The fate of the Earth?
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From: dow on 12 Sep 2009 11:33 On Sep 12, 10:54Â am, Sam Wormley <sworml...(a)mchsi.com> wrote: > oriel36 wrote: > > By Kepler's reckoning a 872 year orbital period has a cube root of > > 9.55 and this value squared is 90.75 AU which is a long way from the > > APOD value given as 70 AU or the Wikipedia value of 115 AU. > > Â Â Kepler's reckoning applies ONLY to our solar system, Gerald. > > Â Â Gerald--You need to learn algebra and understand Newton's version > Â Â of Kepler's third law, and the fact that it applies all over > Â Â the cosmos including the solar system. > > Â Â Fomalhaut's mass is about 2 solar masses. > Â Â Fomalhaut-b's orbital RADIUS is 115 astronomical units, Gerald. Â a = 115 AU. > Â Â Fomalhaut-b's orbital PERIOD is 872 years, Gerald. Â T = 872 years. > > Â Â And using Kepler's third law, we get, > > Â Â Â T^2 = (2Ï)^2 a^3 / G M > Â Â (872 yr)^2 = (2Ï)^2 (115 AU )^3 / G (3.978 Ã 10^30 kg) > > Â Â Kepler's third law works beautifully for the Fomalhaut system! The > Â Â observations agree beautifully with Kepler's law of Harmony! I suspect you are wearing out your keyboard in vain. He is not going to be convinced by logical argument. It's worth pointing out that Kepler died before Newton was born, and published his laws of planetary motion before Galileo studied the planets with a telescope. He derived his laws from naked-eye observations of the six then-known planets. Obviously, these did not include any planets of other stars, nor even the satellites of Jupiter. Newton derived his ideas from Kepler's findings, not the other way round. dow
From: Sam Wormley on 12 Sep 2009 13:10 dow wrote: > On Sep 12, 10:54 am, Sam Wormley <sworml...(a)mchsi.com> wrote: >> oriel36 wrote: >>> By Kepler's reckoning a 872 year orbital period has a cube root of >>> 9.55 and this value squared is 90.75 AU which is a long way from the >>> APOD value given as 70 AU or the Wikipedia value of 115 AU. >> Kepler's reckoning applies ONLY to our solar system, Gerald. >> >> Gerald--You need to learn algebra and understand Newton's version >> of Kepler's third law, and the fact that it applies all over >> the cosmos including the solar system. >> >> Fomalhaut's mass is about 2 solar masses. >> Fomalhaut-b's orbital RADIUS is 115 astronomical units, Gerald. a = 115 AU. >> Fomalhaut-b's orbital PERIOD is 872 years, Gerald. T = 872 years. >> >> And using Kepler's third law, we get, >> >> T^2 = (2Ï)^2 a^3 / G M >> (872 yr)^2 = (2Ï)^2 (115 AU )^3 / G (3.978 Ã 10^30 kg) >> >> Kepler's third law works beautifully for the Fomalhaut system! The >> observations agree beautifully with Kepler's law of Harmony! > > I suspect you are wearing out your keyboard in vain. He is not going > to be convinced by logical argument. > > It's worth pointing out that Kepler died before Newton was born, and > published his laws of planetary motion before Galileo studied the > planets with a telescope. He derived his laws from naked-eye > observations of the six then-known planets. Obviously, these did not > include any planets of other stars, nor even the satellites of > Jupiter. Newton derived his ideas from Kepler's findings, not the > other way round. > > dow True.
