How Simple Line of Sight Proves Planet Earth Is Not Flat
How does one calculate a visual line of sight for objects at a given height that are distant enough that the Earth’s curvature needs to be considered?
Why might a photographer find such information useful? Some examples of what one might want to know: Whether or not a distant mountain can be seen from the top of another mountain. By how many degrees the rising full moon will be blocked by a distant mountain range in order to estimate whether it might be bathed in warm sunset light.
Whether an alpine lake will catch sunset alpenglow or be blocked by a nearby ridge to the west.
The Earth has a radius of approximately 3965 miles. Using the Pythagorean theorem, that calculates to an average curvature of 7.98 inches per mile or approximately 8 inches per mile (squared). The distance to the horizon in miles from height of an observer is approximately equal to 1.23 times the square root of the height in feet.
For example 1.23 times the square root of 8 divided by 12 equals 1 mile. Inversely given the horizon distance in miles, the height in feet required to be visible equals the distance in miles squared divided by 1.513. The second example above concerning the Moon rising over a distant range also requires some topographic map calculations using the tan trigonometric function.
Thus if a peak rises up 1844 feet at a distance of 10.0 miles or 52,800 feet, it will form an angle of 2 degrees with a theoretical flat horizon. The tan is 1844/52800=0.0349 or 2 degrees. However due to the Earth’s curvature, it would appear as though it was only 1778 feet tall with the lowest 66 feet below the horizon.
Disregarding refraction, on a perfectly flat plain like the Bonneville Salt Flats in Utah, if one’s eyes are 9 inches above the ground, one would be able to see at night a flashlight one mile distant laying on the surface but not if one lowers their eyes to 7 inches. For example per the above diagram, that might be between the tangent point and Object B.
If a 64 inch tall person’s eyes are at a height of 60 inches or 5 feet, they might be able to see at night, a flashlight laying on the ground at 1.23 the root of 5 = 2.75 miles. They would also be able to see another like standing person’s headlamp twice that distance or at 5.5 miles distance, since each person would be able to see the midway tangent point.
For example per the above diagram, that might be between the Object A and Object B. Likewise one of those person’s would be able to see the last inch of a 9 inch tall object 2.75+1.0=3.75 miles distant. Lake Tahoe is 12 miles wide and 22 miles long.
For a person’s eyes at a height of 5 feet above the water on the south shore, a streetlight at night on the north shore needs to be up on a nearby hill at least 370 feet above the shore, else it is below the horizon.
Mount Shasta rises 14,262 feet about 50 miles north of the end of the Sacramento Valley. According to the below chart, one ought to be able to see the mountain from about 147 miles away. Elevations south in the valley at that distance are a relatively insignificant 200 feet in elevation.
By checking a map, one will see that Shasta ought to be visible on clearest days once one has gone just a few miles north of the town of Colusa along the Sacramento River. Near Colusa are the Sutter Buttes that rise to as high as 2117 feet.
Thus the Buttes might be seen from the top of Mount Shasta. A bit less than 100 miles south rising above San Francisco Bay to the east, Mount Diablo rises to 3849 feet. From the chart, one can see that volcanic peak is about 2800 feet too short to see Shasta.
In the real world there are however atmospheric effects of mainly ray refraction that tend to cause objects beyond the theoretical horizon to sometimes be visible. Thus the visible setting sun is usually a little below the theoretical horizon. In like manner, the effect is to increase the apparent height of distant peaks.
Some approximate heights and distance in the below table:
Distance Height Miles Feet -------------------------- 1.0 0.67 1.23 1.0 3.0 5.95 3.9 10 6.0 23.8 10 66 12.3 100 20 264 30 595 39 1000 40 1060 50 1650 60 2380 70 3240 87 5000 100 6610 110 8000 120 9520 123 10000 129 11000 135 12000 140 13000 146 14000 148 14496
See more here: davidsenesac.com
Header image: Vox
Please Donate Below To Support Our Ongoing Work To Defend The Scientific Method
PRINCIPIA SCIENTIFIC INTERNATIONAL, legally registered in the UK as a company 
incorporated for charitable purposes. Head Office: 27 Old Gloucester Street, London WC1N 3AX.
Trackback from your site.
Alcheminister
| #
VERY simplified.
Very few people consider that the atmosphere is essentially a “fluid” and that light indeed does not travel in a straight line, as a result.
Density gradients (one of the mistakes Maxwell made was considering the aether as constant, due to his perspective, observational limits and perhaps other intentional bastardizations).
There simply is no “space”.
Reply
Herb Rose
| #
Hi Alcheminister,
Minor correction. There is no empty space. The size of an object is determine by the fields (both electric and energy) that it radiates, not by its matter. These fields continue to expand until they meet fields radiated by other objects of equal strength. There is no “space” between the objects and the distance from one object to another is from the equilibrium point of their fields to the source of the other object’s fields. The equation (for magnets) should be M3 = M1/d1 + M2/d2, not F = M1M2/d^2. The elemental hydrogen atoms found in “space” have a diameter of 1 cm.
Herb
Reply
Mark Tapley
| #
This curvature of the earth explains why sailing ships far away, appear to be approaching uphill.
Reply
jamesbbkk
| #
Perspective and diminishing angular resolution (or increasing angular resolution in your example) also explain this apparent phenomenon. Appearing to be approaching uphill /= actually approaching uphill.
