Gravitational Lensing?

Question

How great must the force of gravity be to "bend" light in space? For example does light crossing near the centre of our galaxy get refracted much? Or would it require a much stronger force?

Answer 1

Gravitational lensing occurs with any bit of matter - even your body.  However, for the effect to be observable the larger the mass the shorter the focal length of the "lens."

Our sun deflects light that passes near it.  In fact, this was the first major confirmation of Einstein's general theory of relativity.  It happen in 1919 and was a measurement of the deflection of stars in the field around a total eclipse of the sun.

Einstein predicted that a gravitational field should bend rays of light much more than was expected by Newton’s theory of gravity. Although the effect was too small to be observed in the laboratory, Einstein calculated that the immense gravity of the massive sun would deflect a ray of light by 1.75 seconds of arc – less that one thousandth of a degree, but twice as large as the deflection according to Newton, and significant enough to be measured.

Arthur Eddington, Plumian Professor of Astronomy at Cambridge, made the observations, on the island of Principe, off the coast of West Africa, one of the best locations for observing the 1919 eclipse.  Eddington compared his eclipse photos with images taken when the sun was not present, and announced that the sun had caused a deflection of roughly 1.61 seconds of arc, a result that was in agreement with Einstein’s prediction, thereby validating the theory of general relativity.

Answer 2

gravitational lensing occurs wherever there is gravity. Light, just like everything else, is effected by gravity.

but for the effect to be visible to us, the force of gravity needs to be much much bigger.

aka, it has to be a black hole.

the center of our galaxy has been mathematically shown to have a HUGE black hole

so there would be lots of gravitational lensing there,

but in less massive black holes, there is still gravitational lensing.

I think it has to be a black hole though for it to be obviously noticeable I think that the big stars that make black holes don't have a high enough density to pull it off, but I have no clue

when they measured it on earth it was something crazy small that was lensed

Answer 3

As mentioned, it happens anytime gravity bends light, which is really all the time, everywhere. It's just difficult to measure except when it's a large object, like a galaxy, bending the light rays. One of the first instances of it was noticed when stars near to the sun (from our point of view) were observed during an eclipse. They were a few tiny fractions off from where they should have been.

Answer 4

If a light ray comes within a distance "r" of a body whose mass is "M", then the gravitational potential energy is

GM/r

at the point of closest approach, where "G" is Newton's gravitational constant.  The angle of deflection of the light in radians is

4GM/(rc^2)

Where c is the speed of light.  So, you see any object causes some bending.  The closer you come (small "r"), the more the bending.  The bigger the mass, the more the bending.

If GM/r, the gravitational potential energy, is nearly c^2, then the bending angle is big, and this formula needs higher order terms added to it.  But GM/r ~ c^2 only happens near very dense objects, most particularly near the Schwarzschild radius of a Black Hole.

We can calculate the bending from the Sun.

M = 2 x 10^30 kg

r = 7 x 10^8 m  (we assume the closest approach of the light ray just grazes the solar surface)

G = 6.7 x 10^-11 m^3 kg^-1 s^-2

c = 3 x 10^8 m s^-1

4GM/(rc^2) = 8.4 x 10^-6 radians = 1.8 seconds of arc