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cosmicsurfer

USA
507 Posts

Posted - 16 Dec 2008 :  14:40:00  Show Profile  Visit cosmicsurfer's Homepage  Send cosmicsurfer a Yahoo! Message  Reply with Quote
Hi Larry, Regarding my earlier comments about an FTL gravity wave. I think that 'pooled circulating gravitons'[ripple effect like throwing stones on a pond] would act like a BEC and if a super nova exploded the graviton wave would ripple on top of this BEC and should interact at the electric local level as a frequency that is passed instantly from the explosion. So, when technology catches up to theory, we will some day be able to develop deep space monitoring above light frequencies. John
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Jim

1823 Posts

Posted - 16 Dec 2008 :  15:55:13  Show Profile  Reply with Quote
Has anyone here explained why gravity is considered some kind of energy rather than a force? It seems to me gravity has always been a force and how the idea of energy got into the force is not clear. I hope this is not too confusing for this thread or off the main topic.
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cosmicsurfer

USA
507 Posts

Posted - 16 Dec 2008 :  17:21:51  Show Profile  Visit cosmicsurfer's Homepage  Send cosmicsurfer a Yahoo! Message  Reply with Quote
Hi Jim, The 'force of gravity' is an effect caused by the graviton capture process and graviton cycle. It takes an exchange of ENERGY to create MASS in motion which is caused by the FTL circulation of gravitons. I hope my explanation helps. John
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Joe Keller

USA
957 Posts

Posted - 16 Dec 2008 :  22:08:49  Show Profile  Reply with Quote
Solar System Acceleration from Pulsar Timing

Using the millisecond pulsars in Taylor's 1995 catalog, I've made my own estimate of our Solar System's acceleration. Pdot was given for 31 of these, but, to get a more homogeneous group of pulsars, I considered only the eight whose Pdot/P ranges from 0.23/10^17 to 0.36 (I'll drop the /10^17 from now on, in this post). There were clusters of three at 0.36 and two at 0.23.

The nearest (in Pdot/P) other pulsars, to these eight, had Pdot/P = 0.48, 0.20, 0.19 & 0.18. However, the last three became 0.093, 0.175 & 0.058 after subtracting the Shklovskii correction term for transverse speed. This put them even farther from the group of eight. Only one of the group of eight, had known proper motion; its Shklovskii correction was almost negligible (0.333 --> 0.325). So, I applied no Shklovskii corrections to the group of eight.

The correlation coefficient with the cosine of the angle with (l,b) = (264.31,+48.05) (Lineweaver's estimate of the heliocentric CMB dipole, ArXiv.org, 1996) is -0.702. This is equivalent, using the line of best fit for acceleration vs. cosine, to an acceleration toward the (+) CMB dipole, 1/8 of what the Barbarossa system should cause. Remarkably, this acceleration equals the centripetal galactic acceleration in magnitude, though the latter should not be observed if this region of the galaxy rotates as a solid disk. Searching, the best correlation was -0.813 (sigma = approx. 2.54, p = 1%), with (l,b) = (304,+54).
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nemesis

84 Posts

Posted - 17 Dec 2008 :  11:54:20  Show Profile  Reply with Quote
Joe, do you think this indicates the Barbarossa system is less massive than you thought, more distant, or both?
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Joe Keller

USA
957 Posts

Posted - 17 Dec 2008 :  18:59:40  Show Profile  Reply with Quote
quote:
Originally posted by nemesis

Joe, do you think this indicates the Barbarossa system is less massive than you thought, more distant, or both?



(Regarding Barbarossa detection from pulsar timing)

In my foregoing study, I started with such a narrow range of Pdot/P, that even if the correlation, with the cosine of the angle to Barbarossa, had been perfect, the implied mass would have been only 1/6 what I estimate (from outer solar system precession resonances, the CMB dipole strength, the variation of the Pioneer 10/11 anomalous acceleration, & Paul Wesson's J/M^2 relation). I chose a densely populated but narrow range of Pdot/P, to get a homogeneous sample of objects (objects resembling each other).

The correlation coefficient confirms the acceleration direction (toward the CMB dipole) to roughly sigma = sqr(8-3)*0.5*ln((1+0.702)/(1-0.702)) = 1.95; p = 5%, two-tailed. The implied mass, 1/8 what I predict for the Barbarossa system, is only a lower bound for the actual mass.

