Flat Earth debunks - Celestial mechanics

{{pseudoastronomy}}
{{ArticleSeries|Flat Earth|the Flat Earth}}
Flat-Earthers have made several incorrect observations to claim the Earth is flat. This article refutes claims made by flat-Earthers about celestial mechanics.
=="So why can't we feel Earth's rotation affecting us?"==

The centrifugal acceleration is a force that reduces how heavy gravity makes us feel by 1/290. If the Earth suddenly decided to double its spinning speed, a 70kg person would feel themselves 1.39%, or just under 1kg lighter. Because the Earth spins at constant angular speed, we don't feel changes in the force it wants to eject us.

The lateral g-forces an individual feels when cornering around the axis of the Earth is the same as making an average (10m radius) turn in a car at the speed of 0.582m/s or 2.1km/h, which is the speed of a [https://www.youtube.com/watch?v=s9owa3BiXhQ walking tortoise]. That's why you don't feel it.

{{collapse|See calculations|width=500}}

[[File:Car cornering speed compared to cornering around earth.svg|600px]]
<!-- <math>
\begin{align}
a_c &= \omega^2 r, \quad \omega = \frac{2\pi}{86400 \, \text{s}} \approx 7.272 \times 10^{-5} \, \text{rad/s}, \quad r = 6378000 \, \text{m}, \\
a_c &= (7.272 \times 10^{-5} \, \text{rad/s})^2 \times 6378000 \approx 0.034 \, \text{m/s}^2, \\
\text{Lateral g-force} &= \frac{0.034}{9.81} \approx 0.00346 \, g, \\
0.00346 \times 9.81 &= \frac{v^2}{10}, \quad 0.0339 = \frac{v^2}{10}, \quad v^2 = 0.339, \quad v = \sqrt{0.339} \approx 0.582 \, \text{m/s}
\end{align}
</math> -->

{{collapse end}}

=="So why can't we feel the cornering forces as we turn around the Sun?"==
The lateral g-forces an individual feels when cornering around the Sun on Earth is the same as making an average (10m radius) turn in a car at the speed of 0.243m/s, which is the [https://youtu.be/PC19StjuOD4?si=e3bXNB4SGbNwOUNQ&t=23 walking speed of an elderly person]. That's why you don't feel it.

{{collapse|See calculations|width=500}}

[[File:Car cornering speed compared to earth cornering around sun.svg|700px]]
<!-- <math>
\begin{align}
a_c &= \frac{v^2}{r}, \quad v \approx 29{,}800 \, \text{m/s}, \quad r \approx 1.496 \times 10^{11} \, \text{m}, \\
a_c &= \frac{(29{,}800)^2}{1.496 \times 10^{11}} \approx 5.93 \times 10^{-3} \, \text{m/s}^2, \\
\text{Lateral g-force} &= \frac{a_c}{9.81} = \frac{5.93 \times 10^{-3}}{9.81} \approx 6.05 \times 10^{-4} \, g, \\
6.05 \times 10^{-4} \times 9.81 &= \frac{v^2}{10}, \quad 5.93 \times 10^{-3} = \frac{v^2}{10}, \quad v^2 = 5.93 \times 10^{-2}, \quad v = \sqrt{5.93 \times 10^{-2}} \approx 0.243 \, \text{m/s}
\end{align}
</math> -->

{{collapse end}}

==So why can't we feel the cornering forces as we turn around the galaxy's center?==

The lateral g-forces an individual feels when cornering around the Milky Way (our galaxy) at the orbital speed of our Sun, is the same as making an average (10m radius) turn in a car at the speed of 50.4 cm/h, which is the speed of a [https://www.youtube.com/watch?v=xSv3RX9kYUE slow mollusk]. That's why you don't feel it.

