Earth-sun distance

Earth-sun distance

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I understand that the moon - Earth distance is increasing as the friction of tidal action causes energy loss. Does this mechanism happen with the Earth and other planets, is the Earth - Sun distance changing?

Yes, the Earth is moving away from the Sun in a course of millions of years, so the moving away is about as fast as the Moon's from Earth. However don't worry because as the Sun gets older it also gets hotter so the habitable zone moves together with Earth or so. At the peak of the Sun's red giant phase the Earth is said to be either there where Mars currently is (about 50% farther from the Sun) or there where Jupiter currently is (about 5 times farther). We don't know exactly, there are several models. But we do know that the Earth and the Sun move slowly away of each other, just like the Moon from the Earth (the Moon reportedly moves away at about 1.6 inches a year on average, and with Earth-Sun it is similar). All planets' orbits are moving away from the Sun slowly.

Earth-Sun distance

Well, it can't quite be put qute as simply as that. If you look at the period of 1800 AD-2050 AD you will see that the Earth-moon barycenter recedes at a rate of .00000562 AU/century or about 2000 km over that period of time.

However, during the period of 3000 BC - 3000 AD,(Which includes the above time period) the E-M barycenter actually approaches the sun at an average rate of -.00000003 AU/century or about 270 km over that time.

Semi-major axis is a periodic orbital element, just like the other orbital elements. But it has a very small amplitude. As far as the Earth's average distance from the Sun, there's 2 ways to define average: average with respect to position, and average with respect to time. The semi-major axis is the average with respect to position. Perihelion is as far interior to semi-major axis as Aphelion is exterior to it. But objects move slower at aphelion, and hence, spend more time there. So the time-averaged distance is a function of eccentricity, which has a much larger amplitude than semi-major axis.

But the more eccentric the orbit, the more solar flux we receive over the course of a year. Even though the Earth tends to loiter a little longer at aphelion, the extra flux received at perihelion, governed by inverse square, more than makes up for it.

I did eventually find an answer to my own question in a Wikipedia article.
"The Sun, as part of its solar lifespan, will expand to a red giant in 5 Gyr. Models predict that the Sun will expand out to about 99% of the distance to the Earth's present orbit (1 astronomical unit, or AU). However, by that time, the orbit of the Earth may have expanded to about 1.7 AUs because of the diminished mass of the Sun."

So the Earth-Sun distance doesn't increase at a regular rate (thanks Janus) but on average, over extremely long periods of time, conservation of angular momentum causes the distance to increase as the sun loses mass. That makes sense. There are obviously other factors at work too. I'll keep looking.

Now all we have to do is to decide if we believe the Wikipedia article :-(. Unfortunately, that particular statement doesn't appear to be sourced.

If we assume angular momentum is conserved, then GMmr = (ang mom)^2 = constant, so the article is implying the sun's mass drops to 1/1.7 = .58.

But is this the correct assumption?

Trying to find independent confirmation, I ran across, which seems to suggest that this number is a bit high, and also suggests using conservation of energy rather than angular momentum.

The source above isn't peer reviewed, but is by an astronomer and is in genuine print, so it's at the low end of the confidence scale IMO.

There was also some useful information on the Wikipedia talk page at

pogge/Lectures/vistas97.html [Broken], but if I'm reading it right, the increased mass loss due to enhanced solar wind won't happen until after the sun has already become a red giant.

I also didn't see the 1.7 figure in the current version of the wikipedia article (I was going to flag it with a citation needed).

So at this point I don't know what to think, there may be room for considerably more discussion. At this point, I'm not even positive whether it's angular momentum or energy that should be conserved, though I'm leaning towards angular momentum.

"Astronomical Unit," or Earth-Sun Distance, Gets an Overhaul

Without fanfare, astronomers have redefined one of the most important distances in the Solar System. The astronomical unit (au) &mdash the rough distance from the Earth to the Sun &mdash has been transformed from a confusing calculation into a single number. The new standard, adopted in August by unanimous vote at the International Astronomical Union's meeting in Beijing, China, is now 149,597,870,700 meters &mdash no more, no less.

The effect on our planet&rsquos inhabitants will be limited. The Earth will continue to twirl around the Sun, and in the Northern Hemisphere, autumn will soon arrive. But for astronomers, the change means more precise measurements and fewer headaches from explaining the au to their students.

