observational techniques that famous astronomers used

Hi,

I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

Were the astronomers measuring angles relative to some fixed star over
time? Or just the angular position in the skip (2 angles) and then
converting this some how to account for the location of earth in its
orbit?

Thanks,

Ted

In article , writes:
I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

There are people who know a lot more about history than I do, so
perhaps someone will correct me. As I understand it, Tycho Brahe
measured the positions of visible planets for many years. These
would have been right ascension and declination (or possibly ecliptic
longitude and latitude) at the times of observation. I think his
instrument was probably a transit circle.

The observations themselves were just positions in the sky. Kepler's
theory had to account for the changing position of Earth in order to
explain the observations.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

wrote in message
...
Hi,

I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

Were the astronomers measuring angles relative to some fixed star over
time? Or just the angular position in the skip (2 angles) and then
converting this some how to account for the location of earth in its
orbit?

Kepler used Tycho Brahe's measurements with various mural transit
instruments, so effectively Tycho obtained Declination and Right Ascension,
which could easily be converted to ecliptic coordinates of celestial
latitude and longitude (I say easily, but this routine calculation was
difficult enough because it all had to be done with paper and pencil). By
(in essence) using observations of Mars that were one sidereal martian year
apart, the actual position of Mars could be calculated by triangulation from
the two different positions of Earth. With many pairs of observations the
shape of the orbit could be determined to be an ellipse. There are a lot of
additional details but that's the principle of the method.

--
Mike Dworetsky

(Remove "pants" spamblock to send e-mail)

In article ,
Steve Willner wrote:

The observations themselves were just positions in the sky. Kepler's
theory had to account for the changing position of Earth in order to
explain the observations.

As I understand it, Kepler assumed that the planets had recurring
orbits. That is, Mars (for instance) returned to the same point in
space every Martian year. With that assumption, it's straightforward
to work out Mars's 3-D orbit from Tycho's 2-D observations.

First, you figure out the period of the orbit. You can get this by
measuring the synodic period (interval between times when Mars is in
the same place relative to the Earth, such as oppositions). The
synodic and sidereal periods are related in a simple way.

Then, you take pairs of observations taken one Martian year apart. By
hypothesis, Mars is in the same place at both times, but Earth isn't.
So you can triangulate to pinpoint Mars's position. Do this for many
such pairs of observations, and you map out Mars's orbit.

Of course, this means Kepler was somewhat lucky. It's pretty much a
coincidence that the orbits of the planets do turn out to recur. If
gravity had been an inverse-cube force or something, then they
wouldn't.

-Ted

--
[E-mail me at , as opposed to .]

Where could I find out more of these details?

Thanks,

Ted

Mike Dworetsky wrote:
wrote in message
...
Hi,

I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

Were the astronomers measuring angles relative to some fixed star
over
time? Or just the angular position in the skip (2 angles) and
then
converting this some how to account for the location of earth in
its
orbit?

Kepler used Tycho Brahe's measurements with various mural transit
instruments, so effectively Tycho obtained Declination and Right
Ascension,
which could easily be converted to ecliptic coordinates of celestial
latitude and longitude (I say easily, but this routine calculation
was
difficult enough because it all had to be done with paper and
pencil). By
(in essence) using observations of Mars that were one sidereal
martian year
apart, the actual position of Mars could be calculated by
triangulation from
the two different positions of Earth. With many pairs of
observations the
shape of the orbit could be determined to be an ellipse. There are a
lot of
additional details but that's the principle of the method.

--
Mike Dworetsky

(Remove "pants" spamblock to send e-mail)

Steve Willner wrote:
In article , writes:
I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

There are people who know a lot more about history than I do, so
perhaps someone will correct me. As I understand it, Tycho Brahe
measured the positions of visible planets for many years. These
would have been right ascension and declination (or possibly ecliptic
longitude and latitude) at the times of observation. I think his
instrument was probably a transit circle.

The observations themselves were just positions in the sky. Kepler's
theory had to account for the changing position of Earth in order to
explain the observations.

--
Steve Willner Phone 617-495-7123

Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

The major representation of the motion of Mars against the backdrop of
stars from a geocentric view was called Kepler's Lenten Pretzel or
Panis Quadragesimalis.From that representation taken over many years
(with the familiar retrograde loop) it is almost possible, with
hindsight, to see elliptical motion fall out of the criss-crossing of
orbital lines and despite the maligning of Ptolomeic Equant,I'm sure
Kepler made use of that feature in coming to the insights on the shape
and motion of planetary orbits.

