Help with gravity lens formula?

I see two formulae listed, one by A. Albo Michigan State, that goes
the angle of deflection of light going by a large mass as A= 4GM/C^2*R^2 and by others as A=4GM/C^2* R (Note, R NOT squared). I have tried contacting astronomers and 'ask the astronomer' and tried to send to A. Abdo but so far, 2 weeks later, no response. I am trying to do a paper for publication somewhere but till I get this cleared up, I am stymied, have two results to graph out, only one is correct. Thanks for looking at this. This is the formula that Einstein used to get the famous 1.75 arc seconds of deflection of light that put him on the map. What ticks me off about this is giving the angle in arc seconds instead of the right units, radians. That threw me off for a couple of years!

Originally posted by sonhouse
I see two formulae listed, one by A. Albo Michigan State, that goes
the angle of deflection of light going by a large mass as A= 4GM/C^2*R^2 and by others as A=4GM/C^2* R (Note, R NOT squared). I have tried contacting astronomers and 'ask the astronomer' and tried to send to A. Abdo but so far, 2 weeks later, no response. I am trying to do a paper for publ ...[text shortened]... e in arc seconds instead of the right units, radians. That threw me off for a couple of years!

Do both formulas measure the angles in the same units?

Originally posted by adam warlock
Do both formulas measure the angles in the same units?

Yes, the only dif is measuring the angle, I guess the one that gives 1.75 arc seconds would be the one, eh. Have to do the math and check out each one then. I think we did that here for the non squared version, do you remember that?

Originally posted by sonhouse
Yes, the only dif is measuring the angle, I guess the one that gives 1.75 arc seconds would be the one, eh. Have to do the math and check out each one then. I think we did that here for the non squared version, do you remember that?

I don't remember seeing a thread that was about this topic. But I was away from the forums for a while too.

I'd need to know how which formula was derived, or at least at which situations do the apply (for example one equation could be regarding one approximation and the other equation regarding some other approximation), so I could give you a better help. I'll do a google search and see what I can come up with.

Originally posted by adam warlock
I don't remember seeing a thread that was about this topic. But I was away from the forums for a while too.

I'd need to know how which formula was derived, or at least at which situations do the apply (for example one equation could be regarding one approximation and the other equation regarding some other approximation), so I could give you a better help. I'll do a google search and see what I can come up with.

Never mind, I just did the math, one of them has to end up with a 1.75 arc second answer for the sun and I did that and the version with straight R wins. The first foci for light skimming by the surface of the sun (one Radii up from the center) focuses at about 50 billion miles out. The version with R^2 instead focuses at about 6 million LIGHT YEARS away! Not right. So now I am going to bitch at that guy Adbo for putting me through this! He has it right on a publication, 1/R^2, the rat🙂

You could have verified the correct formula quite easily by checking the units; an angle should be dimensionless.

Originally posted by KazetNagorra
You could have verified the correct formula quite easily by checking the units; an angle should be dimensionless.

You mean the change from 1/R to 1/R^2 introduces dimensioned units? Never thought about that one! Interesting. But just plugging in the #'s showed the 1/R^2 was totally bogus. I think we only had maybe a couple of days covering units in school.

Originally posted by KazetNagorra
You could have verified the correct formula quite easily by checking the units; an angle should be dimensionless.

Isn't it more accurate to state that an answer in radians should be (would be) dimensionless?

Originally posted by sonhouse
Isn't it more accurate to state that an answer in radians should be (would be) dimensionless?

Yeppers!

Originally posted by sonhouse
I see two formulae listed, one by A. Albo Michigan State, that goes
the angle of deflection of light going by a large mass as A= 4GM/C^2*R^2 and by others as A=4GM/C^2* R (Note, R NOT squared). I have tried contacting astronomers and 'ask the astronomer' and tried to send to A. Abdo but so far, 2 weeks later, no response. I am trying to do a paper for publ ...[text shortened]... e in arc seconds instead of the right units, radians. That threw me off for a couple of years!

The true formula is

Theta =4*G*M/c^2/r (not r squared)

Or

Theta =4*G*M/(r*c^2) (not r squared)



The angle is measured in radians. To convert this to degrees we have to multiply by 180/pi. To get the value in seconds we multiply by 180/pi*60*60


For Einsteins famous prediction of light from a star grazing the son we get


Theta =4*6.7e-11*2e30/3e8^2/7e8 *180/3.1416*60*60 =1.75 arc seconds

R is the radius of the sun.It is the closest point that the light ray comes to the son.

Originally posted by tony4
The true formula is

Theta =4*G*M/c^2/r (not r squared)

Or

Theta =4*G*M/(r*c^2) (not r squared)



The angle is measured in radians. To convert this to degrees we have to multiply by 180/pi. To get the value in seconds we multiply by 180/pi*60*60


For Einsteins famous prediction of light from a star grazing the son we get


Theta =4*6.7e ...[text shortened]... conds

R is the radius of the sun.It is the closest point that the light ray comes to the son.

I tried to get in touch with the dude who wrote the paper using R squared but was unsuccessful, guys name was Abla. The math is a lot easier to get the actual first focal point by just inverting the radian answer, that gives the effective 'f stop', the ratio between the diameter and the focal point, which for the answer for our sun, comes out at about 8.5E-6 radians, invert that and you get 117,000 and change, multiply that by the radius and you avoid all those other steps to get the first focal point, about 83 billion Km out from the sun.

I was in contact with an Italian scientist by the name of Maccioni who started the ' To the solar Foci' project, the 1000 AU probe, which of course we don't have the propulsion just yet to do that, Ion rockets looks like the best bet for that using some kind of nuclear source.

Get to that 1000 AU area, just take telescopes, and other kind of sensors and turn around and aim back at the sun and you get lots of free gain for everthing from neutrino detectors (neutrino's have some mass so the actual first focus may be a bit closer, the would be a way to peg the mass of the neutrino independently, btw, take an EM reading for just where first focus is for light or radio and then move in to see a peak in the neutrino field and the difference should peg the mass of the neutrino. That's my take on it anyway.

I have already finished my first paper on that and submitted it to my son-in-law who is a physicist and could vet the ideas submitted. It was a long project, I would put it aside for a couple of years, then think about it again and come up with some new insites about our local gravity lens environment.

The big boys concentrate on the galactic Einstein rings and such to get images and information otherwise unobtainable about extremely distant galaxies and such but my interest had always been, what about our own sun, what are the implications of our own gravity lens for science? I came up with some interesting conclusions I think. So We'll see it the paper passes peer review, eh.