From: oriel36 on 12 Sep 2009 17:08 On Sep 12, 3:54Â pm, Sam Wormley <sworml...(a)mchsi.com> wrote: > oriel36 wrote: > > By Kepler's reckoning a 872 year orbital period has a cube root of > > 9.55 and this value squared is 90.75 AU which is a long way from the > > APOD value given as 70 AU or the Wikipedia value of 115 AU. > > Â Â Kepler's reckoning applies ONLY to our solar system, Gerald. > The AU is not only a discrete distance,it is also a ratio of one planetary radius to one orbital circumference hence it all operates against the background of the Pi proportion.Appealing to the status of Fomalhaut as a different solar system in order to invalidate the 1 to 1 ratio of planetary radius/orbital circumference using Earth values is like trying to tamper with the oldest and most basic correlation of all,the proportion between diameter and circumference otherwise known as Pi. If people were honest and interested,they would inquire as to what Isaac was up to in attempting to rope Kepler's reasoning on orbital periods and distance from the Sun into his agenda but few would have the skills and the background to go through the elaborate mess which really has greed at the bottom of it or more likely,are entirely content to continue with this destructive charade based on distorting astronomy and the genuine insights based on planetary dynamics. > Â Â Gerald--You need to learn algebra and understand Newton's version > Â Â of Kepler's third law, and the fact that it applies all over > Â Â the cosmos including the solar system. > If Jupiter's orbital radius is 5 times that of the Earth,its orbital circumference is also 5 times that of the Earth,the same for Saturn which is 9.5 times distant from the Sun as the Earth is and also has an orbital circumference 9.5 times that of the Earth. I spotted the error in Kepler's reasoning which becomes telescoped as the distances from Earth become greater hence this explicit bungling with Fomalhaut b with values which range from 70 AU to 115 AU,a range that is so large that it is better just to start from scratch and work things out by direct observation.The sampling needed to determine where Fomalhaut b is in its orbit would take about 20 years or more but nothing is going to get done as long as this empirical mess continues. > Â Â Fomalhaut's mass is about 2 solar masses. > Â Â Fomalhaut-b's orbital RADIUS is 115 astronomical units, Gerald. Â a = 115 AU. > Â Â Fomalhaut-b's orbital PERIOD is 872 years, Gerald. Â T = 872 years. > An AU is a discrete orbital radius distance and also a discrete orbital circumference,I have been through all this before and will not do so again,the orbital period calculated in Earth years/orbital distance must correspond to a ratio of the Earth's radius otherwise you will have problems with the Universal correlation between diameter and circumference otherwise known as Pi. > Â Â And using Kepler's third law, we get, > > Â Â Â T^2 = (2Ï)^2 a^3 / G M > Â Â (872 yr)^2 = (2Ï)^2 (115 AU )^3 / G (3.978 Ã 10^30 kg) > > Â Â Kepler's third law works beautifully for the Fomalhaut system! The > Â Â observations agree beautifully with Kepler's law of Harmony! Repeat this as many times as you like,what looks good at close range,and in Kepler's era,things only went as far as Saturn,but his correlation between orbital periods and orbital radii does not work.
From: Sam Wormley on 12 Sep 2009 17:23 oriel36 wrote: > On Sep 12, 3:54 pm, Sam Wormley <sworml...(a)mchsi.com> wrote: >> oriel36 wrote: >>> By Kepler's reckoning a 872 year orbital period has a cube root of >>> 9.55 and this value squared is 90.75 AU which is a long way from the >>> APOD value given as 70 AU or the Wikipedia value of 115 AU. >> Kepler's reckoning applies ONLY to our solar system, Gerald. >> > > The AU is not only a discrete distance,it is also a ratio of one > planetary radius to one orbital circumference hence it all operates > against the background of the Pi proportion. No Gerald -- In 1976, the International Astronomical Union revised the definition of the AU (a unit of distance) for greater precision, defining it as that length for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time. An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day, or that length for which the heliocentric gravitational constant (the product GMâ) is equal to (0.01720209895)^2 AU^3/d^2. It is approximately equal to the mean EarthâSun distance and is a convenient distance unit in astronomy for planetary systems. It is NOT a ratio! Appealing to the status of > Fomalhaut as a different solar system in order to invalidate the 1 to > 1 ratio of planetary radius/orbital circumference using Earth values > is like trying to tamper with the oldest and most basic correlation of > all,the proportion between diameter and circumference otherwise known > as Pi. No Gerald--Fomalhaut has a different mass from the sun. Kepler's Third law in this form T^2 = (2Ï)^2 a^3 / G M takes the mass of the parent