Light Bent by Gravity: Precision Down to Billionths of a Degree express
A light ray passing by a massive body slightly changes its direction, like a stream of water bending around a rock in a creek. In the solar system, there are many such "rocks": planets, their moons, asteroids. And each one, with its own gravity, bends the path of light coming from distant stars.
The authors of the article calculated this bending for the case when the light source and the observer are at finite distances from the massive body. The observer, for instance, is located at the Lagrange point L2 of the Sun–Earth system (a special point in space where a telescope can "hover" stationary relative to Earth and the Sun). The bodies can be of any shape, with any internal structure and rotation: their gravity is described by a full set of time-varying mass and spin multipoles (a mathematical description of mass distribution and rotation).
For axisymmetric bodies (those that look the same when rotated around an axis), the deflection is expressed through Chebyshev polynomials — a set of mathematical functions that allow a compact description of complex dependencies. This makes it possible to compute the deflection to any accuracy, taking into account all multipoles.
It is shown that the total light deflection, when the source and observer are infinitely far from the body, serves as an upper limit for any real case. It's as if the maximum bend of a water stream around a rock occurs when the rock sits in an infinitely long and calm creek.
These calculations are needed for future astrometric measurements with accuracy down to the sub-microarcsecond level. Such precision would allow, for example, more accurate determination of star positions and testing of fundamental laws of physics.
The deflection of light by the Sun's gravity is only 1.75 arcseconds: that's the angle at which a finger is seen at arm's length, divided by a thousand.