The distance between the Earth and the Sun is one of the most long-standing values in astronomy. The first precise measurement was made in 1672 by the famed astronomer Giovanni Cassini, who observed Mars from Paris, France, while his colleague Jean Richer observed the planet from French Guiana in South America. Taking the parallax, or angular difference, between the two observations, the astronomers calculated the distance from Earth to Mars and used that to find the distance from the Earth to the Sun. Their answer was 140 million kilometers &mdash not far off from today&rsquos value.

Until the last half of the twentieth century, such parallax measurements were the only reliable way to derive distances in the Solar System, and so the au continued to be expressed as a combination of fundamental constants that could transform angular measurements into distance. Most recently, the au was defined as (take a deep breath): &ldquothe radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (known as the Gaussian constant)&rdquo.

The definition cheered fans of German mathematician Carl Friedrich Gauss, whose constant sits at the heart of the whole affair, but it caused trouble for astronomers. For one thing, it left introductory astronomy students completely baffled, says Sergei Klioner, an astronomer at the Technical University of Dresden in Germany. But, more importantly, the old definition clashed with Einstein&rsquos general theory of relativity.

As its name implies, general relativity makes space-time relative, depending on where an observer is located. The au, as formerly defined, changed as well. It shifted by a thousand meters or more between Earth&rsquos reference frame and that of Jupiter&rsquos, according to Klioner. That shift did not affect spacecraft, which measure distance directly, but it has been a pain for planetary scientists working on Solar System models.

The Sun posed another problem. The Gaussian constant is based on Solar mass, so the au was inextricably tied to the mass of the Sun. But the Sun is losing mass as it radiates energy, and this was causing the au to change slowly as well.

The revised definition wipes away the problems of the old au. A fixed distance has nothing to do with the Sun&rsquos mass, and the meter is defined as the distance traveled by light in a vacuum in 1 / 299,792,458 of a second. Because the speed of light is constant in all reference frames, the au will no longer change depending on an observer&rsquos location in the Solar System.

Redefining the au has been possible for decades &mdash modern astronomers can use spacecraft, radars and lasers to make direct measurements of distance. But &ldquosome of them thought it was a little bit dangerous to change something,&rdquo says Nicole Capitaine, an astronomer at the Paris Observatory in France. Some feared the change might disrupt their computer programs, others held a sentimental attachment to the old standard. But after years of lobbying by Capitaine, Klioner and others, the revised unit has finally been adopted.

Capitaine and Klioner say that the streamlined au is already having a positive impact on their lives. Lobbying for the change has been time-consuming, Capitaine says: &ldquoI will have more time to devote to my research.&rdquo

&ldquoI'm happy that I don't have to explain it to my students any longer,&rdquo adds Klioner. The new definition &ldquois much easier to understand now for everybody.&rdquo

This article is reproduced with permission from the magazine Nature. The article was first published on September 14, 2012.

Astronomy Digital Notebook- Earth, Moon, & Sun | Distance Learning

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New Earth-Sun Distance Decided by Vote

In a solar-system-shaking victory for lay language, scientists have voted to redefine one of the most foundational measurements in all of astronomy, the mean distance between the sun and the Earth.

Next time a 5-year-old asks you how far the sun is, know you have the unanimous support of the International Astronomical Union (IAU) in answering clearly and confidently: 149,597,870,700 meters (about 92,955,807 miles).

The IAU voted in August to change the definition of the distance, called the astronomical unit (AU), to a plain old number. Before that, the unit had been defined by a roundabout equation that was bad for precise calculations and layman comprehension alike.

According to the news site of the journal Nature, the distance was said to be "the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day (known as the Gaussian constant)."

Along with making things unnecessarily difficult for astronomy professors, that definition actually didn't jibe with general relativity. Using the old definition, the value of AU would change depending on an observer's location in the solar system. If an observer on Jupiter used the old definition to calculate the distance between the Earth and the sun, the measurement would vary from one made on Earth by about 1,000 meters (3,280 feet).

Moreover, the Gaussian constant depends on the mass of the sun, and because the sun loses mass as it radiates energy, the value of AU was changing along with it.

Astronomers hadn't come up with the more abstruse and indirect definition just for their own amusement. Before the advent of spacecraft and radar, there was no method for making a direct measure of the distance between the Earth and the sun.

The Earth orbits the sun in an ellipse, and its distance from the sun varies from about 147 billion meters (91 million miles) to about 152 billion meters (94.5 million miles).


