I wonder if any of the more scientifically minded people on here could help me, please.

[Horsa]

Some people who speak AmE dialect (perhaps most) think that United States of America is a name of a continent. At the same time, when faced with a trivia question to name one country that starts with 'U', said people stumble and are unable to move their brains. Both of these cognitive problems are likely related. We can multiply such examples.
My answer to said trivia would be Uruguay, with a nod to mrzz, their neighbour. Similarly, I would name Uganda if speaking to a friend from Africa, or USSR to a friend from Europe. Well, the latter is a former country, so a bit old fashioned answer, with a promotion of old-fashioned, discredited ideology, but still better than the promotion of 'The Land of Dumbs-Up-Over' as Men at Work should have sung about certain country on American continent.

Really? I know I speak British English but know America is the continent as it doesn't just include the U.S. but also Canada & Central & Southern America too. I call the U.S. America too when being lazy but normally call it the U.S. I'd have answered Uzbekistan for a country beginning with U. I know. Examples I can think of are some people use the terms British synonymously with English but not everything that's British is English (some things that are British are Scottish, Irish or Welsh) & some people think that ferrets are rodents.

 

[Horsa]

Ha! Had a really good laugh with both your posts.

The USA name is a particular case, I would guess, as, differently from most countries, we use the "full name" to refer to it. For example, we don't say "Russian Federation", but Russia, we don't say "Federal Republic of Germany", but Germany. On the other hand, we do say "United States of America", or USA, or just "United States", while, I guess, just -- or mostly -- Americans say "America". Further confusion comes from the fact that "North America" and "South America" are (physical) continents, while there is still the (political) concept of "Central America". So it is in fact a bit hard to grasp exactly what "America" might mean in a given sentence.

Oh, and about Uruguay, lovely place, a lot of beautiful things to see there. Also, best meat in the world -- and this is a subject I really know about. To say something "scientific" about Uruguay, the "Rio de la Plata" (which divides Uruguay and Argentina) is largest estuary in the world -- and gives you a hell of sunset...

I'm glad you found my post funny. I was going to say that in the case Chris mentioned some people would probably think Venus was just a song by Bananarama then. Lol.

Some people still call the U.K. the United Kingdom (me included sometimes) while others call it Britain or Great Britain or refer to the particular country of the U.K. they are talking about specifically. I still call Russia the U.S.S.R. because when I was in middle/high school that's what it was. (In Middle School our headmaster made everyone do an hour of silent reading a day which he put on the time-table as U.S.S.R. which he used as a mnemonic for Uninterrupted Sustained Silent Reading.) I learnt that America itself is a continent but the U.S. was a country & didn't get taught to separate the continent of America into 2 (or 3 including Central) though I say America to refer to the country sometimes.

That sounds nice. I'm a meat-eater too. The best meat I've ever eaten was pheasant what I got for Xmas. I like partridge too but normally my favourite meat is rabbit which I normally eat in a stew or pie. To bring the conversation back to science the wild rabbit is called a hare & Northern European polecats (wild ferrets) used to catch them & have them for dinner.

 

[Horsa]

To get things back on track, I'm going to ask a couple of relevant questions after I've apologised for saying how I really feel about myself at times. No one wanted to know & it only makes people feel bad. Sorry. It was wrong of me to say how I really feel about myself at times especially because of how low my opinion of myself is at times & how different my opinion of myself is to reality at times.

1. I asked about the diameter of the sun. Following on from that, what is the circumference of the sun?
2. Since I've spoken about the sun, I guess I should ask questions about the moon. What is the diameter of the moon?
3. What is the circumference of the moon?

I've read that the moon travels around the earth at 13 million miles per hour & is 1/2 a million miles away from us which brings me to more questions.

4. What speed does the earth travel around the sun at?
5. How far is the sun away from us?
6. What is the diameter of the earth?
7. What is the circumference of the earth?

 

[Chris Koziarz]

To get things back on track, I'm going to ask a couple of relevant questions after I've apologised for saying how I really feel about myself at times. No one wanted to know & it only makes people feel bad. Sorry. It was wrong of me to say how I really feel about myself at times especially because of how low my opinion of myself is at times & how different my opinion of myself is to reality at times.

1. I asked about the diameter of the sun. Following on from that, what is the circumference of the sun?
2. Since I've spoken about the sun, I guess I should ask questions about the moon. What is the diameter of the moon?
3. What is the circumference of the moon?

I've read that the moon travels around the earth at 13 million miles per hour & is 1/2 a million miles away from us which brings me to more questions.

4. What speed does the earth travel around the sun at?
5. How far is the sun away from us?
6. What is the diameter of the earth?
7. What is the circumference of the earth?

1. this is trivial: 2πR = 2*3.14*0.7Gm. Hardly anyone cares about that number cause no one "circles" the sun to experience that. For all astronomical calculations, 2R (diameter) is used. Similarly trivial are 3 after we know 2, and 7 after we know 6, so I don't bother with 3 and 7.

2. can be answered, in identical way we answered the diameter of the sun, after we know the distance to the moon. I'll answer together with the related question 5.

