Schwarzschild Geodesics - Bending of Light By Gravity

Bending of Light By Gravity

See also: Gravitational lens and Shapiro delay

In the limit as the particle mass m goes to zero (or, equivalently, as the length-scale a goes to infinity), the equation for the orbit becomes

\varphi = \int \frac{dr}{r^{2} \sqrt{\frac{1}{b^{2}} - \left( 1 - \frac{r_{s}}{r} \right) \frac{1}{r^{2}}}}

Expanding in powers of rs/r, the leading order term in this formula gives the approximate angular deflection δφ for a massless particle coming in from infinity and going back out to infinity:

\delta \varphi \approx \frac{2r_{s}}{b} = \frac{4GM}{c^{2}b}.

Here, b can be interpreted as the distance of closest approach. Although this formula is approximate, it is accurate for most measurements of gravitational lensing, due to the smallness of the ratio rs/r. For light grazing the surface of the sun, the approximate angular deflection is roughly 1.75 arcseconds, roughly one millionth part of a circle.

Read more about this topic:  Schwarzschild Geodesics

Famous quotes containing the words bending, light and/or gravity:

    “‘Tis this desire of bending all things to our own purposes which turns them into confusion and is the chief source of every error in our lives.”
    —Sarah Fielding (1710–1768)

    “As, therefore, we can have no dependence upon morality without religion;Mso, on the other hand, there is nothing better to be expected from religion without morality;Mnevertheless, ‘tis no prodigy to see a man whose real moral character stands very low, who yet entertains the highest notion of himself, in the light of a religious man.”
    —Laurence Sterne (1713–1768)

    “Grown beyond nature now, soft food for worms,
    They lift frail heads in gravity and good faith.”
    —Derek Mahon (b. 1941)