Hertzsprung and Russell were two astronomers who, independently of each other, produced a diagram that shows the relationship between a star's temperature and luminosity.

The diagram has a prominent diagonal band called the 'main sequence' Here there are stars such as our own with a range of temperatures and luminosity.

Cooler but brighter stars appear as giants toward the top right, while hotter but dimmer stars appear as dwarfs in the bottom left.

We can plot the pattern of a star's evolution on this diagram.

A star like our own will swell to become a giant and then dim to become a white dwarf.

Determining Distance

Astronomers use spectroscopic parallax to estimate the spectral type of a star. They calculate the luminosity of the star and can work out its distance using its apparent brightness. They can then place it on the H-R diagram and find it's absolute magnitude.

We calculate the size of a star using Stefan's Law which relates luminosity and temperature to its radius.

New data about two distant asteroids give a clue to the possible 'Planet Nine'

BTW, as to the "we have never seen this planet, or whatever it is". Back in Dec 2015 planetary scientists who were observing α Centauri using Atacama Large Millimeter/submillimeter Array (ALMA) noticed a fast moving object, in our solar system.

I am not sure if what they saw was planet X(9) or another object in the fringes of our solar system. But this paper was quickly withdrawn until they could gather more information.

Here is the nature article on it.

A super-Earth in our solar system? Not so fast.
Astronomers quietly submitted a research paper claiming they may have found a large planet on the far fringes of our solar system.
By Nathaniel Scharping | Published: Friday, December 11, 2015
While examining the Alpha Centauri star system, the nearest to Earth, they noticed a fast-moving object crossing their field of view.

Its speed and brightness allowed them to rule out another star as the culprit, and based on wavelength readings obtained from ALMA, they believe it could be a Trans-Neptunian Object (TNO) orbiting the sun somewhere between 10 billion and 2 trillion miles from our home star. For comparison, Pluto is less than 4 billion miles away from the sun.

Although the finding is intriguing, the news has been met with a healthy dose of skepticism.

A New Member of the Solar System?

Stars typically emit too much light for astronomers to discern any objects in their immediate vicinity, but the ALMA observatory was built to capture low-frequency wavelengths, allowing researchers to see objects that are closer to stars. This is how researchers noticed a mysterious object moving relative to Alpha Centauri, exhibiting what scientists call “proper motion.” The researchers suggest the object could be one of several celestial bodies, including a brown dwarf , a super-Earth (a planet larger than Earth but smaller than Neptune), or a much smaller, icy body orbiting beyond Pluto.

Here is an abstract of the research paper.

A new submm source within a few arcseconds of α Centauri: ALMA discovers the most distant object of the solar system
R. Liseau, W. Vlemmings, E. O'Gorman, E. Bertone, M. Chavez, V. De la Luz
(Submitted on 8 Dec 2015 (v1), last revised 17 Dec 2015 (this version, v2))

We recently announced the detection of an unknown submillimeter source in our ALMA observations of alpha Cen AB. The source was detected in two epochs, a strong detection at 445

GHz and one at lower significance at 343.5

GHz. After valuable feedback of the community, it turns out that the detection at 343.5

GHz could not be reproduced with a different reduction software nor with fitting within the (u,v)-plane. The detection at 445

GHz has been further confirmed with modeling of the (u,v)-data and was shown to be robust at >12σ, confirming our detection of this unknown source. However, based on only one epoch, further analysis and preferably new data are needed, before publication of an article in which the nature of the new source can be discussed. The analysis has indicated the importance of both (u,v)-plane fitting and alternative data reduction when dealing with low signal to noise source detections.

Comments: withdrawn until further data is available
Subjects: Solar and Stellar Astrophysics (astro-ph.SR)
Cite as: arXiv:1512.02652 [astro-ph.SR]
(or arXiv:1512.02652v2 [astro-ph.SR] for this version)

What these scientists saw could be the super-massive Earth, planet 9 (X) or another object in the fringes of the solar system.

BTW, I am aware that in the Nature paper they say "it could also be a smaller object close to Pluto. But here is the thing.

Two teams of researchers, one from Mexico the other one from Sweden, using ALMA both found two different objects in the outer reaches of the Solar System. The team from Mexico say that they think what they discovered could be a brown dwarf.

These two teams of scientists saw two different objects.

Here is another article referencing this find, and showing a couple of pictures of the object.

We exclude [this object] to be a sub-/stellar member of the α Centauri system, but argue that it is either an extreme TNO, a Super-Earth or a very cool brown dwarf in the outer realm of the solar system.