Reply
Squidly
| #
It amazes me that there are actually people stupid enough to honestly believe that our Earth is flat. Just boggles the mind.
Reply
Alcheminister
| #
Either the notion of a flat or a round earth is, kinda wrong. Coz flat would be a plane, and round would be a sphere. Both of those are convex. The Earth is clearly not convex, unless you’ve not seen valleys or mountains.
Reply
Mark Tapley
| #
Hi Squidly:
There are a lot of them because of the disinformation artists on sites like Bitchute. The technique is to submerge the nonsense in with something that is real. This is commonly done with political issues as when Alex Jew Jones covers for Israel and the Zionist puppet Trump for the fake right wing.. There are even lots of people being sucked in by sites promoting space aliens. The Zionist operative Hitler is still very popular with the white nationalists crowd and lots of people are roped in by the environmental front groups run by the global elite pushing the climate change narrative. The nuclear weapon scam started almost 80 years ago with the fire bombing of Hiroshima and Nagasaki is still going strong to keep the goyim in fear. One of the most effective psy ops. of all time has to be the germ theory pathogen scam begun by Pasteur and ramped up by the Rockefeller foundation, that founded the criminal CDC, paved the way for big Pharma and launched the blood toxin fake vaccine programs like Polio, measles and MMR, conditioning the sheep for the present fake virus and deadly graphene oxide injections.
https://www.bitchute.com/video/IsIZBFsGZfEo/
https://www.bitchute.com/video/qjiBAPIA6Pnv/
Reply
Artelia
| #
I went to a measles party and caught measles as a kid, as did my brother. My eldest had measles despite having had two jabs. Another child seemed to get chicken pox twice unless it was something else one of the times.
Reply
jamesbbkk
| #
That’s a big list of major scams. But NASA at $63,000,000 per day is for sure not among them? How to sort the nonsense from something that is real?
Reply
rob
| #
The Flat Earth People are just ‘having a laugh’, in today’s parlance, trolling. A visit to the Flat Earth Society webpage will confirm that. They even deny gravity!
You can become a member, anonymously if you wish.
2400 years ago the circumference of Earth was calculated to be 25,000 miles by Eratosthenes of Alexandria, and that’s just the earliest recorded example. Three hundred years before that Pythagoras had proposed a spherical Earth.
But also, in philosophical/scientific/relativistic terms, if humans were in their proper place without the enhancements of technology the world would indeed be perceived to be flat.
Reply
Mark Tapley
| #
Hello Artelia:
The measles “virus” is what microbiologist Stephan Lanka used in the German Supreme court to prove that viruses do not exist. He still has 1.5 million euro reward for anyone who can prove to the court the existence of any virus. A few years ago the Jew MSM had a big ruckus about a bunch of kids at (((Disney Land))) that got the measles. Later it was discovered that almost all of them had been “vaccinated.” It is now well known that kids that go through the typical childhood ailments without any blood toxin injections are healthier for life and have less problems.
https://www.bitchute.com/video/AIJ4pE3aBHgC/
https://www.bitchute.com/video/aPjT6t8N2cyY/
Reply
Linden
| #
When flying at full altitude on Concorde (which I was privileged to do) the curvature of the earth was very clear indeed.
Reply
jamesbbkk
| #
Neil Tyson says you cannot see curve at 3X airplane altitude (c. 30,000 ft.). Was Concorde at c. 40,000 ft. when you thought you saw this? https://twitter.com/neiltyson/status/431554750119550976
Reply
ant I
| #
Not me but this guy thinks your wrong. https://nobulart.com/the-plasma-event/
Reply
Tom
| #
Oh heck…I always thought the earth was a buckwheat pancake covered with butter and syrup with lumps of chocolate chips for mountains.
Reply
Jerry Krause
| #
Hi PSI Readers,
What phenomena to “bend” light (radiation) are likely to have been observed by humans since their creation??? “Now the LORD God had planted a garden in the east, in Eden, and there he put the man he formed. … A river watering the garden flowed from Eden; from there it was separated into four head waters.” (Holy Bible, Genesis 2: 5, 10)
So the man could have seen that light was reflected from the smooth surface of a river and seen that the light which penetrated to a river’s bottom was refracted, if the man looked as we can look today.
Today, astronomers observed that we see the sun rise over a horizon before it should. And this observation is explained by the phenomenon of refraction by the atmosphere because its refractive index changes as its density changes as it’s altitude changes.
And at some.previous time I have noted that the Sun must have an atmosphere which bends the direct radiation from the sun as its light passes through its atmosphere just the Earth’s atmosphere bends the light of the rising Sun.
Have a good day, Jerry
Reply
MattH
| #
Gerardus Mercator created the flat earth.
Reply
jamesbbkk
| #
Sounds like David is ready to have a conversation with Nathan Oakley and participants about the subjects of tangent lines, physical vs. apparent horizon, sextant operation, the effects of atmospheric refraction, IIUC the prerequisite to refraction that there is a boundary between and change in characteristics of different media through which light is [passing]. Something like 3 Bitcoin available for a takedown of Nathan Oakley. And he’s a real jerk. So that would be awesome. Should be pretty easy though. He’s on Discord I think.
Reply
jamesbbkk
| #
Or clouds that weigh millions of tons supposedly.
Reply