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June 11, 2009 04:06 AM
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The formula for the radius of an Einstein ring is
(x gravitational constant x mass of lensing object / speed of light squared x between observer and lensed object / (distance between observer and lensing object x distance between lensing object and lensed object))
where the distances are "angular diameter distances" measured in terms of the object's actual size divided by its angular diameter. Given the radius of the Einstein ring and the mass of the lensing object, the *relative* distances of the quasar and its lens can be calculated, but the actual distance to one is needed to know the distance to the other.
Usually, though, the distances to the lens and the background object are determined by measuring their redshifts.
Source(s):
http://en.wikipedia.org/wiki/Einstein_ring
http://en.wikipedia.org/wiki/Angular_diameter_distance
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How can scientist tell the distance of a quasar viewed through a Einstein ring?
How do scientist know the position of the Einstein ring and deduce the distance of the quasar?
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| June 11, 2009 11:36 AM |
(x gravitational constant x mass of lensing object / speed of light squared x between observer and lensed object / (distance between observer and lensing object x distance between lensing object and lensed object))
where the distances are "angular diameter distances" measured in terms of the object's actual size divided by its angular diameter. Given the radius of the Einstein ring and the mass of the lensing object, the *relative* distances of the quasar and its lens can be calculated, but the actual distance to one is needed to know the distance to the other.
Usually, though, the distances to the lens and the background object are determined by measuring their redshifts.
Source(s):
http://en.wikipedia.org/wiki/Einstein_ring
http://en.wikipedia.org/wiki/Angular_diameter_distance
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The equation does not reveal how the scientist know the distance from observation and the lensing material. I'm supposing they look at the degree of light bending, figure out the mass of the dark matter and stellar matter, and they decided on a distance. Reverse engineering based on a distance, they can determine, the actual distance of the lensed quasar being viewed, and deduce that it is 6 billion light years away.