Newton was flat-out wrong by adopting Flamsteed's isochonical framework
for planetary motion,it is great for identifying positions of planets
based on the calendrical system however by transfering celestial Lat
and Long based on a axial rotational/stellar circumpolar equivalency to
mean Sun/Earth orbital distances it shuts off the ability to
incorporate any greater rotational motion such as the Solar system's
galactic orbital motion and its influence on heliocentric planetary
orbital motion.

Put it this way,Kepler was working off mean orbital motion from a line
drawn through the center of the Earth's orbital motion about the Sun
while Newton used mean Sun/Earth distances,these are two very different
astronomical points of view.



"That the fixed stars being at rest, the periodic times of the five
primary planets, and (whether of the sun about the earth, or) of the
earth about the sun, are in the sesquiplicate proportion of their mean
distances from the sun." Newton

http://members.tripod.com/~gravitee/phaenomena.htm

"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

Ultimately it is not about returning to Keplerian methods and given the
technology availible today who would wish to, however,Newtonian
perspectives place such a restriction for astronomical advancement that
only a theorist could love it.

"Cor. 2. And since these stars are liable to no sensible parallax from
the annual motion of the earth, they can have no force, because of
their immense distance, to produce any sensible effect in our system.
Not to mention that the fixed stars, every where promiscuously
dispersed in the heavens, by their contrary actions destroy their
mutual actions, by Prop. LXX, Book I."

A more attractive avenue appears to be jettisoning the explanation of
planetary motion through terrestial ballistics laws and focusing on how
the solar system's galactic orbital motion influences planetary
heliocentric motion and specifically how it varies the shape of the
orbit while retaining Kepler's second law.

In other words in really is important to go back and review the details
and data availible to Kepler and astronomers in his era.

In article , "Mike
Dworetsky" writes:

wrote in message
...
Hi,

I was just curious about what exactly measurements astromoners made
that provided data to those like Kepler to determine
the relationship between period and radius of a planet.

Were the astronomers measuring angles relative to some fixed star over
time? Or just the angular position in the skip (2 angles) and then
converting this some how to account for the location of earth in its
orbit?

Kepler used Tycho Brahe's measurements with various mural transit
instruments, so effectively Tycho obtained Declination and Right Ascension,
which could easily be converted to ecliptic coordinates of celestial
latitude and longitude (I say easily, but this routine calculation was
difficult enough because it all had to be done with paper and pencil). By
(in essence) using observations of Mars that were one sidereal martian year
apart, the actual position of Mars could be calculated by triangulation from
the two different positions of Earth. With many pairs of observations the
shape of the orbit could be determined to be an ellipse. There are a lot of
additional details but that's the principle of the method.

The discrepancy in the position of Mars which prompted Kepler to
postulate elliptical orbits was 8 minutes of arc, about a quarter of the
size of the full moon (or, equivalently, a pea held at arm's length),
not bad for pre-telescope observations.

In message ,
writes

"Cor. 2. And since these stars are liable to no sensible parallax from
the annual motion of the earth, they can have no force, because of
their immense distance, to produce any sensible effect in our system.
Not to mention that the fixed stars, every where promiscuously
dispersed in the heavens, by their contrary actions destroy their
mutual actions, by Prop. LXX, Book I."

A more attractive avenue appears to be jettisoning the explanation of
planetary motion through terrestial ballistics laws and focusing on how
the solar system's galactic orbital motion influences planetary
heliocentric motion and specifically how it varies the shape of the
orbit while retaining Kepler's second law.

In other words in really is important to go back and review the details
and data availible to Kepler and astronomers in his era.

It's more important to stick to reality. The solar system's galactic
orbital motion does not affect planetary motion, because as correctly
noted by Newton the stars are too far away.
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I assure you that the solar system's galactic orbital motion conditions
planetary heliocentric motion in terms of Keplerian motion.

Even in principle,it is impossible to isolate the motion of the Sun
around the galactic orbital center from the motion of the planets
simultaneously around the Sun and in the direction of the solar
system's galactic orbital motion.

The trajectory of the Sun around the galactic axis,by definition,
determines that planetary motion is conditioned by that greater
rotation.


By all means remain with the Newtonian view but it means excluding the
motion of the local Milky Way stars (along with our own star) and
accepting that solar system is an isolated entity with no other
influences acting on it.

[Mod. note: the numbers for the centripetal accelerations of the two
orbits involved are instructive and simple to calculate -- mjh.]