Kelper & Tycho - how did they come to their conclusions?

fret_wimp2 wrote: »

What I cant figure out and can find no info on is HOW they made their discoveries. Can anyone elaborate on the details of the experiments and measurements they took, and how they were done.

Wikipedia can tell you.

Tycho built and used instruments that measured the positions of the stars in the sky very precisely. The lack of measurable parallax for "new stars" and comets showed that they were far away, like the stars, not in the atmosphere. This disproved the idea that the heavens were unchanging.

Tycho's precise measurements of the positions of the planets allowed Kepler to work out his laws.

fret_wimp2 wrote: »

Thanks guys. To get more specific ( my question was badly phrased), lets say just using the standard tools in my garrage or perhaps purchase a rudamentary instrument that would have been easily constructed back at the time of copernicus or Kelper, how could I, in my back garden prove the same thing they did.

Im interested in the exact method of how they did what they did without very accurate clocks or advanced equipment.

Sure, it takes many years to become accustomed to their exact methods but if you want what is effectively the ' inverse square law' even though it isn't a law nor is it a description of planetary dynamics .

"The proportion existing between the periodic times of any two planets is exactly the sesquiplicate proportion of the mean distances of the orbits, or as generally given,the squares of the periodic times are proportional to the cubes of the mean distances." Kepler

If you have a real interest in what Kepler did and how he did it you would do something I can't which is post the relevant image showing the motion of the Earth and the motion of Mars over a 16 year period because there is nothing in your garage that will help you. If you want a more expanded version of Kepler's statement above then here it is -

"But it is absolutely certain and exact that the ratio which exists between the periodic times of any two planets is precisely the ratio of the 3/2th power of the mean distances, i.e., of the spheres themselves; provided, however, that the arithmetic mean between both
diameters of the elliptic orbit be slightly less than the longer diameter." Kepler

What he and his contemporaries did is gauge the length of time it took a planet to pass through the background field of stars and return to the same position against those stars. It takes the Earth one year to return to the same position, Jupiter 12 years, Saturn roughly 30 years and so on. Now there is a lot of work involved and it is not always as straightforward as this however ,for the purpose here, you are looking at a correlation between the time it takes a planet to make a circuit of the Sun and its distance from the Sun.

"And so if any one take the period, say, of the Earth, which is one year, and the period of Saturn, which is thirty years, and extract the cube roots of this ratio and then square the ensuing ratio by squaring the cube roots, he will have as his numerical products the most just ratio of the distances of the Earth and Saturn from the sun. For the cube root of 1 is 1, and the square of it is 1; and the cube root of 30 is greater than 3, and therefore the square of it is greater than 9. And Saturn, at its mean distance from the sun, is slightly higher than nine times the mean distance of the Earth from the sun." Kepler

You have all this explained by Kepler rather than me but there are now tools which help the contemporary observer streamline these insights into visual narratives where they can be then used properly.

Zubeneschamali wrote: »

Well, no. Anyone can do that in their back yard, using just their bare eyes. Ptolemy knew that stuff around 150 AD.

Tycho measured the distances to the planets using parallax, and disproved Ptolemy's system. You can't measure parallax without precise, accurate instruments.

(Tycho also drew entirely the wrong conclusions from his measurements of stellar parallax, which is why he is always mentioned with Kepler, who used Tycho's data to better effect).

Make yourself useful and post this APOD image for me - ' Jupiter and Saturn Pas De Deux' .

djpbarry wrote: »

You think you can whack something together in your shed and replicate the work of Tycho Brahe?

It never ceases to depress me when people are so incredibly dismissive of brilliant science.

He asked a basic and valid question and is likely to be bombarded with bluff and voodoo when he can easily read what Kepler wrote and ,with the aid of graphics and images, can see how the original astronomers worked out the Earth is sandwiched between the inner and outer planets in our common orbit around the Sun.

I am hampered by not being able to demonstrate the original astronomical arguments which set the Earth and other planets in motion around the Sun using imaging along with the words of the great astronomers but it is all very simple to the eyes and the mind.

Zubeneschamali wrote: »

Tycho made all of those brilliant observations, measured the distances to the Sun and planets and proved Ptolemy wrong, but he still concluded that the Earth was stationary at the centre of the universe, and that the sun went around it.

The original question in the title of this thread is how did Kepler arrive at his conclusions and there are multiple considerations to take into account but most can be easily identified with imaging,graphics and so on.

One of the main arguments relied on the time it took a celestial object to return to the same area against the background stars or the 'periodic times' argument -

" The 10th argument,taken from the periodic times, is as follows; the apparent movement of the Sun has 365 days which is the mean measure between Venus' period of 225 days and Mars' period of 687 days.Therefore does not the nature of things shout out loud that the
circuits in which those 365 days are taken up has a mean position between the circuits of Mars and Venus around the Sun and thus this is not the circuit of the Sun around the Earth -for none of the primary planets has its orbit arranged around the Earth,as Brahe admits,but the circuit of the Earth around the resting Sun,just as the other planets,namely Mars and Venus,complete their own periods by running around the Sun." Kepler.