Fig. 1. Left: Band 7 observation of α Cen AB on 7 July 2014. Apart from the well known binary αCenA and αCenB, a previously un- known source, and designated U, is seen NNE of the secondary B. Right: That object is more clearly evident in our Band 8 observation on 2 May 2015, 5′·′5 north of α Cen A.

Where would this brown dwarf be in this scenario? Would it be beyond Planet 9, or inside the orbit of Planet 9?

It would be far beyond planet 9 and somewhere in the Oort cloud.

There are brown dwarfs which have planet orbiting around them, so why do you think it is logical that such a brown dwarf would only slingshot planets out of the solar system? Although eventually it would happen, it takes a long time for it to happen. The pull of a brown dwarf would be small tugs which would take millions if not billions of years to eventually eject such planet/object.

First Planet Discovered Orbiting a Brown Dwarf

Astronomers have long supposed that planets can form around brown dwarfs just as they do around ordinary stars. Now they’ve found the first example

The fact that ETNOs, and planet 9 have such highly elliptical orbits point to something out there causing them to orbit in such a manner. If only the sun exists in the solar system and there was no companion failed star (brown dwarf) then ETNOs and planet 9 would have more circular orbits.

Other planets can and do cause elliptical orbits, but highly elliptical orbits can only be caused by the interaction of massive objects with those planets, or by collisions. When you see outer planetary bodies with such highly elliptical orbit there has to be something massive with a stable orbit around that solar system causing such highly elliptical orbits.

A planet could have a more eccentric orbit for a number of reasons. For example, collisions during the formation period could knock it out of its circular orbit.

Interactions with other planets could also change how they travel around their stars. Of the highly eccentric planets discovered, 78 percent of those with eccentricities greater than 0.5 have only one planet in the system, Hulsebus said. While the other planets could have been kicked out over the course of their evolution, Hulsebus and his team looked for a third option — the presence of a distant brown dwarf that could wreak havoc on the orbit of planets.

As a failed star which never accreted the necessary mass to start fusion in its core, a brown dwarf can be a few times heavier than Jupiter or reach masses up to 80 times as great. Because orbiting bodies travel more slowly the farther away they are from their stars, a distant brown dwarf may barely move across the sky while an interior planet races around its star. As a result, the two bodies would interact gravitationally at roughly the same time of the inner planet’s year. The smaller planet experiences a gravitational tug that pulls it ever-so-slightly away from its star and closer to the brown dwarf. Over time, the process would stretch the orbit of the inner planet, making it steadily more elliptical.

Although it is true that eventually such a brown dwarf would cause planets and other objects in the solar system to eventually move away from the sun, and could eject out of that system if the brown dwarf doesn't capture it, it would take millions if not billions of years for this to happen.

Just take a look at object 2014 FE72 which has an eccentricity of 0.980 ± 0.014. Something is pulling it farther, and farther away from the sun. Once it's eccentricity reaches 1 or more, it would have enough momentum to eject out of gravity pull from the sun, and if it is not captured by the brown dwarf it would eject out of the solar system.

There is another solar system anomaly which could also be explained by a brown dwarf companion to our sun.

The secular increase of the astronomical unit in the solar system. What that is is that for some unexplained reason the distance between all planets and the sun is increasing at a rate that cannot be explained in the realm of classical physics or in the usual four-dimensional framework of the Einsteinian general relativity.

Secular increase of the astronomical unit and perihelion precessions as tests of the Dvali–Gabadadze–Porrati multi-dimensional braneworld scenario
Lorenzo Iorio JCAP09(2005)006 doi: 10.1088/1475-7516/2005/09/006

How BIG Is Our Solar System? | Earth Lab

New science kid on the block Dominic Burgess uses the scientific football pitch method to try and give us an idea of just how big our solar system really is.

1) 2 x distance from sun to the limit of its gravitational pull = 4 light years

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How Big is the Solar System?

How big is the solar system? We head to Carson-Newman University and create a scale model of the entire solar system starting with a soccer ball sun. If the sun were a soccer ball, how big would the earth be, and how far away? What about the biggest planet, Jupiter, or the furthest planet, Neptune?

Today, we're mapping out the sun and all eight planets on a college campus to visualize their size and distances.

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DRONE Solar System Model- How far is Planet 9?