Suppose I want to know the effect of nutrition on height. Many factors affect height. In medical studies, these are removed by limiting the study to a homogeneous group, e.g. Danish men. What if the only thing I know about the men, is their height? Height isn't the best criterion for choosing, but it's my only option. So, I study men between 5'4" & 5'6", excluding most European and African men, and studying mainly Asian men, a more homogeneous group. I find that nutrition indeed correlates positively with height; 5'6" men are significantly better nourished than 5'4" men. Of course I find that nutrition makes a difference of less than two inches. This is an underestimate because I excluded tall and short men from my study. If I had excluded no one, I might have had so much scatter, from Pygmies & Watusis, that I would not have detected a significant correlation of nutrition with height, at all.
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evolivid

USA
206 Posts

Posted - 18 Dec 2008 :  19:06:56  Show Profile  Send evolivid a Yahoo! Message  Reply with Quote
quote:
Originally posted by Jim

Has anyone here explained why gravity is considered some kind of energy rather than a force? It seems to me gravity has always been a force and how the idea of energy got into the force is not clear. I hope this is not too confusing for this thread or off the main topic.



I think I might have a answer you can see it at the DARKMATTER, REPLICATION, GRAVITY WAVES, WORMHOLES
topic

It might be that electrons and positrons spinning at the speed of light in the intera of the proton distort space time and produce gravity waves?

MARX
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Larry Burford

USA
2100 Posts

Posted - 18 Dec 2008 :  22:06:43  Show Profile  Reply with Quote
[Jim] "Has anyone here explained why gravity is considered some kind of energy rather than a force? It seems to me gravity has always been a force and how the idea of energy got into the force is not clear."

Jim,

Gravity comprises several related concepts:
gravitational force
gravitational acceleration
gravitational energy

So trying to say that gravity is energy rather than force (or vice versa) is a false dichotomy.

===

Force and energy are closely related through the concept of work.

work = F * d  (force times distance)
*** also
work = E2 - E1    (final energy minus initial energy)


We can combine these two concepts like this, 

    work   E2 - E1
F = ---- = -------
     d        d

===

A basic units analysis then looks like this:

force (f) has units of kg * m / sec^2     (mass times acceleration)
energy (E) has units of kg * m^2 / sec^2  (mass times speed squared)
distance (d) has units of m               (length)


kg * m / sec^2 = kg * m^2 / sec^2 / m 
               = kg * m / sec^2


Regards,
LB
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Larry Burford

USA
2100 Posts

Posted - 18 Dec 2008 :  22:54:53  Show Profile  Reply with Quote
Oh yeah, gravitational acceleration

           M 
g = -G * -----
          d^2

and the force due to gravity

         M * m
Fg = G * -----
          d^2

where 
M is the gravitating mass
m is the test mass
d is the distance between them
G is the universal garvitational constant

M and m have units of kg        (mass)
G has units of m^3 / kg /sec^2  (derived)


Little m here is the same as the the mass mentioned in my previous post.
Big M here does not appear in my previous post.

Big M creates a gravitational force field around itself by absorbing and scattering some of the graviton flux that is continuously passing through it. It also creates a gravitational potential field.

Little m experiences the force field as a force in the direction of M. It experiences the potential field as very small speed and altitude dependent variations in the force field. These small variations are what we mean when we talk about relativistic phenomena such as clock slowing.

This is not the entire story, but it covers many of the major points. If anyone else is interested in taking a shot at this, be my guest.

Regards,
LB
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Joe Keller

USA
957 Posts

Posted - 19 Dec 2008 :  15:04:40  Show Profile  Reply with Quote
Pulsar "Pdoubledot" Confirms Barbarossa Mass

My foregoing study essentially repeats that of Zakamska & Tremaine, but using only the eight Taylor (1995 catalog) millisecond pulsars (P < 30 ms) whose Pdot/P ranges from 0.23 to 0.36 (/10^17 per sec). Not only is this the densest and most distinct cluster of Pdot/P values, but the endpoints happen to equal 1.0 or 1.5 * 72km/s/Mpc, the most accepted value of the Hubble parameter. The reciprocal of what would be Earth's precession period, if subject only to the torque of the outer planets, lies at the midpoint of this interval.