4. Speed is distance/time. In case of Earth orbital speed, the distance is 2πa, where a is "astronomical unit" or the distance to the sun equal 150Gm (that we are going to find out in 5), and time is 1year = 365*24*3600sec. So v = 2π*150Gm/(365*24*3600)sec = 30km/sec

5. Here we are talking about distance measuring in astronomy. Universal astronomical measuring tool is the observation of parallax: Due to parallax, foreground objects displace on the distant background when observer changes position
https://en.wikipedia.org/wiki/Parallax
https://en.wikipedia.org/wiki/Parallax#/media/File:Stellarparallax2.svg
Astronomical Parallax can be
- diurnal (due to Earth spinning) when an observer changes position every 12h by 2R (where R is Earth radius)
- annual (due to Earth circling the sun) when an observer changes position every 6months by 2a (where a is an astronomical unit)
First, you measure short distances, like a distance to the moon, using diurnal parallax. If you know the earth radius (from 6 below), and observe moon diurnal parallax of about 1 degree (a very large value for a star gazer!), you can calculate the distance as about 380Mm.
Then you can e.g. check the angle between moon and sun when moon is at 1st or 3rd phase precisely (thus forming a right angle with the sun. Knowing a distance to the moon (calculated from diurnal parallax), you can calculate the distance to the sun by resolving the right triangle. However, this method may be inaccurate because the sun-moon-earth triangle is very elongated (moon-sun angle of interest will be close to 90degrees, something like 89.5) and not stopping at that value, because earth goes in between sun and moon during a full moon phase, and the angle in question grows above 90 degrees. The more accurate measure is by triangulation between sun-earth-venus triangle, provided you know the distance to venus. The triangle is not much elongated, and more importantly, It is possible to pinpoint the moment when the right triangle is formed, when venus is at the greatest elongation i.e. the farthest from the sun venus can appear in the sky. That moment can be pinpointed because the angle between sun and venus does not grow beyond 90 degrees, i.e.: the earth does never enter between venus and sun. This is described with some pictures for example here:
http://curious.astro.cornell.edu/ab...stance-between-earth-and-the-sun-intermediate
It is mentioned therein, that the distance between venus and earth that we need to know, can be obtained using radar (by measuring a time of the electromagnetic echo traveling at speed 2c). Well, people did not know radar before The Battle of Britain in 1940 (and radars were not powerful yet sensitive enough to use in astronomy until 1960) yet astronomers knew most distances in the solar system before that. They used diurnal parallax measure to track the distance to venus as venus traveled towards earth while tracking the sun-venus angle up to the greatest elongation.

Anticipating that you next ask how we measure the distance to the stars, the answer is: with annual parallax. This parallax is really a wonderful measuring tool. Have you heard of an astronomical unit of distance called "parsec"? It's a short of "parallax angle of 1 second". So, it's a distance, that a displacement of 1 astronomical unit (distance to the sun subject of this point) creates a parallax angle of one second (1/3600 of degree). You can calculate 1 parsec to be 3.086e+16 metres or 3.262 light-years (LY). The distance to the closest star was measured using annual parallax as a bit over 1 parsec. So the parallax angle of that star is a bit less than 1 sec. We have measured the distances to the stars up to some 1000 LY away using the best telescopes, while more recently Hobble telescope measured up to 10,000 LY.

6. This is the basic distance we have to know to start measuring anything in astronomy, including all of the above. There are several methods, but most of them are calculation of the earth surface curvature, e.g. by rising to a known altitude above the sea level and observing the distance of the horizon or by how much the known objects are "hidden" below the horizon line. One of the methods is shown here:

U can also measure the difference in sun rays angle at two different locations, if you have two synchronised observers at the same time, as Eratosthenes did more than 2000y ago:
https://www.earth.northwestern.edu/people/seth/107/Time/erathos.htm.
Earth radius is about 6.37Mm, yielding the circumference of 40Mm (a better known number for "early" applications).

 

[Horsa]

1. this is trivial: 2πR = 2*3.14*0.7Gm. Hardly anyone cares about that number cause no one "circles" the sun to experience that. For all astronomical calculations, 2R (diameter) is used. Similarly trivial are 3 after we know 2, and 7 after we know 6, so I don't bother with 3 and 7.

2. can be answered, in identical way we answered the diameter of the sun, after we know the distance to the moon. I'll answer together with the related question 5.

4. Speed is distance/time. In case of Earth orbital speed, the distance is 2πa, where a is "astronomical unit" or the distance to the sun equal 150Gm (that we are going to find out in 5), and time is 1year = 365*24*3600sec. So v = 2π*150Gm/(365*24*3600)sec = 30km/sec