I heart space but sometimes it can be hard to comprehend. I try to fix that in this video with junk you can find lying around your house. Also, if you’ve wondered how there could be a ninth planet that we’ve never noticed till now I try to clear that up too by demonstrating just how impossibly far away it is.

Make your own scale model of the Solar System using this spreadsheet I made. If you put in the size of the object you’re using for a Sun it will scale everything else for you:

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The Formation of the Solar System in 6 minutes!

The story of how our Earth was formed 4.5 billion years ago, told from the perspective of an asteroid called Bennu (which has survived until now). NASA sent a satellite to study Bennu to help us learn more about the beginning of our solar system.

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Planet Earths Size Compared to Our Solar System & Galaxy - Great Animation

Earth vs the solar system: Amazing animation reveals how massive - and tiny - our planet is compared to other cosmic bodies. The scale of the universe in terms of size is mind-bending enough – but considering the mass of planets can provide a new perspective. How big is the Sun compared to the Earth? It’s difficult to comprehend the size of that big burning ball of gas in the sky, especially as it is 149,600,000 kilometers (92,957,130 miles) away. 1,300,000 Earths could fit into an empty sphere the size of the Sun. Earth, the third planet from the sun is the densest in the solar system.It is the 5th largest planet, in the solar system, and has a radius of 6,378 km at the equator.

Light can circle our planet about seven and a half times in a single second.

The moon marks the end of Earth’s gravitational dominance. This satellite can be found orbiting at a distance of 385,000 km, which is about 60 times larger than Earth’s radius.

It takes light about 1.3 seconds to travel from Earth to the moon.

There are currently some 7 billion people on our planet. However, there have been some estimates 106 billion people over Earth’s history.

A solid iron ball that is 1,500 miles wide sits at the center of the planet.

In the Solar System, all of the sudden, Earth starts looking small. The total mass of the solar system is about 333,345.997 Earth masses.

Meaning that Earth makes up about 0.0003% of the total mass of our solar system.

For comparison, Earth makes up about 0.2% of the total mass of the planets.

We orbit the sun at an average distance of 93 million miles, which is equal to 1 Astronomical Unit.

It takes light a little over 8 light-minutes to travel from the Sun to Earth (that means, if the sun vanished right now, you wouldn’t know it for another 8 minutes).

The farthest planet from the Sun, Neptune, orbits at an average distance of 30 AU.

Voyager is about 119 AU from Earth.

The dwarf planet Sedna, the farthest such (known) object from the Sun, orbits at an average of 526 AU.

The solar system has an estimated radius of about two light-years.

Our closest star is Proxima Centauri at a distance of four light-years. About 53 star systems inhabit the Local Interstellar Cloud. Excluding our own solar system, there are six known planets in our neighborhood and another two suspected planets. Our local cloud is about 30 light-years across.

Home to our solar system, we orbit the galactic center at an average distance of 28,000 light-years.

One orbital period (one galactic year) is equal to about 250 million years.

We have completed about 15 orbits since life started on Earth.

The Milky Way itself is about 100,000 light-years across and is home to about 400 billion stars.

The bulge at the center is roughly 12,000 light-years in diameter.

Based on data acquired from the Kepler Space Telescope, there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of sun-like stars and red dwarf stars within the Milky Way Galaxy (that’s a lot of planets that could have life as we know it).

The Milky Way has a halo of dark matter that makes up over 90% of its mass. Yes, 90%.

The Milky Way is thought to have some 300 billion stars. The largest known galaxy, IC 1101, has over 100 trillion stars.

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To Scale: The Solar System

On a dry lakebed in Nevada, a group of friends build the first scale model of the solar system with complete planetary orbits: a true illustration of our place in the universe.

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What Happens If We Bring the Sun to Earth?

Distances: Crash Course Astronomy #25

How do astronomers make sense out of the vastness of space? How do they study things so far away? Today Phil talks about distances, going back to early astronomy. Ancient Greeks were able to find the size of the Earth, and from that the distance to and the sizes of the Moon and Sun. Once the Earth/Sun distance was found, parallax was used to find the distance to nearby stars, and that was bootstrapped using brightness to determine the distances to much farther stars.