The direction correlating best with -Pdot/P, for these eight, differs only 25 deg (p = 5%, one-tailed) from the (+) CMB dipole (i.e., the predicted position of Barbarossa). Narrowly limiting Pdot/P to get a pristine subject group, limits the mass estimate to an inaccurate lower bound, about 1/8 of expected.

Yesterday I used the "Topic Search" of "Web of Science" (online Science Citation Index) to find (and at least glance at, online or in print) almost all the ~100 articles about these eight pulsars. When I found secondhand data, I traced it when possible. The two explicit "Pdoubledot" determinations I found, are for J1012+5307 (Lange et al, MNRAS 326:274+, 2001; Webb et al, A&A 419:269, 2004). This is a "field" millisecond pulsar; i.e., not in a globular cluster. Webb's table misprints Pdot as 0.7...; it should be 1.7... .

Note that Pdot^2 << Pdoubledot*P. Lange, and Webb, analyzed their long strings of data on this pulsar, to find Pdoubledot values giving (d/dt)(Pdot/P) = 0.97, and 4.74/10^28 per sec^2, resp. The derivative of the apparent acceleration toward the pulsar, is (d/dt)(-Pdot/P * c). The derivative of the sun's acceleration due to Barbarossa is 3.78/10^28 per sec^2 * c. The angle, between Barbarossa's orbital velocity vector (i.e., between the derivative of the sun's acceleration vector toward Barbarossa), and the radius to this pulsar, is 180 - 55.75 deg. So, the expected value of (d/dt)(Pdot/P), is 2.13/10^28. The measurements of Lange, and Webb, confirm the mass and direction of Barbarossa within a factor of two.

For two more of these pulsars, I found significant, consistent data from which to calculate Pdoubledot myself. J0613-0200 (Bell et al, MNRAS 286:463, 1997, Table 1; Hotan, Bailes & Ord, MNRAS 369:1502, 2006, Table 3) lacks sufficiently precise Pdot at the earlier epoch reported, but P is precise enough for quadratic interpolation. The two reports are by the same research group. I estimate Pdot at the midpoint, from delta(P)/delta(t), then estimate Pdoubledot by differencing with the later epoch's Pdot. Observed (d/dt)(Pdot/P) is thus 10.88/10^28 per sec^2. The angle between Barbarossa's orbital velocity, and this pulsar, is 180 - 30.36 deg, so expected is 3.27/10^28.

B1855+09 (a.k.a. J1857+0943)(Kaspi, Taylor & Ryba, ApJ 428:713, 1994, Table 2; Hotan et al, op. cit.) has sufficiently precise Pdot at both epochs reported. The two reports are by different research groups. Differencing Pdot, gives observed (d/dt)(Pdot/P) as -0.48/10^28. The angle is 41.53 deg, so expected is -2.83/10^28.

Summary: observed vs. expected, for (d/dt)(Pdot/P), is

J1012+5307: obs +0.97 or +4.74, exp +2.13 (/10^28 per sec^2)
J0613-0200: obs +10.88, exp +3.27
B1855+09: obs -0.48, exp -2.83

Averaging the two observed values for J1012+5307, gives a correlation of +0.836, p = 8%, one-tailed. The best-fitting line corresponds to a time derivative of acceleration, only 50% bigger than that expected from Barbarossa.

This corroborates the theoretical time rate of change of the sun's acceleration due to Barbarossa. Factors corroborated include Barbarossa's mass, distance, angular speed and sense, and ecliptic longitude.

From these journal articles, I found some proper motions, and if not there, some in Hobbs' 2004 (online, VizieR) pulsar catalog. Only two PMDecl and one PMRA value now are missing, for these eight pulsars. The pulsar with no PM information is J2129+1209H, which lies in a globular cluster, M15. Shklovskii transverse motion correction, and correction for differential galactic acceleration (assuming our sun lies at a maximum of v(r)), separately or together, greatly worsen the correlation of -Pdot/P, with the direction to Barbarossa.

The derivative of acceleration includes a Shklovskii-like term with factors (PM)^2 and (RV)^1, a galactic acceleration term, and cross-terms. Insofar as due to galactic-size motions, all these are negligible because Barbarossa's period is 1/100,000 that of the galaxy.