body into account and is accurate for all planetary system. Your untutored self has trouble with the concept because you don't understand simple algebra. Do som self education, Gerald! > > If people were honest and interested,they would inquire as to what > Isaac was up to in attempting to rope Kepler's reasoning on orbital > periods and distance from the Sun into his agenda but few would have > the skills and the background to go through the elaborate mess which > really has greed at the bottom of it or more likely,are entirely > content to continue with this destructive charade based on distorting > astronomy and the genuine insights based on planetary dynamics. > >> Gerald--You need to learn algebra and understand Newton's version >> of Kepler's third law, and the fact that it applies all over >> the cosmos including the solar system. > > If Jupiter's orbital radius is 5 times that of the Earth,its orbital > circumference is also 5 times that of the Earth,the same for Saturn > which is 9.5 times distant from the Sun as the Earth is and also has > an orbital circumference 9.5 times that of the Earth. > > I spotted the error in Kepler's reasoning which becomes telescoped as > the distances from Earth become greater hence this explicit bungling > with Fomalhaut b with values which range from 70 AU to 115 AU,a range > that is so large that it is better just to start from scratch and work > things out by direct observation.The sampling needed to determine > where Fomalhaut b is in its orbit would take about 20 years or more > but nothing is going to get done as long as this empirical mess > continues. > > >> Fomalhaut's mass is about 2 solar masses. >> Fomalhaut-b's orbital RADIUS is 115 astronomical units, Gerald. a = 115 AU. >> Fomalhaut-b's orbital PERIOD is 872 years, Gerald. T = 872 years. >> > > An AU is a discrete orbital radius distance and also a discrete > orbital circumference, No Gerald--In 1976, the International Astronomical Union revised the definition of the AU (a unit of distance) for greater precision, defining it as that length for which the Gaussian gravitational constant (k) takes the value 0.01720209895 when the units of measurement are the astronomical units of length, mass and time. An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with a mean motion of 0.01720209895 radians per day, or that length for which the heliocentric gravitational constant (the product GMâ) is equal to (0.01720209895)^2 AU^3/d^2. It is approximately equal to the mean EarthâSun distance and is a convenient distance unit in astronomy for planetary systems. It is NOT a ratio! I have been through all this before Gerald--You keep getting it wrong! Learn some algebra! and will not > do so again,the orbital period calculated in Earth years/orbital > distance must correspond to a ratio of the Earth's radius otherwise > you will have problems with the Universal correlation between diameter > and circumference otherwise known as Pi. > > >> And using Kepler's third law, we get, >> >> T^2 = (2Ï)^2 a^3 / G M >> (872 yr)^2 = (2Ï)^2 (115 AU )^3 / G (3.978 Ã 10^30 kg) >> >> Kepler's third law works beautifully for the Fomalhaut system! The >> observations agree beautifully with Kepler's law of Harmony! > > Repeat this as many times as you like,what looks good at close > range,and in Kepler's era,things only went as far as Saturn,but his > correlation between orbital periods and orbital radii does not work. >
From: dow on 12 Sep 2009 17:47
On Sep 12, 5:08Â pm, oriel36 <kelleher.ger...(a)gmail.com> wrote: > > Repeat this as many times as you like,what looks good at close > range,and in Kepler's era,things only went as far as Saturn,but his > correlation between orbital periods and orbital radii does not work. Give me one example in which this equation does not work: T^2 = (2Ï)^2 a^3 / (G M) where G is the gravitational constant, T is the orbital period, a is the semi-major axis of an elliptical orbit (which equals the radius if the orbit is circular), and M is the mass of the primary, i.e. the star or whatever that the object is going around. It works for all the planets, asteroids, etc., in our solar system, using the mass of the sun for M, for all the satellites of Jupiter, using Jupiter's mass for M, ditto for the satellites of the other planets, and, yes, for Formalhaut b, using the mass of Formalhaut a as the value of M. Kepler could look at only the planets in our solar system, out as far as Saturn. So all his examples had the same value of M, namely the sun's mass. He empirically found an accurate relation between T and a, but had no reason to include a variable M in it. Don't blame him for that! What he did, with the few tools available to him, was brilliant. And his relationship between T and a works for objects in our solar system far beyond Saturn, not only Uranus and Neptune, but all the Kuiper Belt objects out to Eris, about 100 AU from the sun, and comets that go even further. dow |