Semi-minor Axis

Hi,

I've been lurking and gaining a great deal of knowledge from this
newsgroup for quite some time now but I have a very basic question that
I have not seen asked.

I used to think that Aphelion referred to the semi-major axis of the
ellipse described by the Earth (or any planet) on its journey around the
Sun and Perihelion was the semi-minor axis. Having read most of the
planetary data from 'The Nine Planets' web site I now see that the sum
of Aphelion and Perihelion is in fact the major axis of that ellipse.
What I cannot understand is the statement in the Glossary that Aphelion
is also the 'average' or mean distance of the planet from the Sun.

Surely the maximum distance cannot also be the mean?

What I really want to know is how to calculate the semi-minor axis.
Given the 'Mean' and the eccentricity I can readily calculate the Major
as a(1+e) and the Minor as a(1-e) but if the mean is also the Major then
this doesn't make sense.

JG

Wasn't it JG who wrote:
Hi,

I've been lurking and gaining a great deal of knowledge from this
newsgroup for quite some time now but I have a very basic question that
I have not seen asked.

I used to think that Aphelion referred to the semi-major axis of the
ellipse described by the Earth (or any planet) on its journey around the
Sun and Perihelion was the semi-minor axis. Having read most of the
planetary data from 'The Nine Planets' web site I now see that the sum
of Aphelion and Perihelion is in fact the major axis of that ellipse.
What I cannot understand is the statement in the Glossary that Aphelion
is also the 'average' or mean distance of the planet from the Sun.

Surely the maximum distance cannot also be the mean?

What I really want to know is how to calculate the semi-minor axis.
Given the 'Mean' and the eccentricity I can readily calculate the Major
as a(1+e) and the Minor as a(1-e) but if the mean is also the Major then
this doesn't make sense.

The aphelion is not the mean distance, and it doesn't say so in the nine
planets glossary:

http://www.nineplanets.org/help.html
aphelion
the point in its orbit where a planet is farthest from the Sun; when
refering to objects orbiting the Earth the term apogee is used; the
term apoapsis is used for orbits around other bodies. (opposite of
perihelion)

Nine Planets says that the *semimajor axis* is the average distance of
the planet from the Sun. (I'd claim that that depends what you mean by
"average". If you average over time, then you get a result that's longer
than the semimajor axis because the planet moves more slowly when
further from the Sun.)

--
Mike Williams
Gentleman of Leisure

Mike Williams said

Wasn't it JG who wrote:

I used to think that Aphelion referred to the semi-major axis of the
ellipse described by the Earth (or any planet) on its journey around the
Sun and Perihelion was the semi-minor axis. Having read most of the
planetary data from 'The Nine Planets' web site I now see that the sum
of Aphelion and Perihelion is in fact the major axis of that ellipse.
What I cannot understand is the statement in the Glossary that Aphelion
is also the 'average' or mean distance of the planet from the Sun.

Surely the maximum distance cannot also be the mean?

What I really want to know is how to calculate the semi-minor axis.
Given the 'Mean' and the eccentricity I can readily calculate the Major
as a(1+e) and the Minor as a(1-e) but if the mean is also the Major then
this doesn't make sense.

The aphelion is not the mean distance, and it doesn't say so in the nine
planets glossary:

Agreed Mike - it _was_ late in the day (or very early if you prefer) and
I knew I'd made a major error the second I hit the 'send' button.


http://www.nineplanets.org/help.html
aphelion
the point in its orbit where a planet is farthest from the Sun; when
refering to objects orbiting the Earth the term apogee is used; the
term apoapsis is used for orbits around other bodies. (opposite of
perihelion)

Nine Planets says that the *semimajor axis* is the average distance of
the planet from the Sun. (I'd claim that that depends what you mean by
"average". If you average over time, then you get a result that's longer
than the semimajor axis because the planet moves more slowly when
further from the Sun.)

I did some further calculations once I had sent the question -
simply writing the question out created further enlightenment - and I
can now see that it is perfectly obvious why the term Mean or Average
could be applied (I still don't understand your point about averaging
over time but that might come with further study).

What I now see (from my calculations) is that the semi-minor axis is in
fact the same as the Perihelion distance. Which probably explains why I
used to think that Aphelion and Perihelion referred to the semi-major
and semi-minor Axies, ie. I was half right.

Thanks for the input.

JG

Wasn't it JG who wrote:
What I now see (from my calculations) is that the semi-minor axis is in
fact the same as the Perihelion distance. Which probably explains why I
used to think that Aphelion and Perihelion referred to the semi-major
and semi-minor Axies, ie. I was half right.

No that's not right either.

If you take a look at this ellipse,
http://upload.wikimedia.org/wikipedi.../d3/Elipse.png
you can see that in this case the perihelion (A-F1) is much shorter than
the semi-minor axis (b). [That diagram is correctly drawn. I checked.]

Both your ideas would have been right if the Sun were at the centre of
the ellipse, but it isn't. The Sun is at one focus of the elliptical
orbit and the other focus is empty.

--
Mike Williams
Gentleman of Leisure

To William

The Equation of Time holds the key to discerning Keplerian orbital
geometry for the natural inequality in the length of a day reflects
constant axial rotation passing through a change in orbital
orientation.The change in orbital orientation reflects what you call
'Kepler's second law',around the perihelion it takes longer for axial
rotation to return back to noon as the change in orbital orientation is
more pronounced while at the aphelion the change in orbital orientation
is less hence the return of the Earth's axial rotation to to noon
(Sun's center) takes a shorter time * .

Of course there was a 17th century reason for fudging the Equation of
Time correction to make terrestial longitudes fit into a
calendrical/celestial sphere system so they give the Earth are variable
axial tilt to the Sun -

http://www.cerrilloshills.org/analemma/eight5.htm

It probably escapes your notice that the Equation of Time is a
correction that is valid from pole to pole and has non hemispherical
seasonal connotations.

So live with the 17th century analemmatic fudge that facilitates
nothing only astrological conceptions as those guys found a way to
force an astrological explanation into geometry.No wonder Newton had no
problem with transfering the Flamsteed's sidereal value into a
geocentric/heliocentric orbital equivalency for your mean Sun/Earth
distances.




* http://www.mhhe.com/physsci/astronom...ages/04f15.jpg

Mike Williams said

Wasn't it JG who wrote:
What I now see (from my calculations) is that the semi-minor axis is in
fact the same as the Perihelion distance. Which probably explains why I
used to think that Aphelion and Perihelion referred to the semi-major
and semi-minor Axies, ie. I was half right.

No that's not right either.

If you take a look at this ellipse,
http://upload.wikimedia.org/wikipedi.../d3/Elipse.png
you can see that in this case the perihelion (A-F1) is much shorter than
the semi-minor axis (b). [That diagram is correctly drawn. I checked.]

Both your ideas would have been right if the Sun were at the centre of
the ellipse, but it isn't. The Sun is at one focus of the elliptical
orbit and the other focus is empty.

The detail of the ellipse shown at the URL is precisely why I was (am)
having problems understanding.

I am fully aware of that the length F1-X-F2-F1 is constant and is what
defines the ellipse and that is why I could not fathom why my
calculations showed that the Perihelion was equal to the semi-minor
axis. I was also fully aware that the Sun is at one focus and the other
is empty.

I understand that A-F1 is the Perihelion and that F1-B is the Aphelion
and that 'a' is the mean/average radius.

What I can't yet understand is how one calculates 'b' given Mean/Average
Radius and Eccentricity - is it in fact possible, or does one need
some other information?

Am I correct in thinking that the Eccentricity is given by 1-(CD/AB) ?

JG

Wasn't it JG who wrote:

Am I correct in thinking that the Eccentricity is given by 1-(CD/AB) ?

e = sqrt(1-(CD^2/AB^2))

--
Mike Williams
Gentleman of Leisure

The confusion may lie in the term "semi-major axis", which is not an axis in
its own right but a term for half the length of the "major axis". As the
"major axis" is the straight line perihelion-Sun-aphelion (or their
equivalents for other primary bodies), half this distance is the average of
the perihelion and aphelion distance. If I have got my geometry right it is
also the distance from the Sun to either end of the "minor axis", but is
more than half the length of the "minor axis" itself because the Sun is not
on that "axis".

"JG" wrote in message
news:313030303331393043B5CA7669@crescentcomputing. co.uk...
Hi,

I've been lurking and gaining a great deal of knowledge from this
newsgroup for quite some time now but I have a very basic question that
I have not seen asked.

I used to think that Aphelion referred to the semi-major axis of the
ellipse described by the Earth (or any planet) on its journey around the
Sun and Perihelion was the semi-minor axis. Having read most of the
planetary data from 'The Nine Planets' web site I now see that the sum
of Aphelion and Perihelion is in fact the major axis of that ellipse.
What I cannot understand is the statement in the Glossary that Aphelion
is also the 'average' or mean distance of the planet from the Sun.

Surely the maximum distance cannot also be the mean?

What I really want to know is how to calculate the semi-minor axis.
Given the 'Mean' and the eccentricity I can readily calculate the Major
as a(1+e) and the Minor as a(1-e) but if the mean is also the Major then
this doesn't make sense.

JG

To Charles

Your thinking is strictly Newtonian quasi-geocentric, an astronomical
conception that owes more to astrology than Copernican heliocentricity
or its antecedent Ptolemaic geocentricity.If you are in any doubt or
are completely unfamiliar with Newton's mangling of Copernican
heliocentricity and its later Keplerian refinement then that is O.K.
but I assure you the Newton conception is horrific in comparison to
Ptolemaic astronomy never mind Copernican.

" PHENOMENON IV.
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."

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

Even the Ptolemaics had severed the motions of the planets from the
stellar background to generate their idea of epicycles and although
they attributed the position of the Sun between Venus and Mars,where
the hell are you going to justify the position of the Sun in Newton's
really dumb "(whether of the sun about the earth, or) of the earth
about the sun,"

Not only has the greatest Western heliocentric achievement and its
appreceation been destroyed but even the antecedent nobility of the
planetary motion plotting of Ptolemaic astronomers joins the
destruction.

The planetary motions in retrograde refer to the plotting with the
stellar background ,what the Ptolemaics seen as epicycles,the
Copernican heliocentrists rightly identified as a faster Earth ,moving
in an inner orbital circuit overtaking the slower moving outer planets
-

http://antwrp.gsfc.nasa.gov/apod/ima...2000_tezel.gif

No jumping to the Sun to infer heliocentricity and no retrogrades
involved *,just the altering of a Ptolemaic stationary Earth to an
annual orbital motion.

* "For to the earth they appear sometimes direct, sometimes stationary,
nay, and sometimes retrograde. But from the sun they are always seen
direct.."

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

Newton and his disciples did not just destroy heliocentric
astronomy,they ruined a heritage that stretches back millenia.

Newtonian yes, geocentric no. If you are thinking of my "equivalents for
other primary bodies" I mean, for example, major planets relative to their
own moons, not to each other or the Sun!

Since you are now accusing me, I will use the opportunity to make some
points about your comments in general.
(1) You cite references to the phases of Venus as being geocentric. In fact
the ability to see them was evidence against a heliocentric model, as they
showed that Earth and Venus were sometimes the same side of the Sun and
sometimes opposite sides.
(2) One of your quotations of Newton says that from Earth the planets APPEAR
sometimes direct, sometimes stationary, sometimes retrograde. In other words
he was acknowledging that that was an illusion caused by Earth's own
movement relative to the Sun.
(3) Yes, references to things being in constellations are astrological, but
they are being used as a METAPHOR. I have myself been criticised for
pedantry about such matters. It is easier for readers to picture a location
relative to an arbitrary alignment of unrelated stars than to a set of
numerical coordinates.

"oriel36" wrote in message
oups.com...
To Charles

Your thinking is strictly Newtonian quasi-geocentric, an astronomical
conception that owes more to astrology than Copernican heliocentricity
or its antecedent Ptolemaic geocentricity.If you are in any doubt or
are completely unfamiliar with Newton's mangling of Copernican
heliocentricity and its later Keplerian refinement then that is O.K.
but I assure you the Newton conception is horrific in comparison to
Ptolemaic astronomy never mind Copernican.

" PHENOMENON IV.
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."

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

Even the Ptolemaics had severed the motions of the planets from the
stellar background to generate their idea of epicycles and although
they attributed the position of the Sun between Venus and Mars,where
the hell are you going to justify the position of the Sun in Newton's
really dumb "(whether of the sun about the earth, or) of the earth
about the sun,"

Not only has the greatest Western heliocentric achievement and its
appreciation been destroyed but even the antecedent nobility of the
planetary motion plotting of Ptolemaic astronomers joins the
destruction.

The planetary motions in retrograde refer to the plotting with the
stellar background ,what the Ptolemaics seen as epicycles,the
Copernican heliocentrists rightly identified as a faster Earth ,moving
in an inner orbital circuit overtaking the slower moving outer planets
-

http://antwrp.gsfc.nasa.gov/apod/ima...2000_tezel.gif

No jumping to the Sun to infer heliocentricity and no retrogrades
involved *,just the altering of a Ptolemaic stationary Earth to an
annual orbital motion.

* "For to the earth they appear sometimes direct, sometimes stationary,
nay, and sometimes retrograde. But from the sun they are always seen
direct.."

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

Newton and his disciples did not just destroy heliocentric
astronomy,they ruined a heritage that stretches back millennia.