Now, I am hamstrung with the inability to present imaging to demonstrate the methods used to provide greater detail to these points however there is a huge modification made possible by contemporary imaging which allows observers to appreciate the difference between inner and outer planetary retrogrades.

fret_wimp2 wrote: »

Hang on a second.
1. I dont think i can replicate anything, hence why i asked the question.
2. Not once has the brilliance of any of these giants of science been questioned.

My question stems from the fact that although these men were brilliant, they didnt have satellites, computers, a wealth of knowledge in a library, very accurate clocks, the internet or even electricity. Yet they still managed to come to amazing conclusions.

To try and explain my question a bit better, we know their conclusions are true, but if all the books, internet and electricity disappeared tomorrow how would you prove it all again, with the limited means available?


It never ceases to depress me how condescending some people can be when they expect everyone to be at their level of knowledge, and put down those who ask questions to try to learn.

There's a reason these guys are famous. The observations and their interpretation were extremely far from easy or obvious. The poster who wants to show you the pictures that makes it all obvious to the modern mind is, perhaps, missing the point of your question: the answer is "it was damn hard". They were also hamstrung by earlier scientific, mathematical, religious and occult prejudices. The Tychonic system attempts to combine Ptolemy and Copernicus, but gets it wrong. Kepler was obsessed at one stage about a possible relationship between the planetary periods and the Platonic solids, based on the assumption that God created the universe according to a mathematical plan. He also fumbled for the right mathematical tools to perform his analysis and along the way contributed to the development of calculus.

You say "we know their conclusions were true", but remember the typical potted history of science winnows out all the missteps, the blind alleys, the bowing to conventional wisdom ... and leaves what looks like an unerring trajectory toward the modern viewpoint. Some of their conclusions were true, and the rest are generally glossed over. In the end, I think, the reason they are remembered is that Tycho was obsessive about the quality and accuracy of his measurements, and Kepler was honest in their interpretation, going where the data led, as well as having profound insights about their relationships.

Depending on how deep you want to delve, you will find a great deal of information online about the two men, their contemporaries, their influences, and the state of contemporary science and maths. If you want to start with Tycho and his amazing instruments, which were the most advanced of the pre-telescopic era, you could start with the evolution of the mural quadrant during the time of the medieval Arabic astronomers, and from even earlier marine navigational aids. I found some great online material (not Wikipedia) previously, will see if I can dig it out.

You will see that improvement in observational accuracy was a painstaking, incremental process. Mostly it was used to provide updates to Ptolemy's Almagest which was still the basic seminal work for 1300 years. (And even it built on the lost work of Hipparchus, 300 years earlier). These efforts could still not be reproduced by "the man in the street" without specialist education.

"There's a reason these guys are famous. The observations and their interpretation were extremely far from easy or obvious. The poster who wants to show you the pictures that makes it all obvious to the modern mind is, perhaps, missing the point of your question: the answer is "it was damn hard". " ps200306

The question was how did they come to their conclusions rather than whether it was hard or not. My point is that there is nothing difficult about these things nowadays as long term observations can be condensed into easily understandable form where the planets move around the Sun and against the backdrop of the field of stars.

I sat in the waiting room of my gp and picked up a brochure about quitting smoking and the description was focused on how hard it is to stop and all the nicotine replacements that are available to curb the pangs however I did read a book a dozen years ago by Allan Carr which said the absolute opposite in that it is easy to stop smoking and I found it to be the case. The parallel point is that observers today approach astronomy with a fear that there is something difficult about the endeavor when nothing could be further from the truth and especially now when visual narratives translate long term imaging into context of the Earth's motion,the structure of the solar system, cause and effect between dynamics and terrestrial sciences and so on.

Kepler and Brahe worked off a particular perspective that becomes troublesome when dealing with observations seen from Earth separating the inner and outer planets but this involves actually looking at the motions as they appear to us and dealing with them. I would ask the moderator to remove the newbie block on links needed to present the arguments but respect that it may not be possible.

ps200306 wrote: »

The question was how they worked it all out without benefit of modern equipment or hindsight.

Be my guest, you have the Panis Quadragesimalis of Kepler in front of your on Wikipedia page showing the extent of retrogrades as the Earth overtakes Mars and the variations with each orbital pass but that won't help you with Venus and Mercury as the inputs are different.

Care to present the image where I cannot as a newbie along with an APOD image of Mars in retrograde to give it a contemporary treatment ?.