Table of Contents
Ancient Greeks Finding the Size of the Earth 1:07
Earth/Sun Distance Began Our Use of Parallax 5:39
Brightness Relation to Distance 9:07

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Lunar Ecplise [credit: Phil Plait]
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New Horizons Approaching Pluto and Charon [credit: NASA/JHU APL/SwRI/Steve Gribben]
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61 Cygni [credit: Caltech / National Geographic Society / STScI]
Proxima Centauri [credit: ESA/Hubble & NASA]
Dying Star [credit: NASA, ESA, HEIC, and The Hubble Heritage Team (STScI/AURA)]
Exploding Star [credit: NASA, ESA, J. Hester, A. Loll (ASU)]
Animation of a Variable Star [credit: NASA, ESA, M. Kornmesser]
Hubble's High-Definition Panoramic View of the Andromeda Galaxy [credit: NASA, ESA, J. Dalcanton, B.F. Williams, and L.C. Johnson (University of Washington), the PHAT team, and R. Gendler]

What if a Black Hole entered our Solar System? + more videos | #aumsum #kids #education #children

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Firstly, Black hole's gravity will cause complete chaos in our Solar System. Orbits of Planets as well as Comets will be significantly altered. Initially comets and meteorites might start hurtling towards us. Later even the planets might start colliding with each other.
Secondly, even if a gigantic planet like Jupiter comes in the path of the Black hole it will be devoured.
Thirdly, if the Black hole comes near Earth, initially its intense gravitational pull will cause devastating earthquakes and volcanoes. When the Black hole reaches our orbit there will be nothing left but an uninhabitable magma-laden rock.
Lastly, our Sun might offer some resistance to start with. A gravitational tug of war might ensue. But eventually even our beloved Sun will be ripped apart to pieces.

The Sun, Earth, and Moon - Solar System for Kids

In this video you will be taken on a spectacular adventure to the Earth, Sun and Moon. You will learn interesting facts about these 3 aspects of the solar system for kids. Specifically your child will learn the length of Earths orbit, length of the Suns diameter and why we always see the same side of the moon. If your child is interested in the Solar System, this is a great video that will teach them about the Sun, Earth and Moon.

This video is part of a collection of videos that is focused on teach children about the Solar System. Have your little astronaut join Smile and Learn on this spectacular adventure.

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Vax Facts H.S.

Students from Kalanai High School and Kamehameha Schools interview state experts on vaccinating teens against Covid-19. Topics include: weighing risks of vaccination vs. covid, the science of mRNA vaccines, … Ещё good information vs. disinformation, and the relationship between vaccine distribution and health justice.

Amika Matteson, Kalani High School
Allison O’Connor, Kalani High School
Hoakalei Watanabe, Kamehemeha Schools

Public Health and Vaccine Experts:
Joshua Green, Lieutenant Governor and emergency room doctor
Sarah Kemble, Acting State epidemiologist
Taylor Tashiro, Microbiology lecturer, Leeward Community College and Hawai‘i Pacific University Pearl City High School… Ещё

UH Better Tomorrow Speaker Series

Friday, June 25th at 1PM join our webinar, "Dispatches from ‘Oumuamua: New Research on a Mysterious Visitor from Outside Our Solar System." Mahalo to our sponsors Institute For Astronomy, UH Manoa, Hawaii … Ещё Community Foundation, and the University of Hawaii at Manoa. With astronomer and astrobiologist Karen Meech and Michael S. Bruno (Provost at the University of Hawaii at Manoa). Register at

UH Better Tomorrow Speaker Series опубликовал(-а) видео в плейлисте BTSS Interviews.


IT is now demonstrated that the earth is a plane, and therefore the distance of the sun may be readily and most accurately ascertained by the simplest possible process. The operation is one in plane trigonometry, which admits of no uncertainty and requires no modification or allowance for probable influences. The principle involved in the process may be illustrated by the following diagram, fig. 56.

Let A be an object, the distance of which is desired, on the opposite side of a river. Place a rod vertically at the point C, and take a piece of strong cardboard, in the shape of a right-angled triangle, as B, C, D. It is evident that placing the