{{collapse|See calculations|width=500}}

[[File:Car cornering speed compared to sun cornering around milkyway.svg|550px]]
<!-- <math>
\begin{align}
a_c &= \frac{v^2}{r}, \quad v \approx 220{,}000 \, \text{m/s}, \quad r \approx 2.46 \times 10^{20} \, \text{m}, \\
a_c &= \frac{(220{,}000)^2}{2.46 \times 10^{20}} \approx 1.97 \times 10^{-10} \, \text{m/s}^2, \\
\text{Lateral g-force} &= \frac{a_c}{9.81} = \frac{1.97 \times 10^{-10}}{9.81} \approx 2.01 \times 10^{-11} \, g, \\
2.01 \times 10^{-11} \times 9.81 &= \frac{v^2}{10}, \quad 1.97 \times 10^{-10} = \frac{v^2}{10}, \quad v^2 = 1.97 \times 10^{-9}, \\
v &= \sqrt{1.97 \times 10^{-9}} \approx 1.4 \times 10^{-5} \, \text{m/s} = 0.014 \, \text{cm/s}, \\
v &= 0.014 \, \text{cm/s} \times 3600 = 50.4 \, \text{cm/h}
\end{align}
</math> -->

{{collapse end}}

=="But those values add up! We're spinning like crazy!"==

Even if we assume all three speeds are perpendicular to maximize their effect, the total effect of rotation around the earth's axis, going around the Sun that's going around the Galaxy, we get the car cornering force, that matches the speed of

<!-- <math>v_{\text{total}} = \sqrt{0.582^2 + 0.243^2 + \left(50.4 \times \frac{1}{100} \times \frac{1}{3600}\right)^2} \approx 0.63 \, \text{m/s}</math> -->
[[File:Values add up.svg|500px]]

which is way too weak for us to properly notice it.

If you still don't believe us, try standing up and swinging your arm fast. You can feel the centripetal force pack blood into your fingers. Next, assuming your arm, when measured from the mid-point of the shoulder joint, to tip of the finger, is 30 inches, or 75cm, try rotating your other arm at a rate where one revolution takes 28 seconds. That's very close to the total cornering forces our Earth's spin around its axis, Earths orbit around the Sun, and the Sun's orbit around our galaxy, when combined, create. Can you feel the blood packing to your fingertips? No? Thought so.

=="But Sundials wouldn't remain accurate due to all the movement!"==

[https://youtu.be/N9CQPMOzeRs?si=WB3iZa5judcmsGs_&t=4985 Argues] Eric Dubay. Dubay claims that "Earth's, the Sun's, and the Moon's revolving, rotating, wobbling, and spiraling motions would make the Sundials inaccurate". This is an attempt to overwhelm the mind of the listener with irrelevant information.
* A {{wpl|Moondial|moon dial}} is about telling the phases of the Moon, so we can ignore that as completely irrelevant.
* The Sun revolving around Milkyway does not play role at all, as sundials are about the relative movement between the Sun and the Earth. 
* Since the spiraling motion is relative motion of the Sun and Earth observed from the CMB's rest frame (i.e., if nothing in the universe affected you), we can ignore that too.

So now we're left with Sun and Earth.

* The Sun's rotation around its axis takes 27 days, but since we know Sun doesn't have dark days, can ignore that completely.

* The {{wpl|Milankovitch_cycles}} are about Earth's axial tilt varying between 22.1° and 24.5° (so at most 2.4° variance) which is barely noticeable. Secondly, the wobble cycle takes 41,000 years. Meaning in 43,000 CE, it will have reset itself to current position. Also, since the axial tilt shifts 0.013° per century, and because, according to {{wpl|Sundial#History|Wikipedia|,}} the sundial is only 3,500 years old, the total change in the axis direction has been 0.35°, barely noticeable. Installation errors of ancient sundials are likely around 0.5°-2°.

* The Earth's rotation around its axis determines the length of the solar day. Because the Moon is slowing Earth's rotation slowly, Earth's day length grows by 1.8ms every century, or, 49.3 nanoseconds per day. The {{wpl|Sexagesimal|}} system and thus the concept of seconds have existed since ancient Sumerians came up with it, 5000 years ago. The sundials have existed for 3,500 years, during which days have grown 6.3 seconds longer. During the times sundials were regularly used, they were perfectly adequate to measure time. Ancient Egyptians had average life expectancy of 25 years for males and 37 for females. So days getting 0.67 milliseconds longer during their lifetimes played no role. No hourglass has ever had that kind of resolution, and measuring things as a function of time had to wait until Galilei's pendulum experiments in the 1582. So again, historically, the sundial was practical for daily use, but in modern world, it's unable to keep track of absolute time. Scientific experiments require precise measurement. Extremely fast computer systems need to be kept in sync around the world with atomic clocks. Also, humans live on different time-zones, and the solar time a sundial tells won't be the same in two adjacent cities, let alone inside one's country.