5. Here we are talking about distance measuring in astronomy. Universal astronomical measuring tool is the observation of parallax: Due to parallax, foreground objects displace on the distant background when observer changes position
https://en.wikipedia.org/wiki/Parallax
https://en.wikipedia.org/wiki/Parallax#/media/File:Stellarparallax2.svg
Astronomical Parallax can be
- diurnal (due to Earth spinning) when an observer changes position every 12h by 2R (where R is Earth radius)
- annual (due to Earth circling the sun) when an observer changes position every 6months by 2a (where a is an astronomical unit)
First, you measure short distances, like a distance to the moon, using diurnal parallax. If you know the earth radius (from 6 below), and observe moon diurnal parallax of about 1 degree (a very large value for a star gazer!), you can calculate the distance as about 380Mm.
Then you can e.g. check the angle between moon and sun when moon is at 1st or 3rd phase precisely (thus forming a right angle with the sun. Knowing a distance to the moon (calculated from diurnal parallax), you can calculate the distance to the sun by resolving the right triangle. However, this method may be inaccurate because the sun-moon-earth triangle is very elongated (moon-sun angle of interest will be close to 90degrees, something like 89.5) and not stopping at that value, because earth goes in between sun and moon during a full moon phase, and the angle in question grows above 90 degrees. The more accurate measure is by triangulation between sun-earth-venus triangle, provided you know the distance to venus. The triangle is not much elongated, and more importantly, It is possible to pinpoint the moment when the right triangle is formed, when venus is at the greatest elongation i.e. the farthest from the sun venus can appear in the sky. That moment can be pinpointed because the angle between sun and venus does not grow beyond 90 degrees, i.e.: the earth does never enter between venus and sun. This is described with some pictures for example here:
http://curious.astro.cornell.edu/ab...stance-between-earth-and-the-sun-intermediate
It is mentioned therein, that the distance between venus and earth that we need to know, can be obtained using radar (by measuring a time of the electromagnetic echo traveling at speed 2c). Well, people did not know radar before The Battle of Britain in 1940 (and radars were not powerful yet sensitive enough to use in astronomy until 1960) yet astronomers knew most distances in the solar system before that. They used diurnal parallax measure to track the distance to venus as venus traveled towards earth while tracking the sun-venus angle up to the greatest elongation.

Anticipating that you next ask how we measure the distance to the stars, the answer is: with annual parallax. This parallax is really a wonderful measuring tool. Have you heard of an astronomical unit of distance called "parsec"? It's a short of "parallax angle of 1 second". So, it's a distance, that a displacement of 1 astronomical unit (distance to the sun subject of this point) creates a parallax angle of one second (1/3600 of degree). You can calculate 1 parsec to be 3.086e+16 metres or 3.262 light-years (LY). The distance to the closest star was measured using annual parallax as a bit over 1 parsec. So the parallax angle of that star is a bit less than 1 sec. We have measured the distances to the stars up to some 1000 LY away using the best telescopes, while more recently Hobble telescope measured up to 10,000 LY.

6. This is the basic distance we have to know to start measuring anything in astronomy, including all of the above. There are several methods, but most of them are calculation of the earth surface curvature, e.g. by rising to a known altitude above the sea level and observing the distance of the horizon or by how much the known objects are "hidden" below the horizon line. One of the methods is shown here:

U can also measure the difference in sun rays angle at two different locations, if you have two synchronised observers at the same time, as Eratosthenes did more than 2000y ago:
https://www.earth.northwestern.edu/people/seth/107/Time/erathos.htm.
Earth radius is about 6.37Mm, yielding the circumference of 40Mm (a better known number for "early" applications).

That was fascinating. Thank you very much for your answers.

I wasn't going to ask that question next but found the information very interesting & didn't know that speed measurement unit you mentioned. Thank you very much. My next questions were actually going to be the diameters & circumferences of all the planets in our solar system except the earth which you've already answered & Saturn because of its rings & the speeds of all the other planets orbit around the sun except the earth which you've already answered & the distance of the other planets from the earth.

 

[mrzz]

1. this is trivial: 2πR = 2*3.14*0.7Gm. Hardly anyone cares about that number cause no one "circles" the sun to experience that. For all astronomical calculations, 2R (diameter) is used. Similarly trivial are 3 after we know 2, and 7 after we know 6, so I don't bother with 3 and 7.

2. can be answered, in identical way we answered the diameter of the sun, after we know the distance to the moon. I'll answer together with the related question 5.

4. Speed is distance/time. In case of Earth orbital speed, the distance is 2πa, where a is "astronomical unit" or the distance to the sun equal 150Gm (that we are going to find out in 5), and time is 1year = 365*24*3600sec. So v = 2π*150Gm/(365*24*3600)sec = 30km/sec

