 * 24 = 40020 ... error of 0.125%
Form 2. we have CE = 1671.2 * 24 = 40109 ... error of 0.097%
Form 3. we have CE = 1673.46 * 24 = 40163 ... error of 0.232%

All errors way below 1%.

Now let's try full span from Jilib to Libreville:
Distance 1135 + 1591 + 984 = 3710 km
Longitude difference 42.78 - 9.47 = 33.31 degrees
Solar noon speed 3710 / 33.31 * 15 = 1670.67 km/h
Calculated Equator circumference 1670.67 * 24 = 40096 km - error of 0.064%.

Looks like our distancecalculator.net works well.

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Now you can trust this, or you can do same thing yourself for other places (or other distance tool).

Once you verify you have two tools:
One tool for Sun and one for distances.

I have SunCalc.org and DistanceCalculator.net.

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When people know that anone can verify things for themselves, they are careful what they publish.
For daily news it is not so important, because people read newspaper and watch TV for entertainment, and it will all be forgotten soon.

For web pages with scientific data the situation is different. Same pages stay online for long time. They have to be accurate.

Macarios

Re: Solar noon Sun altitude tool, to help with Zetetic approach
« Reply #3 on: January 25, 2018, 12:15:18 PM »
Next step could be comparison of distances shown between DistanceCalculator.net and Google Maps.
Why?
Because in Google Maps you have latitudes, longitudes and distances together.
Collecting those data together from one place is easier and gives you more time to focus on relations you want to investigate.
I tested for myself, and came to conclusion that I can trust Google Maps.

You have two choices:
You can trust me, and people who read distances from Google Maps on daily basis.
Or you can make your own list of places and compare distances shown between them in Distance Calculator and in Google Maps.
« Last Edit: January 25, 2018, 12:17:30 PM by Macarios »