Though Hobbs' 2004 catalog lists Nudoubledot (the second time derivative of 1/P) for most of these eight pulsars, only one (J0613-0200) was significantly nonzero, and that was of opposite sign to my finding above. More accurate determinations of Pdoubledot likely will reveal Barbarossa's mass and orbit.
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Joe Keller

USA
957 Posts

Posted - 23 Dec 2008 :  17:08:14  Show Profile  Reply with Quote
Yesterday a moderate-size remote-control college telescope photographed Barbarossa and Frey in one frame. (This is not the Bradford telescope, which has had my job "waiting" for a week. Nor is it the Slooh pay-per-reservation telescope, from which I also have been unable to get any photos during the same period. Both these are on Tenerife; bad weather is part of the explanation.)

Here is my letter to the full professor who supervises the telescope:


Dear Prof. *********:

Our one and only photo, #350 (which you helped me take at my coordinates, and courteously emailed to me immediately) does seem to show the bodies I seek. I assume that the epoch of this photo (or rather, median of stacked photos) is approx. 13:00 GMT Dec. 22, 2008 (the meridian, and still astronomically dark in *******).

The best candidate image for "Barbarossa", the more massive body, is at RA 11:28:22.079 Decl -9:16:6.42. Barbarossa lies at some especially dark pixels of the (FITS version) ESO POSS2 Red sky survey. This region is not available in the ESO POSS2 Blue survey; and due to "issues" downloading Java, I can't get Aladin. The extremely bright nearby star is USNO-B 0807-0228814 (USNO-B Red2 magnitude +15.40). Barbarossa is much dimmer in our photo than USNO-B 0807-0228808 (Red2 mag +18.15), and slightly dimmer than USNO-B 0807-0228824 (R2 mag +19.07). So, I estimate its magnitude as +19.4.

The best candidate for "Frey", the main moon of Barbarossa, is at RA 11:29:4.656 Decl -9:07:2.28. Frey likewise lies at some especially dark pixels of the (FITS version) ESO POSS2 Red sky survey. Frey is much dimmer in our photo than the very bright nearby star, USNO-B 0808-0228849 (USNO-B Red2 mag +18.14). On the ESO POSS2 Red, USNO-B 0808-0228845 (R2 mag +19.18) is bright; yet it is hardly if at all detected on our photo. USNO-B 0808-0228852 (R2 mag +19.05) is only slightly brighter than Frey on our photo. So, though our photo was not red filtered, I estimate Frey's magnitude as +19.1. This is consistent with the magnitudes of Frey and Barbarossa found on sky surveys.

I found the center of mass (c.o.m.) using the ratio 0.877::0.123 I determined in early 2007 from online sky surveys and amateur photos (Joan Genebriera of Barcelona working in the Canary Is., the first to photograph Barbarossa, except for sky surveys; Steve Riley of southern California, the first to photograph Frey, except for sky surveys; and Robert Turner of England working with the Bradford College remote telescope on Tenerife, who has photographed Frey). Mathematically, linear extrapolation of 1986 & 2007 heliocentric celestial coordinates is precise enough. These coordinates as I gave them, really are centered at the barycenter of the known solar system. Today I made the small correction for the movement of Jupiter and Saturn, and estimated expected geocentric coords., accounting for Barbarossa's inclination, Earth's eccentricity, and to first order the curvature of the celestial sphere. The c.o.m. of Barbarossa & Frey is within 1" of predicted in RA, and only 4" too far North in Declination. On about half the previous photos, the presumed c.o.m. ecliptic latitude was too far N or S; the longitude has been much more consistent.

On several photos, Barbarossa or Frey have seemed to have rings roughly parallel to Barbarossa's orbital plane around the sun. It was Robert Turner who first explicitly advocated to me the idea of rings around Barbarossa.

Sincerely,
Joseph C. Keller, M. D.
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Stoat

United Kingdom
964 Posts

Posted - 24 Dec 2008 :  04:34:22  Show Profile  Reply with Quote
Hi Joe, this is sounding good. Is there any chance of sending the fits to Marsrocks to let him do his photoshop magic on the image?

(Edited) Hi Joe, I would think that your letter to this astronomer will have piqued his curiosity, has he got back to you yet for a time for your next image shot? I suppose it depends on where Frey is in its orbit. Hopefully it's not moving towards or away from us, as that will make blink comparison difficult.