5. Here we are talking about distance measuring in astronomy. Universal astronomical measuring tool is the observation of parallax: Due to parallax, foreground objects displace on the distant background when observer changes position
https://en.wikipedia.org/wiki/Parallax
https://en.wikipedia.org/wiki/Parallax#/media/File:Stellarparallax2.svg
Astronomical Parallax can be
- diurnal (due to Earth spinning) when an observer changes position every 12h by 2R (where R is Earth radius)
- annual (due to Earth circling the sun) when an observer changes position every 6months by 2a (where a is an astronomical unit)
First, you measure short distances, like a distance to the moon, using diurnal parallax. If you know the earth radius (from 6 below), and observe moon diurnal parallax of about 1 degree (a very large value for a star gazer!), you can calculate the distance as about 380Mm.
Then you can e.g. check the angle between moon and sun when moon is at 1st or 3rd phase precisely (thus forming a right angle with the sun. Knowing a distance to the moon (calculated from diurnal parallax), you can calculate the distance to the sun by resolving the right triangle. However, this method may be inaccurate because the sun-moon-earth triangle is very elongated (moon-sun angle of interest will be close to 90degrees, something like 89.5) and not stopping at that value, because earth goes in between sun and moon during a full moon phase, and the angle in question grows above 90 degrees. The more accurate measure is by triangulation between sun-earth-venus triangle, provided you know the distance to venus. The triangle is not much elongated, and more importantly, It is possible to pinpoint the moment when the right triangle is formed, when venus is at the greatest elongation i.e. the farthest from the sun venus can appear in the sky. That moment can be pinpointed because the angle between sun and venus does not grow beyond 90 degrees, i.e.: the earth does never enter between venus and sun. This is described with some pictures for example here:
http://curious.astro.cornell.edu/ab...stance-between-earth-and-the-sun-intermediate
It is mentioned therein, that the distance between venus and earth that we need to know, can be obtained using radar (by measuring a time of the electromagnetic echo traveling at speed 2c). Well, people did not know radar before The Battle of Britain in 1940 (and radars were not powerful yet sensitive enough to use in astronomy until 1960) yet astronomers knew most distances in the solar system before that. They used diurnal parallax measure to track the distance to venus as venus traveled towards earth while tracking the sun-venus angle up to the greatest elongation.

Anticipating that you next ask how we measure the distance to the stars, the answer is: with annual parallax. This parallax is really a wonderful measuring tool. Have you heard of an astronomical unit of distance called "parsec"? It's a short of "parallax angle of 1 second". So, it's a distance, that a displacement of 1 astronomical unit (distance to the sun subject of this point) creates a parallax angle of one second (1/3600 of degree). You can calculate 1 parsec to be 3.086e+16 metres or 3.262 light-years (LY). The distance to the closest star was measured using annual parallax as a bit over 1 parsec. So the parallax angle of that star is a bit less than 1 sec. We have measured the distances to the stars up to some 1000 LY away using the best telescopes, while more recently Hobble telescope measured up to 10,000 LY.

6. This is the basic distance we have to know to start measuring anything in astronomy, including all of the above. There are several methods, but most of them are calculation of the earth surface curvature, e.g. by rising to a known altitude above the sea level and observing the distance of the horizon or by how much the known objects are "hidden" below the horizon line. One of the methods is shown here:

U can also measure the difference in sun rays angle at two different locations, if you have two synchronised observers at the same time, as Eratosthenes did more than 2000y ago:
https://www.earth.northwestern.edu/people/seth/107/Time/erathos.htm.
Earth radius is about 6.37Mm, yielding the circumference of 40Mm (a better known number for "early" applications).

Thank you very much for that. Astronomy was what got me in to science, and I was fascinated by the distances and the methods and everything when I was a kid. Reading your post, for a moment I could remember how I felt back then.

 

[Horsa]

Thank you very much for that. Astronomy was what got me in to science, and I was fascinated by the distances and the methods and everything when I was a kid. Reading your post, for a moment I could remember how I felt back then.

It is fascinating.

I was fascinated by the constitutions of animals & birds & how they worked as a child as well as our constitution & how we worked though I was fascinated by a lot of other things. As you've probably guessed I'm very easy to inspire & wonder about many things even now. (I come from a dog family. My parents had my 1st dog before they had me. My aunts & uncles always had dogs &/ cats. I've also had cats, guinea pigs, rabbits, canaries, cockatiels, lovebirds, parrots, gold fish, frogs & ferrets *obviously not at the same time though* so that got me into animals, their constitutions & how they work.)

I've got more astronomical questions but decided to keep them for myself for now.

 

[Chris Koziarz]

That was fascinating. Thank you very much for your answers.

I wasn't going to ask that question next but found the information very interesting & didn't know that speed measurement unit you mentioned. Thank you very much. My next questions were actually going to be the diameters & circumferences of all the planets in our solar system except the earth which you've already answered & Saturn because of its rings & the speeds of all the other planets orbit around the sun except the earth which you've already answered & the distance of the other planets from the earth.