triangle to the eye, and looking along the side D, B, the line of sight D, B, H, will pass far to the left of the object A. On removing the triangle more to the right, to the position E, the line E, F, will still pass to the left of A but on removing it again to the right, until the line of sight from L touches or falls upon the object A, it will be seen that L, A, bears the same relation to A, C, L, as D, B, does to B, C, D: in other words, the two sides of the triangle B, C, and C, D, being equal in length, so the two lines C, A, and C, L, are equal. Hence, if the distance from L to C is measured, it will be in reality the same as the desired distance from C to A. It will be obvious that the same process applied vertically is equally certain in its results. On one occasion, in the year 1856, the author having previously delivered a course of lectures in Great Yarmouth, Norfolk, and this subject becoming very interesting to a number of his auditors, an invitation was given to meet him on the sea-shore and among other observations and experiments, to measure, by the above process, the altitude of the Nelson's Monument, which stands on the beach near the sea. A piece of thick cardboard was cut in the form of a right-angled triangle, the length of the two sides being about 8 inches. A fine silken thread, with a pebble attached, constituted a plumb line, fixed with a pin to one side of the triangle, as shown at P, . The purpose of this plumb line was to enable the observer to keep the triangle in a truly vertical position just as the object of the rod C, in fig. 56 was to enable the base of the triangle to be kept in one and the same line by looking along from E and L towards C. On looking over the triangle held vertically, and one side parallel with the plumb line P, from the position A, the line of sight fell upon the point B but on walking gradually backwards, the top of the helmet D, on the head of the figure of Britannia, which surmounts the column, was at length visible

from the point C. On prolonging the line D, C, to H, by means of a rod, the distance from H to the centre of the Monument at O, was measured, and the altitude O, D, was affirmed to be

the same. But of this no proof existed further than that the principle involved in the triangulation compelled it to be so. Subsequently the altitude was obtained from a work published in Yarmouth, and was found to differ only one inch from the altitude ascertained by the simple operation above described. The foregoing remarks and illustrations are, of course, not necessary to the mathematician but may be useful to the general reader, showing him that plane trigonometry, carried out on the earth's plane or horizontal surface, permits of operations which are simple and perfect in principle, and in practice fully reliable and satisfactory.

The illustrations given above have reference to a fixed object but the sun is not fixed and therefore a modification of the process, but involving the same principle, must be adopted. Instead of the simple triangle and plumb line, represented in fig. 57, an instrument with a graduated arc must be employed, and two observers, one at each end of a north and south base line, must at the same moment observe the under edge of the sun as it passes the meridian when, from the difference in the angle observed, and the known length of the base line, the actual distance of the sun may be calculated. The following case will fully illustrate this operation, as well as its results and importance:

The distance from London Bridge to the sea-coast at Brighton, in a straight line, is 50 statute miles. On a given day, at 12 o'clock, the altitude of the sun, from near the water at London Bridge, was found to be 61 degrees of an arc and at the same moment of time the altitude from the sea-coast at Brighton was observed to be 64 degrees of an arc, as shown in fig. 58. The base-line from L to B, 50 measured statute miles the angle at L, 61 degrees and the angle at B, 64 degrees. In addition to the method by calculation, the distance of the under edge of the sun may be ascertained from these elements by the method called "construction." The diagram, fig. 58, is the above case "constructed" that is, the base-line from L to B represents 50 statute miles and the line L, S, is drawn at an angle of 61 degrees, and the line B, S, at an angle of 64 degrees. Both lines are produced until they bisect or cross each other at the point S. Then, with a pair of compasses, measure the length of the base-line B, L, and see how many times the same length may be found in the line L, S, or B, S. It will be found to be

sixteen times, or sixteen times 50 miles, equal to 800 statute miles. Then measure in the same way the vertical line D, S, and it will be found to be 700 miles. Hence it is demonstrable that the distance of the sun over that part of the earth to which it is vertical is only 700 statute miles. By the same mode it may be ascertained that the distance from London of that part of the earth where the sun was vertical at the time (July 13th, 1870) the above observations were taken, was only 400 statute miles, as shown by dividing the base-line L, D, by the distance B, L. If any allowance is to be made for refraction--which, no doubt, exists where the sun's rays have to pass through a medium, the atmosphere, which gradually increases in density as it approaches the earth's surface--it will considerably diminish the above-named distance of the sun so that it is perfectly safe to affirm that the under edge of the sun is considerably less than 700 statute miles above the earth.

The above method of measuring distances applies equally to the moon and stars and it is easy to demonstrate, to place it beyond the possibility of error, so long as assumed premises are excluded, that the moon is nearer to the earth than the sun, and that all the visible luminaries in the firmament are contained within a vertical distance of 1000 statute miles. From which it unavoidably follows that the magnitude of the sun, moon, stars, and comets is comparatively small--much smaller than the earth from which they are measured, and to which, therefore, they must of necessity be secondary. and subservient. They cannot, indeed, be anything more than "centres of action," throwing down light, and chemical products upon the earth.