* The largest error comes from the Earth's revolution around Sun, which when combined with the axial tilt, dictate the season. Ignoring the absolute time discussed above, if we'd still live by solar days and if we didn't care about each day getting 49 nanoseconds shorter or rely on absolute time measurement, the only thing the axial tilt would do, is affect the altitude of the Sun during the day. Due to the elliptic orbit of Earth around the Sun, {{wpl|Position_of_the_Sun#Equation_of_time|as per Wikipedia}}, the Sun's speed in the sky varies, and thus sundials can be up to 16 minutes too fast or slow depending on the time of the year. So it's not accurate for measuring time intervals. However, since the Orbit doesn't really change, the error doesn't accumulate, except for the slowdown of Earth around in its orbit. As [https://www.forbes.com/sites/startswithabang/2020/12/04/ask-ethan-does-earth-orbit-the-sun-more-slowly-with-each-new-year/ this] Forbes article shows, the orbital speed drops by about 3 nanometers-per-second, every year. So the speed has changed by 1.05 micrometers / second since the sundial was invented. Since this is visible on Earth only as the absolute length of each season growing by nanoseconds each year, it doesn't matter. It's detectable, but not by a sundial.

Finally, as seen in [https://sundialsoc.org.uk/wp-content/uploads/all_about_sundials/Horiz.png this image], the gnomon of the sundial is adjusted to be parallel to Earth's rotational axis. This makes no sense on a flat Earth.

=="But in absolute terms, we are going really fast, why can't we feel it?"==
A commercial airplane travels at 700km/h, yet for most of the trip, it doesn't feel like it. The {{wpl|Mechanoreceptor|mechanoreceptors}} of the human body respond to pressure. We feel the airplane seat pushing us as we '''accelerate''' due to a force affecting us, just like in a car or a bus. During landing, we feel the forces that decelerate us: the friction from our bench that stretches our skin, and the pressure in our hands as we lean against the backside of the seat in front of us. But during flight, when the plane is moving at a constant speed, the sensation of movement disappears aside from hearing the humming of the engines.

The much bigger sense of speed we feel in a convertible with its top-down moving at '''constant''' speed comes from the breeze, i.e., the air that's not part of the closed system inside the car, which is hurtling by our ears. We also associate the sound of the car's engine (which is close to us) with speed, and we feel the vibrations coming from the tires. We also see objects around us passing through our field of view very fast.

The Earth's entire atmospheric system is revolving and moving at the same speed as the ground. For the same reason a hairdryer works normally (independently of cruising speed) inside a car with a top, wind can blow independently in Earth's closed atmospheric system while that system flies through space. The reason space doesn't cause a breeze that would '''a)''' mess up Earth's air currents, and '''b)''' help us sense the speed at which we traverse, is because space is a vacuum and the planet is thus not moving against some space wind. For this same reason, our planet does not need a firmament as a "windshield" for us to not feel space. On the side facing the prograde direction, the atmosphere remains in place as there is no space headwind compressing the air mass from above, and because the Earth is not accelerating, nothing is compressing the air mass from "below". All of the matter, including the gasses in the Earth's atmosphere have had its orbital speed ever since Earth formed, 4.54 billion years ago. Furthermore, there is also no engine needed that would make a noise, and no tires are vibrating against some space road. The objects in space are so large and distant we lack any experience to estimate how fast they're moving in the absolute sense. The low angular velocity is throwing our perception off, as it makes them seem to be almost still. For the same reason we can't tell the speed of a car just by looking from its side window how our viewing angle of a mountain in the horizon changes (although if one knows the distance of the mountain and the distance of trees closer to the road they can calculate their speed exactly by measuring the parallax of the objects passing by). So with nothing to cue us about the absolute speed, no wonder we can't feel ourselves hurtling through space.