In order to come up with the scale-down model of the solar system, you don;t need to measure the actual inter-plenetary distances. All you need to do is observe the trajectories of the planets on the sky (geo-centric image) and transform said trajectories to the helio-centric Copernicus model. The pre-Copernicus (let's call them "dark ages") models were extremely complicated, and involved so called "epi-cycles":
https://www.khanacademy.org/partner-content/nasa/measuringuniverse/spacemath1/a/planets-epicycles
Copernicus first noted, and calculated that when we assign Sun to be motionless at the centre, all planetary motions become trivial circles co-centred at Sun in the same plane, with orbital periods growing with growing distances from the sun. I think only planets from venus until saturn were known at that time. Some 50y after Copernicus, Kepler made more precise measurements and calculations and concluded that earth as well as other planet orbits were tiny elongated ellipses rather than perfect circles. Kepler also formulated his famous laws of planetary motions, relating the planetary orbital speed to the size of the orbit with a simple quadratic equation. Today, we derive said equation from the Newton's law of universal gravitation applied to free falling objects, but remember that Newton was to be only born 100years after Kepler. So Kepler was a very good observer and clever mathematician so as to come up with simple motion equation without knowing its reason, equations so remarkable that we use them until today in classic mechanics. I think Newton also benefitted from Kepler's equations with the formulation of the gravity details. Astronomers today talk alot about Kepler but less so about Copernicus. But IMO, the first step of establishing the right model, rejecting the silly ego-centrism of dark ages, with its intractable "epi-cycles", was a far bigger revolution than making the model more precis. And all that work against the will of church authorities for whom Copernicus worked. So Copernicus deserves more appreciation than Kepler.
So, thanks to Kepler, all relative distances between sun and planets were already known before 1600. But the scale of the model was missing. You could make a model as small as you wanted for educational purposes: say Earth's 150Gm orbit down to 10cm, while Saturn 1.4Tm (tera-metres) orbit down to ~1m. But that was just a model not reality. To know the reality, you needed to measure just the actual distance between two any orbits, e.g. between earth and mars.
https://spaceplace.nasa.gov/review/dr-marc-solar-system/planet-distances.html
And that's pecisely what Cassini did in 1672 using... you guessed it: diurnal parallax.
Actually, Cassini used the base of parallax as the distance between Paris and French Guyana (where he sent his associate to make the same observation at the same time), so although his base distance was shorter than earth diameter, he didn't have to wait 12h between observations, so did not have to adjust for mars movement around the sun in his parallax measure. At the same time, Flamsteed made another measure, this time using diurnal parallax but he had to adjust his parallax angle by an orbital movement of the Mars within 12h. Both achieved the same accuracy of few % (50Gm lower than today's figure of 55Gm) but that first result was still remarkable. Once one distance in the solar system is known, we can calculate all distances including earth-sun, from Kepler. That fascinating history is described here:
https://briankoberlein.com/2015/01/08/martian-chronicles/
100 years after Cassini, more precise measurment was done, this time between the orbits earth-venus by observing venus at the background of sun (by that time the special light dimming instruments existed, previously unavailable to Cassini), using... again parallax! But this time it was parallax between N & S poles (well in reality such places as N tip of Norway & S tip of NZ but still a good vertical separation), so the two images of venus were traced on the sun disk, vertically separated, allowing to measure the parallax angle with far more precision. So a distance to venus between earth & sun was measured precisely as 38Gm. Other solar distances were extrapolated and since them, we know the astronomical unit to be 150Gm.
http://www.exploratorium.edu/venus/question4.html
By now, you must realise that two human eyes are a case of "mini-parallax" with the base distance of 62mm for women & 64mm for men. That's how our brain creates the perception of depth, using said mini-parllax. It works only up to about few dozen metres. We can increase our depth perception to maybe couple hundred m by moving our head from side to side and reasoning that closer objects are "moving with our head" more than more distant objects. BTW, do men rely on their eye sight depth more than women do, because evolution gave then slightly larger parallax base? Then, in astronomy, to "see" the depth of the solar system, we need to use diurnal parallax with the base of earth diameter 12Mm. Then to "see" the depth within Milky Way, we must use annual parallax with the base of 2a (300Gm). We already placed satellite on the other side of earth orbit so that we can make simultaneous observations wit anual parallax (no need to wait 6months) but unfortunately, they are not as powerful as Hubble (it would be nice if they were). We still need larger parallax to "see" the whole Milky Way not to mention beyond. Perhaps setting the obesrvatory around mars or other planets? But the communication over such distances are becoming problematic needless to say delayed by several hours so I doubt when and if that happens before our civilisation cease to exist.

 

[mrzz]

Just as a comment, there were heliocentric models in "classical times" (Greek word), but unfortunately they were not able to completely supersede the geocentric ones. There is a good article here, but there is one more interesting name that I wish I could remember that it is not mentioned there -- another Plato student which was more in to mathematics whose ideas ended up influencing a bit his much more famous contemporary Aristotle.

 

[Chris Koziarz]

Just as a comment, there were heliocentric models in "classical times" (Greek word), but unfortunately they were not able to completely supersede the geocentric ones. There is a good article here, but there is one more interesting name that I wish I could remember that it is not mentioned there -- another Plato student which was more in to mathematics whose ideas ended up influencing a bit his much more famous contemporary Aristotle.

I don;t know anything about that Pluto student.
Thanks for that link. The best summary I've seen of heliocentrism in ancient Greece. The most interesting is the fact that even as late 4 century AD, there were still traces of heliocentrism left (Emperor Julian of Byzantium (336-363 AD)) even though Christianity was pushing hard the Dark Ages, and it eventually eradicated not only the heliocentrism but reduced peoples' iimagination to a "flat-earthism" until Magellan times more than 1000y later.

