Who first found the Heliocentric or Geocentric Distances

[Philosophaie]

Historically, how did they first find the Heliocentric and Geocentric distances of the Planets? I would imagine that a rudimentary system of Right Ascension and Declination or at least a Azimuth and Altitude from a fixed base telescope was established. The system was based on the Astronomical Unit, au, of course. Did they use Solar Parallax? Kepler was the first person to get it right with the observations of Mars from Tycho Brahe. Who before that first observed the parallax distance from au?

 

[marcus]

Aristarchus around 250 BC took the first step.

His book presenting the heliocentric model has been lost, but Archimedes in HIS book "Sand Reckoner" presents Aristarchus heliocentric model of solar system (as part of a kind of pedagogical thought experiment).

And so if I remember right, COPERNICUS in his book gives Aristarchus credit for having been the first to think up the heliocentric picture.

You can look up Aristarchus in Wipikidia. He estimated the ratio of the distances to sun and moon by trying to measure the angle between sun and moon when the moon was exactly a half moon, so there would be a long skinny right triangle with the right angle at the moon, the large nearly 90 degree angle at the Earth and the very small angle at the sun.

He reasoned that since the moon and sun have roughly the same angular size, then since the sun was (according to him) much much farther than the moon it must therefore be much much bigger. And therefore, it seemed reasonable to suppose that other things went around it.

 

[Philosophaie]

What meant to ask was who was the first to use the distance from the Earth to the Sun, 1 au, to calculate the distance to another planet possibly using parallax?

 

[marcus]

What meant to ask was who was the first to use the distance from the Earth to the Sun, 1 au, to calculate the distance to another planet possibly using parallax?

Kepler could tell the semi major axis from the period already in around 1610.

Cassini measured the distance to Mars by PARALLAX around 1672, so that squares with what you said.

Hopefully some other people will jump in, I don't know much of the history.

The thing about Kepler's 3/2 power law is that if you know the orbital period in Earth years, and you take the 2/3 power that tells you the average distance from the sun (semi major axis) in AU.

So that is the kind of thing you were asking about, distance from sun in AU.

If the orbit period were 27 years then the distance would have to be 9 AU.
If the orbit period were 8 years the distance to sun would have to be 4 AU.

 

[marcus]

the orbit distances of other planets is so closely linked to the AU that measuring the one is often linked to measuring the others:

==quote Wikipedia "AU" ==
Jean Richer and Giovanni Domenico Cassini measured the parallax of Mars between Parisand Cayenne in French Guiana when Mars was at its closest to Earth in 1672. They arrived at a figure for the solar parallax of 9 1⁄2", equivalent to an Earth–Sun distance of about 22000 Earth radii. They were also the first astronomers to have access to an accurate and reliable value for the radius of the Earth, which had been measured by their colleague Jean Picard in 1669 as 3269 thousand toises. Another colleague, Ole Rømer, discovered the finite speed of light in 1676: the speed was so great that it was usually quoted as the time required for light to travel from the Sun to the Earth, or "light time per unit distance", a convention that is still followed by astronomers today.
==endquote==

The "solar parallax" is basically the angular size of the Earth as seen from the sun, or more precisely the angular size of the Earth's radius.
So if you know that angle, and the Earth's radius, you can calculate our distance from the sun.
If the solar parallax angle is α then the ratio of Earth radius to AU is cotangent α

So if the angle, in radians, is 1/22,000 then the distance to the sun is about 22,000 times the radius of the Earth.

Cassini and Richer measured the distance from Earth to MARS, by parallax from two locations on Earth, and this allowed them to calculate the Earth's distance from the sun, i.e. the "solar parallax" and also incidentally they would have been able to estimate the distance of Mars from the sun.

It seems to me that astronomers must have had some rough idea of the distances of other planets from sun, compared with the AU, for a long time maybe as far back as Copernicus. They knew some rough proportions, ratios. They just did not know the astronomical UNIT very accurately.

Kepler had to have fairly good estimates of orbit distances in order to come up with his 3/2 power law. that the semi major axis of the ellipse is the 2/3 power of the orbit period. (using Earth orbit units).
He had to struggle to get his estimate of the Mars distance because its orbit is so elliptical but the other ones were probably not so hard. After all there is a kind of parallax you get by observing the planet's position when the Earth is at different spots on its orbit, where the baseline is in terms of the AU.

 

[BobG]

Kepler did not have a good estimate of the distance between the Earth and Sun. He could tell Ptolemy's estimate was horribly wrong - that the Earth had to be at least 3 times farther away from the Sun that Ptolemy's estimate, but Ptolemy's estimate was about 7.5 million kilometers (about 0.05 times the actual distance).

But, Kepler's laws did raise interest in determining how far the Earth really was from the Sun.

So, shortly after Kepler's laws, Cassini and Richer determined a decent estimate using Mars as a reference.

And, my favorite, Jeremiah Horrocks made a decent estimate using the first transit of Venus in front of the Sun ever observed with a telescope around the same time frame. Horrocks' observation was significant because another transit of Venus would occur in 1761 and 1769. Astronomers planned for the next transit and observers were dispatched all over the Earth to observe the next transit from as many locations as possible. Those observations gave a very good estimate in spite of lots of difficulties in the observations, including the possibility of being sunk at sea (England and France were at war with each other, making travel hazardous), being declared dead and having one's wife remarry and all of one's property being divided by relatives (if you're going to disappear for 11 years to watch both transits, maybe you ought to write home once in a while).

 

[mfb]

Kepler could tell the semi major axis from the period already in around 1610.

The period alone does not help if you don't have a mass scale. You can get the distance to moon, sure, but not the other distances in the solar system. If everything would be twice as far apart, have twice the radius and 8 times the mass, nothing would change for our observations.

The tiny parallax in Venus transits or the parallax of Mars can be used, precise timing of the Jovian moons can be used, the gravitational influences of the planets on each other can be used, but all those methods are much more complicated than simply taking the period of an orbit.
You can also assume that Venus and Mars don't have a size completely different from Earth to get a rough estimate, but that method is not really reliable.

 

[marcus]

Hi Mfb,
I was trying to address Philosoph's question which I took to be who was the first who calculated a distance to a planet (e.g. a semimajor axis) in terms of the AU unit without worrying about determining the size of the AU in other terms like leagues or miles or stadia etc.
==quote Philo==
What meant to ask was who was the first to use the distance from the Earth to the Sun, 1 au, to calculate the distance to another planet possibly using parallax?
==endquote==
So I pointed out that:
"Kepler could tell the semi major axis from the period already in around 1610."

Not sure when it was, maybe more like 1615, but still pretty early!
If you just want to know the semimajor axis a in AU and you know the period P in years then
a = P^2/3

So, if that was what he was asking you don't need a mass scale, for instance Jupiter period is about 12 years and 12^2/3 very roughly is 5-something---so Jupiter's average distance from the Sun is a bit over 5 AU.

 

[mfb]

Ah okay. Sure, relative semimajor axes can be done based on the period alone.