Zubeneschamali wrote: »

gkell11 wrote: »

Tycho disproved Ptolemy using parallax - and you cannot see that at all without extremely precise instruments.

Kepler used the same data to deduce that orbits are elliptical, rather than circular, and that the speed of a planet in it's orbit depends on its distance from the sun. Nothing you are going to observe yourself in your back yard will prove that, either.

Retrograde motion is nothing to do with parallax or elliptical orbits - Ptolemy's tables described retrograde motion 1000 years before Tycho.

The general run of these things is that participants create a firewall of voodoo and moderation rather than inspect the details of what was observed and how these observations were translated into context. I did call for the relevant images so that if people do genuinely wish to know how Kepler, Galileo and Copernicus looked at these topics using observations they would supply the observations for everyone to inspect ,add comments from the original innovators or create new perspectives. I haven't seen anyone lift a finger in that respect confirming an observation (rather than a complaint) that Galileo made to Kepler even though it is a little bit self-congratulatory -

"My dear Kepler, I wish that we might laugh at the remarkable stupidity of the common herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth" Galileo

In short, astronomy at this level is still a visual pursuit so that were observers interested in what Copernicus,Galileo or the other astronomers achieved they would,of necessity, walk the same path as they did. There is an unresolved issue concerning retrogrades which can only now be explained using modern tools and involving the partitioning between inner and outer planetary retrogrades resolutions but this is a huge undertaking even for those committed to such an endeavor.

It is not an issue about putting anyone on the spot or how well they can use stock phrases that are meaningless but rather on the rare occasion when somebody does ask about the methods used by the original heliocentric astronomers it is an opportunity for engagement.

djpbarry wrote: »

I didn’t mean to be condescending, but have another look at your post. You asked how you could replicate the work of Kepler using “standard tools” in your garage or “rudimentary instruments that would have been easily constructed at the time of Copernicus and Kepler”. You wanted to know how to reproduce their work without “very accurate clocks or advanced equipment”. The simple answer is that you can’t. You could certainly try, but without extremely accurate instruments capable of precise measurements, you are very unlikely to succeed.

The original poster asked how they came to their insights -

"What I cant figure out and can find no info on is HOW they made their discoveries. Can anyone elaborate on the details of the experiments and measurements they took, and how they were done.

I just want to know what they did and get a view of how that proves what they discovered."

There is a step by step process which was not available online,at least until now, so although he may assume that there is some garage experiment that explains the insight of Kepler the fact is that he is looking in the wrong place.

A simple watch can be used to prove Kepler's variations in orbital speed from day-to-day observations however such a proof takes a lot of groundwork by following the path of those astronomers up to a certain point. That is the exciting bit however it does require an effort on the part of the inquirer to supply visual perspectives that I can't presently.

Zubeneschamali wrote: »

Please, do explain how.

The original poster of this thread has to work for it by following a particular set of observations that can be reproduced using images and links along with the original descriptions of the astronomers themselves. I cannot do this presently due to a newbie status nor would I do it anyway,after all, it is a journey rather than a chore.

gkell11 wrote: »

That is incorrect, with two strings, a stopwatch and a normal watch he can demonstrate Kepler's insight that a planet varies its speed as it moves through space.

He is not asking how to demonstrate it, he is asking how Tycho and Kepler made their measurements and deductions. Demonstrating it after you already know the answer is a whole different ballgame.

Kepler's insight that the orbit of Mars is an ellipse was based on years and years of observations: to measure the position of a point on Mars orbit (relative to the Earth) requires a pair of observations one Mars year apart: 687 days. That's the minimum time you'd need to observe Mars to reproduce Kepler's result. Of course, you can't observe Mars every night -sometimes it is too near the Sun and only up during the day. Sometimes the weather is bad.

So in practice, you need observations over a much longer period to give you pairs of measurements 687 days apart.

Of course, given the positions, you can do Kepler's geometry yourself. But Kepler also had to deal with the errors in Tycho's measurements (which were the best ever up to that date, but still only good to 2 or 3 arc-minutes), and the fact that Tycho wasn't trying to measure things exactly one Mars year apart for all those years.

gkell11 wrote: »

This accounts for the motion of the outer planets but does not account for inner planetary retrogrades so Kepler fills in the gap using the periodic times argument which inserts the Earth between Mars and Venus as a means to complete solar system structure from Mercury to Saturn (at leas tin his time).

Telling the OP how Kepler discovered things which Copernicus published before Kepler was even born is perhaps not entirely constructive.

gkell11 wrote: »

When it comes to inner planetary retrogrades then you run into trouble as the periodic times argument which sets the planets in motion against the background stars along with using the Sun's annual motion through the Zodiac fails.

This is complete gibberish. Copernicus understood perfectly well about inner and outer planets: