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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 |
#2
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Semi-minor Axis
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 |
#3
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Semi-minor Axis
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 |
#4
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Semi-minor Axis
JG wrote:
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. Use this glossary instead: http://www.astunit.com/tutorials/glossary.htm :-) Best, Stephen Remove footfrommouth to reply -- + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Stephen Tonkin | ATM Resources; Astro-Tutorials; Astro Books + + (N51.162 E0.995) | http://astunit.com + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + |
#5
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Semi-minor Axis
JG 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. JG Do what Newton did and transfer Flamsteed's axial rotational /stellar circumpolar sidereal equivalency to a geocentric /heliocentric orbital equivalency thereby getting your mean Sun/Earth distances. http://www.pfm.howard.edu/astronomy/...S/AACHCIR0.JPG You get you stretching of distances from a Sun/Earth mean but you also get the ugly spectacle of the Earth travelling faster at the aphelion and slower at the perihelion. Go ahead and fit the dumb sidereal .986 deg orbital displacement into an elliptical framework and watch the Keplerian insight destroyed. Of course nobody here is a heliocentric astronomer and they would not know this. |
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Semi-minor Axis
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 |
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Semi-minor Axis
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. |
#8
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Semi-minor Axis
The second greatest heliocentric representation is Kepler's Panis
quadragesimalis seen on page 86 in the following website - http://mitpress.mit.edu/journals/pdf/POSC_13_1_74_0.pdf Apart from Owen Gingerich at Harvard,very few would recognise that in Kepler's era planetary orbits were observed from the center of the planet's orbit hence the mean motion along the planet's orbit and not mean Sun/Earth distances. Compare Newton's horrible rendition for the deviation of a planet from constant annual orbital speed from Kepler's distinctly heliocentric rendering - "PHÆNOMENON 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. 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 You can get away with the stretching of orbital distances from a mean Sun/Earth distance but what you cannot do is make it fit into an elliptical framework and retain Kepler's second law. http://www.pfm.howard.edu/astronomy/...S/AACHCIR0.JPG All Newton did was make astrology respectable again by re-introducing the celestial sphere/constellations into astronomy. |
#9
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Semi-minor Axis
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 |
#10
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Semi-minor Axis
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 |
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