 

[Horsa]

In order to come up with the scale-down model of the solar system, you don;t need to measure the actual inter-plenetary distances. All you need to do is observe the trajectories of the planets on the sky (geo-centric image) and transform said trajectories to the helio-centric Copernicus model. The pre-Copernicus (let's call them "dark ages") models were extremely complicated, and involved so called "epi-cycles":
https://www.khanacademy.org/partner-content/nasa/measuringuniverse/spacemath1/a/planets-epicycles
Copernicus first noted, and calculated that when we assign Sun to be motionless at the centre, all planetary motions become trivial circles co-centred at Sun in the same plane, with orbital periods growing with growing distances from the sun. I think only planets from venus until saturn were known at that time. Some 50y after Copernicus, Kepler made more precise measurements and calculations and concluded that earth as well as other planet orbits were tiny elongated ellipses rather than perfect circles. Kepler also formulated his famous laws of planetary motions, relating the planetary orbital speed to the size of the orbit with a simple quadratic equation. Today, we derive said equation from the Newton's law of universal gravitation applied to free falling objects, but remember that Newton was to be only born 100years after Kepler. So Kepler was a very good observer and clever mathematician so as to come up with simple motion equation without knowing its reason, equations so remarkable that we use them until today in classic mechanics. I think Newton also benefitted from Kepler's equations with the formulation of the gravity details. Astronomers today talk alot about Kepler but less so about Copernicus. But IMO, the first step of establishing the right model, rejecting the silly ego-centrism of dark ages, with its intractable "epi-cycles", was a far bigger revolution than making the model more precis. And all that work against the will of church authorities for whom Copernicus worked. So Copernicus deserves more appreciation than Kepler.
So, thanks to Kepler, all relative distances between sun and planets were already known before 1600. But the scale of the model was missing. You could make a model as small as you wanted for educational purposes: say Earth's 150Gm orbit down to 10cm, while Saturn 1.4Tm (tera-metres) orbit down to ~1m. But that was just a model not reality. To know the reality, you needed to measure just the actual distance between two any orbits, e.g. between earth and mars.
https://spaceplace.nasa.gov/review/dr-marc-solar-system/planet-distances.html
And that's pecisely what Cassini did in 1672 using... you guessed it: diurnal parallax.
Actually, Cassini used the base of parallax as the distance between Paris and French Guyana (where he sent his associate to make the same observation at the same time), so although his base distance was shorter than earth diameter, he didn't have to wait 12h between observations, so did not have to adjust for mars movement around the sun in his parallax measure. At the same time, Flamsteed made another measure, this time using diurnal parallax but he had to adjust his parallax angle by an orbital movement of the Mars within 12h. Both achieved the same accuracy of few % (50Gm lower than today's figure of 55Gm) but that first result was still remarkable. Once one distance in the solar system is known, we can calculate all distances including earth-sun, from Kepler. That fascinating history is described here:
https://briankoberlein.com/2015/01/08/martian-chronicles/
100 years after Cassini, more precise measurment was done, this time between the orbits earth-venus by observing venus at the background of sun (by that time the special light dimming instruments existed, previously unavailable to Cassini), using... again parallax! But this time it was parallax between N & S poles (well in reality such places as N tip of Norway & S tip of NZ but still a good vertical separation), so the two images of venus were traced on the sun disk, vertically separated, allowing to measure the parallax angle with far more precision. So a distance to venus between earth & sun was measured precisely as 38Gm. Other solar distances were extrapolated and since them, we know the astronomical unit to be 150Gm.
http://www.exploratorium.edu/venus/question4.html
By now, you must realise that two human eyes are a case of "mini-parallax" with the base distance of 62mm for women & 64mm for men. That's how our brain creates the perception of depth, using said mini-parllax. It works only up to about few dozen metres. We can increase our depth perception to maybe couple hundred m by moving our head from side to side and reasoning that closer objects are "moving with our head" more than more distant objects. BTW, do men rely on their eye sight depth more than women do, because evolution gave then slightly larger parallax base? Then, in astronomy, to "see" the depth of the solar system, we need to use diurnal parallax with the base of earth diameter 12Mm. Then to "see" the depth within Milky Way, we must use annual parallax with the base of 2a (300Gm). We already placed satellite on the other side of earth orbit so that we can make simultaneous observations wit anual parallax (no need to wait 6months) but unfortunately, they are not as powerful as Hubble (it would be nice if they were). We still need larger parallax to "see" the whole Milky Way not to mention beyond. Perhaps setting the obesrvatory around mars or other planets? But the communication over such distances are becoming problematic needless to say delayed by several hours so I doubt when and if that happens before our civilisation cease to exist.

That's fascinating. Thank you very much for the information.

That's enough of the social niceties & my opinion on the subject (for now at least). Time for a proper answer. Proper answer coming up.

I remember learning a bit about Copernicus & Pythagoras in the historical maths lesson I've spoken to you about before. All we learnt about space in science was where the planets were, they orbited the sun which was a star, that all the planets have moons which are satellites made of rock, Saturn has rings round it, our solar system is in the galaxy called the milky way & what the constellations are & what eclipses are as well as the fact Galileo invented the telescope which is much different than the ones we have today. I had heard of Kepler but think Copernicus deserves more recognition as my teachers must have done as they taught us about Copernicus but not Kepler.

I did realise.

I think the answer to your question is that in history men had to hunt to feed his family & defend them against predators as well as fornicate to keep his family going while women just needed to look after their family & have children so men did need better depth of eye sight, however, today with the rise of human rights gender roles in todays society are almost non-existent & the individual has some choice in what they do & more choice as to who they are (identity-wise where gender is concerned even to the point of being able to change their gender) & people no longer have to play the gender roles society "wrote for want of a better word" for them.

I've got no more questions at present. Thank you very much for answering my questions. I don't only think my questions bring forward interesting information for me but for other people too.

 

[Horsa]

Just as a comment, there were heliocentric models in "classical times" (Greek word), but unfortunately they were not able to completely supersede the geocentric ones. There is a good article here, but there is one more interesting name that I wish I could remember that it is not mentioned there -- another Plato student which was more in to mathematics whose ideas ended up influencing a bit his much more famous contemporary Aristotle.

That's fascinating. Thank you very much for sharing.

It wouldn't be Socrates by any chance would it? Just a guess.

 

[mrzz]

That's fascinating. Thank you very much for sharing.

It wouldn't be Socrates by any chance would it? Just a guess.

No, my friend. Socrates, in fact, was the teacher of Plato. Actually there are very few real evidences that Socrates really existed, and some scholars even sustain that Socrates is a character invented by Plato. Plato was a very good writer, so this is not so outlandish (in the sense that he could really have created a character as rich as Socrates). But I would guess that the consensus is that Socrates actually existed, just did not write much (as his philosophy is known exactly through Plato's writings).

Plato, by his turn, also had a lot of students. The most famous is Aristotle, but a few others were also important to ancient philosophy.

Just remembered! The other student was Eudoxus! But I must check, maybe he did not have a heliocentric model after all... but he was a much better mathematician than Aristotle, and surely contributed in the process of bringing math to astronomy.

 

[Chris Koziarz]

No, my friend. Socrates, in fact, was the teacher of Plato. Actually there are very few real evidences that Socrates really existed, and some scholars even sustain that Socrates is a character invented by Plato. Plato was a very good writer, so this is not so outlandish (in the sense that he could really have created a character as rich as Socrates). But I would guess that the consensus is that Socrates actually existed, just did not write much (as his philosophy is known exactly through Plato's writings).

Plato, by his turn, also had a lot of students. The most famous is Aristotle, but a few others were also important to ancient philosophy.

Just remembered! The other student was Eudoxus! But I must check, maybe he did not have a heliocentric model after all... but he was a much better mathematician than Aristotle, and surely contributed in the process of bringing math to astronomy.

I must disappoint you that your doubt above is actually true, against your wish... Eudoxus' astronomical model was closely related to that of Aristotle, in fact it was the precursor of the Aristotle geo-centric model with the rest of the universe dancing in silly epi-cycles I refereed to above. Information drawn from EB leaves no doubt about it:
https://www.britannica.com/biography/Eudoxus-of-Cnidus
"Eudoxus’s greatest fame stems from his being the first to attempt, in On Speeds, a geometric model of the motions of the Sun, the Moon, and the five planets known in antiquity. His model consisted of a complex system of 27 interconnected, geo-concentric spheres, one for the fixed stars, four for each planet, and three each for the Sun and Moon." (my emphasis)

 

[Chris Koziarz]

That's fascinating. Thank you very much for the information.

That's enough of the social niceties & my opinion on the subject (for now at least). Time for a proper answer. Proper answer coming up.

I remember learning a bit about Copernicus & Pythagoras in the historical maths lesson I've spoken to you about before. All we learnt about space in science was where the planets were, they orbited the sun which was a star, that all the planets have moons which are satellites made of rock, Saturn has rings round it, our solar system is in the galaxy called the milky way & what the constellations are & what eclipses are as well as the fact Galileo invented the telescope which is much different than the ones we have today. I had heard of Kepler but think Copernicus deserves more recognition as my teachers must have done as they taught us about Copernicus but not Kepler.

I did realise.

I think the answer to your question is that in history men had to hunt to feed his family & defend them against predators as well as fornicate to keep his family going while women just needed to look after their family & have children so men did need better depth of eye sight, however, today with the rise of human rights gender roles in todays society are almost non-existent & the individual has some choice in what they do & more choice as to who they are (identity-wise where gender is concerned even to the point of being able to change their gender) & people no longer have to play the gender roles society "wrote for want of a better word" for them.

I've got no more questions at present. Thank you very much for answering my questions. I don't only think my questions bring forward interesting information for me but for other people too.

I'm happy we've enlightened this thread with some interesting facts about astronomy. Yeah, let's close this subject now. Looks like another subject is looming now...

Well, as a bush regenerator, I first learned the word "fornicated" meaning "a plant bent in an archly shape", e.g. the shape of microlaena stipoides, sorry for bothering about Australian flora that might be far away from our interest herein, but that's what I was taught originally.

But turning our attention to the more popular meaning of the word "fornicate" you're referring to above (that I just learned) we indeed encroach onto the social niceties, and like you, I'm a bit afraid of discussing it honestly because we may break the rules and offend others. It's always risky to discuss morality in general, needless to say the type of morality implied by the fragment I emphasised above. Most religions condemn it although for largely silly reasons. Should we discuss it then?

If so, I never condemn/opine on anything if I don;t understand it. Because for me, understanding the facts pre-empts any moral/religious opinions/beliefs, etc. Religious beliefs and even morality often become outdated as scientific discoveries keep explaining our world. Herein, I just don't understand what you mean that a fornicate acts by man "keeps his family going". Is it just someone's opinion or a fact confirmed by social researchers, at least in some cultures?

 

[Horsa]

No, my friend. Socrates, in fact, was the teacher of Plato. Actually there are very few real evidences that Socrates really existed, and some scholars even sustain that Socrates is a character invented by Plato. Plato was a very good writer, so this is not so outlandish (in the sense that he could really have created a character as rich as Socrates). But I would guess that the consensus is that Socrates actually existed, just did not write much (as his philosophy is known exactly through Plato's writings).

Plato, by his turn, also had a lot of students. The most famous is Aristotle, but a few others were also important to ancient philosophy.

Just remembered! The other student was Eudoxus! But I must check, maybe he did not have a heliocentric model after all... but he was a much better mathematician than Aristotle, and surely contributed in the process of bringing math to astronomy.

O.K. pal. I knew there was a connection between them but forgot what it was.

I've never heard of him.

 

[Horsa]

I'm happy we've enlightened this thread with some interesting facts about astronomy. Yeah, let's close this subject now. Looks like another subject is looming now...

Well, as a bush regenerator, I first learned the word "fornicated" meaning "a plant bent in an archly shape", e.g. the shape of microlaena stipoides, sorry for bothering about Australian flora that might be far away from our interest herein, but that's what I was taught originally.

But turning our attention to the more popular meaning of the word "fornicate" you're referring to above (that I just learned) we indeed encroach onto the social niceties, and like you, I'm a bit afraid of discussing it honestly because we may break the rules and offend others. It's always risky to discuss morality in general, needless to say the type of morality implied by the fragment I emphasised above. Most religions condemn it although for largely silly reasons. Should we discuss it then?

If so, I never condemn/opine on anything if I don;t understand it. Because for me, understanding the facts pre-empts any moral/religious opinions/beliefs, etc. Religious beliefs and even morality often become outdated as scientific discoveries keep explaining our world. Herein, I just don't understand what you mean that a fornicate acts by man "keeps his family going". Is it just someone's opinion or a fact confirmed by social researchers, at least in some cultures?

O.k.

It's o.k. The more different scientific questions & subjects the better here because I made it about science in general which means the more variety the better.

Where I come from fornicate is a euphemistic term for the process by which sexual reproduction takes place. I can understand where your misunderstanding comes from if it means something different where you come from. Therefore unless a man's children die young fornication is the process by which man reproduces as man like other members of the animal kingdom reproduces sexually not asexually like bacteria or plants. I was trying not to be rude or explicit.

I don't mind you mentioning plants here. Botany is a science.

 

[britbox]

Actually there are very few real evidences that Socrates really existed

Sacrilege.

 

[Chris Koziarz]

O.k.

It's o.k. The more different scientific questions & subjects the better here because I made it about science in general which means the more variety the better.

Where I come from fornicate is a euphemistic term for the process by which sexual reproduction takes place. I can understand where your misunderstanding comes from if it means something different where you come from. Therefore unless a man's children die young fornication is the process by which man reproduces as man like other members of the animal kingdom reproduces sexually not asexually like bacteria or plants. I was trying not to be rude or explicit.

I still don't understand completely.
Do you use a term "fornication" here in place of a more general and more formal "sexual reproduction"? The context seems to imply it. Then I understand what you mean.
However, Collins (AWA as all dictionaries I looked up including urban dict) define "fornicate" as "having extra-marital sex" which smells like a morally loaded term and contradicting the familly life you're superposing it with. Certainly rarely anyone nowadays "fornicate" (in Colin's sense) to "keep his family going": virtually all homo sapiens reproductive activity in happening within sanctioned family units (or partnering relations which are recognised in Australia the same as familly units). But maybe you were trying to say that early homo sapiens males have been very promiscuous and their "family" consisted of many females. He was not "married" to any of his female partners, hence your use of the term "fornication" for his sex acts with the "family" (I would use a term "harem" here) of females. Is it the case?

 

[Horsa]

I still don't understand completely.
Do you use a term "fornication" here in place of a more general and more formal "sexual reproduction"? The context seems to imply it. Then I understand what you mean.
However, Collins (AWA as all dictionaries I looked up including urban dict) define "fornicate" as "having extra-marital sex" which smells like a morally loaded term and contradicting the familly life you're superposing it with. Certainly rarely anyone nowadays "fornicate" (in Colin's sense) to "keep his family going": virtually all homo sapiens reproductive activity in happening within sanctioned family units (or partnering relations which are recognised in Australia the same as familly units). But maybe you were trying to say that early homo sapiens males have been very promiscuous and their "family" consisted of many females. He was not "married" to any of his female partners, hence your use of the term "fornication" for his sex acts with the "family" (I would use a term "harem" here) of females. Is it the case?

We do where I live. I guess that we could also use the term copulation to mean that too. Like I said before I was trying not to be rude & too explicit here by not using the term sexual reproduction.

I guess if you're understanding it or defining it under those terms that questions of morals would definitely come in as the people involved would be having an affair &/ using a brothel. However, like you stated early man didn't have the same values as they have today & may have been polygamous or even like animals. Don't forget! Marriage hasn't always been around. Before the advent of marriage, humans would have been as free as animals & able to cop off with anyone of the opposite gender they wanted like animals do in the wild. Who came up with the idea of marriage? An early human or early society. Marriage like many other things including religion is a social construction. They're not natural. We haven't always had them. Society brought them into being.