Changing the subject, I was going to suggest that you gave a brief description of dot notation and the question of pulsars. There are a number of people following your thread, who I think would have to agree, that maths is not their strong point.
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Joe Keller

USA
957 Posts

Posted - 24 Dec 2008 :  12:30:39  Show Profile  Reply with Quote
quote:
Originally posted by Stoat

...a brief description of dot notation and the question of pulsars...



My best recommendation is VM Kaspi, "High-Precision Timing of Millisecond Pulsars and Precision Astrometry", at http://citeseerx.ist.psu.edu

This article is especially good for five reasons:

1. It can be downloaded free from the internet, at least if one has Acrobat Reader. It's only 132 kB because it has no graphs.

2. It's by one author, a founder of pulsar investigation (primary author of one of the articles I relied on for B1855+09's Pdot, i.e., time derivative of P; a collaborator of Taylor, author of the most famous pulsar catalog).

3. It doesn't sweep crucial details under the rug. I haven't seen any article on millisecond pulsars, that better covers the practical issues. Someone who reads this, would be ready to help with the work.

4. It's in the plainest English possible without sweeping crucial details under the rug.

5. It's modular, so usually one can understand a section or paragraph or sentence, without reading the others. It's good for a person who doesn't have time to read it all.
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Joe Keller

USA
957 Posts

Posted - 28 Dec 2008 :  11:39:23  Show Profile  Reply with Quote
email title: "Overwhelming Confirmation of Double Planet Orbit"

Dear Prof. *********,

Thanks for letting me know. I was excitedly checking the ******* [U.S. remote telescope] site and my email every morning...(the weather's been too bad to go to town and I don't have the internet at home). "Slooh" and "Bradford" have failed to get any photos this season, from Tenerife, due, I think, to bad weather, and to the backlog at Bradford, and to an equipment failure at Slooh.

I now have another overwhelming confirmation of the double planet. Though I only have four Barbarossa/Frey sightings that have near-perfect center of mass position (1954 & 1986 sky surveys, 2007 Genebriera/Riley/Turner photos, and the ******* Dec. 2008 photo) I can assume a fifth ellipse point as an adjustable parameter. When I do this, I find that the 4 - 1 = 3 areal rates, become equal (0.13% relative standard deviation, assuming 2+ orbits 1954-1986 & 1+ orbit 1986-2007) using the same adjustable fifth point, which also is about right for the period and implied mass.

I haven't posted this to Dr. Van Flandern's messageboard yet, though I will soon. You are the first astronomer I've told.

Sincerely,
Joe Keller
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Joe Keller

USA
957 Posts

Posted - 28 Dec 2008 :  15:26:03  Show Profile  Reply with Quote
Further Confirmation of Barbarossa/Frey Orbit

Using a Pentium computer, I stretched the apparent counterclockwise Barbarossa/Frey orbit (obtained using that inferred fifth point which equalized the three areal rates, thereby satisfying two equations with one adjustable parameter) in every direction and amount ("homothetic transformations"). The stretch which makes the origin (Barbarossa) a focus (tested by the sum-of-distances definition of an ellipse) gives the real orbit.

The real orbit has semimajor axis (between Frey and Barbarossa) 0.94 AU, eccentricity 0.24, and period 15.225 yr. This implies a mass Barbarossa + Frey = 0.0036 solar masses, a third of what I estimated from several effects on the solar system. So, additional moons, rings and nebular matter are likely.

This disproves the complicated orbit I estimated on this messageboard March 23, 2008. It confirms the other, simple, orbit I estimated on this messageboard Feb. 18, 2008 ( > 0.50 AU; 14.7 yr).

The normal to the Barbarossa/Frey orbit is 90 +/- 23 = 113 or 67 deg from our line of sight. Also, this normal is 48 deg from the normal to the Barbarossa/Sun orbital plane.
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Joe Keller

USA
957 Posts

Posted - 28 Dec 2008 :  16:01:24  Show Profile  Reply with Quote
followup email

Dear Prof. *********,

The other three images, are from sky surveys, and amateur photos in 2007. For almost two years on Dr. Van Flandern's messageboard, I've been writing about the trajectory defined by these three. With one adjustable parameter (the Barbarossa/Frey mass ratio) the 2007 c.o.m. is within a very few arcsec of where it should be, in longitude and latitude (precisely solving two independent equations with one adjustable parameter).

Now, not only does the Dec. 2008 ******* image, assuming the same mass ratio, fall on the same trajectory (4" off) but with four images, I can define the apparent binary orbital ellipse up to one adjustable parameter. Again, I find that with proper choice of this parameter, not one, but two equations (for three equal areal speeds with Barbarossa as the origin) are satisfied (to 0.125% accuracy).

Sincerely,
Joe Keller
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Joe Keller

USA
957 Posts

Posted - 30 Dec 2008 :  13:13:06  Show Profile  Reply with Quote
(to someone listed in a magazine, as an officer of an astronomy club, who asked if I'd emailed him by mistake)

"Hi *******!

I sent that notice to many officers of astronomy clubs. For almost two years, I 've been sending emails (it's not spam, because I only send the emails to those who advertise themselves as people who, likely as not, should be interested in this - often directly or indirectly tax-subsidized), driving around visiting astronomy professors, recruiting people with adequate telescopes, to image this region.

Now I have even more certain proof that there are two massive objects there in binary orbit. The math is basically freshman calculus. I majored in math, cumlaude, at Harvard, so I know how to do the math, or at least Harvard's math dept. thought I knew how to do the math. I just mention that, because the situation is, that astronomers will believe this if and only if they believe the math; but they're not going to bother to check the math unless they believe. So I've had to break a vicious cycle. It's been like making "stone soup".

Anyway, now with the binary orbit proven to about 1" accuracy, it's a certainty that it's right there, and only a matter of time (this winter? 2000 years from now?) before big telescopes take plenty of pictures.

It's like an "orphan drug" - a big advance that's ignored because no one can make a profit as the "discoverer". It already has been imaged by three amateurs, Joan Genebriera, Steve Riley, and Robert Turner, each of whom contributed huge unpaid effort to achieve their results with barely adequate equipment. It's been imaged once again by the robotic telescope at the U. of *********, which now is broken and might or might not be fixed in the next few weeks.

Sincerely,
Joseph C. Keller, M. D. (retired)
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Jim

1823 Posts

Posted - 30 Dec 2008 :  14:04:36  Show Profile  Reply with Quote
Dr Joe, Can you say for sure the math is a sure thing in that math of tha kind has caused most of the confusion in science. Observation is good though, so if the subject is seen it would prove the math works. Maybe proving the math works(in that it really does predict nature)would be more important than finding the subject. And the other way round would be a good thing too. It might be better to stop dumping on the powers that be and look at new ways around the stone in the soup. Just trying to be helpful here.
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Joe Keller

USA
957 Posts

Posted - 30 Dec 2008 :  22:01:56  Show Profile  Reply with Quote
quote:
Originally posted by Jim

Dr Joe, Can you say for sure the math is a sure thing in that math of tha kind has caused most of the confusion in science. Observation is good though, so if the subject is seen it would prove the math works. Maybe proving the math works(in that it really does predict nature)would be more important than finding the subject. And the other way round would be a good thing too. It might be better to stop dumping on the powers that be and look at new ways around the stone in the soup. Just trying to be helpful here.



Thanks for your input!
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Joe Keller

USA
957 Posts

Posted - 30 Dec 2008 :  22:48:36  Show Profile  Reply with Quote
If Frey is at L1, the Mass Matches

Suppose Barbarossa is like the Sun, Barbarossa's most massive moon is like Jupiter, and Frey is like a Trojan asteroid or asteroids, but not at a Lagrange point leading or following; rather, at the Lagrange point L1 between Barbarossa and Barbarossa's massive moon. For convenience, let the distance between Barbarossa and Frey be 1; and the implied total mass, if Frey itself were the massive moon as in previous posts, also be 1. Let the distance from Barbarossa to the presumed center of mass be a = 0.1229 as determined from the 1954, 1986, 2007 & 2008 photos. Let Barbarossa's actual mass be m2, the massive moon's m1, and the actual distance from Barbarossa to the massive moon, r > 1. There are three equations:

For the period, m1 + m2 = r^3

For the center of mass, m2*a = m1*(r - a)

For Frey to be at the Lagrange point L1, the extra centrifugal and centripetal forces balance, m1/(r-1)^2 = m2 - (1-a)

Eliminating m1 & m2 gives a quintic equation with a root r = 1.39, m2::m1 = 10.3::1, and m2 + m1 = 0.0098 solar masses, close to the mass estimated indirectly in several other ways above.
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