=="How can Polaris maintain its alignment straight above the North Pole?"==

[https://youtu.be/SauZfMS-lZo?feature=shared&t=8763 Wonders] Eric Dubay. It doesn't. Dubay makes it seem like {{wpl|Polaris|Polaris}} is the chosen star to show North. It's not. The axis of Earth's rotation will always point to something. The closest star to each pole is called a {{wpl|Pole_star|pole star|.}} 

In 3000 BC, around the time of ancient Egypt, {{wpl|Thuban|Thuban}} was the North pole star. In 1000 BC, it was {{wpl|Beta_Ursae_Minoris|Beta Ursae Minoris (Kochab)|.}} Alpha Ursae Minoris (Polaris) became the North pole star in roughly 500 CE. As explained by Mozibur Ullah [https://hsm.stackexchange.com/a/12627 here], "''In Antiquity, Polaris was not close enough to the celestial pole to be used for navigation and the whole constellation was used. In Old English it was called scip steorra, or ship star. Europeans named it Polaris in the Renaissance from the Latin Stella Polaris or pole star, when it approached the celestial pole to within a few degrees''." By 3000 CE, {{wpl|Gamma_Cephei|Gamma Cephei (Errai)}} will take Polaris' place, and the title passes to {{wpl|Iota_Cephei|Iota Cephei}} in roughly 5200 CE.

So it wasn't God who put it there to guide ships. It's just the best available pole star in our age.

=="Why isn't there a 12-hour night and day everywhere?"==

[[File:Temperature2.jpg|thumb|right|Temperatures on a flat Earth. If the Sun's angle of incidence doesn't matter like Eric Dubay claims, then why is the middle of the ring, that the Sun has orbited around for — according to flerfs — thousands of years, freezing cold? Only a globe Earth has cold poles due to the {{wpl|Effect_of_Sun_angle_on_climate|Sun's angle of incidence}}.]]

Strangely [https://youtu.be/SauZfMS-lZo?feature=shared&t=8589 asked by Eric Dubay], who already [https://youtu.be/SauZfMS-lZo?feature=shared&t=123 knows the answer to be Earth's axial tilt, and knows the tilt to the first decimal], but doesn't think too highly about the fact.

Funnily, Dubay disagrees with the notion that the Sun's angle of incidence would influence it's radiation dispersing into wider surface area. Assuming that's the case, Dubay's pizza-land runs into all sorts of trouble. The Sun, that supposedly orbits above the pizza-land between the tropics, passes over the tropics once a day. At the same time, the Sun, especially during Summer solstice, continuously has its shortest average distance to the center. Yet, as can be seen in [https://youtu.be/WmqE2cRFbPU?si=paZVJ34pPiRHPBLK&t=1044 Dubay's flat Earth heat-map], for some reason, the area where the Sun passes over once a day has a tropical climate, but the Arctic is a frozen wasteland. I mean, when was the last time your stove couldn't melt an ice cube in the center, because heat wouldn't radiate there?

== See also ==

* [[Flat_Earth|Flat Earth]]

Flat Earth debunks

* [[Flat_Earth_debunks_-_The_Earth|The Earth]]

* [[Flat_Earth_debunks_-_The_Moon|The Moon]]

* [[Flat_Earth_debunks_-_The_Sun|The Sun]]
* [[Flat_Earth_debunks_-_Stars|Stars]]
* '''[[Flat_Earth_debunks_-_Celestial_objects|Celestial objects]]'''
* [[Flat_Earth_debunks_-_Astronautics|Astronautics]]
* [[Flat_Earth_debunks_-_Astrophotography|Astrophotography]]
* [[Flat_Earth_debunks_-_The_conspiracy|The conspiracy]]

==Notes==
{{reflist|group=note}}

==References==
{{reflist|2|80%}}

[[Category:Anti-intellectualism]]
[[Category:Conspiracy theories]]
[[Category:Denialism]]
[[Category:Flat Earth]]
[[Category:Pseudoastronomy]]
[[Category:Pseudoscience]]

Categories: Anti-intellectualism, Conspiracy theories, Denialism, Flat Earth, Pseudoastronomy, Pseudoscience