Illustrated Physics
physics, drawn
Concept

Gravitational lensing — where it appears

The bending of light by the gravity of a mass between its source and an observer, which shifts, distorts or multiplies the source's image. The deflection is 4GM/c²b at closest approach b, so the Sun bends a grazing ray 1.75 arcseconds and Jupiter 16 milliarcseconds.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Five rays, and the one that decides which side everything falls on. Light traced past a non-rotating mass at five impact parameters, by integrating the exact null geodesic rather than the weak-field formula. The shaded disc is the horizon and the dashed circle is the photon sphere at three masses. Rays passing closer than 5.196 masses are captured — 2 of the five here — and rays passing further escape, however far they are bent on the way. The two nearest the critical value behave in the most striking way: one wraps 1.06 times round before leaving and the other wraps round before falling in, and between them lies a ray that would circle for ever on the unstable orbit. Far away the same integration reproduces the familiar weak-field deflection: at sixty masses it gives 0.07021 radians against 4M/b = 0.06667, so the strong field and the weak one are one calculation.

The circle light cannot leave

A black hole has three radii and they are all sometimes called its size. The horizon is where nothing can come back from; the photon sphere, half again as far out, is where light can circle and cannot keep circling; and the shadow a distant observer sees is larger than either, because the ray that just escapes was bent on its way out.

astrophysics · Horizons The bend that depends on when the planet was there. The difference, in microarcseconds, between the quasar's deflection computed from Jupiter's position when the light passed it — its position as seen from the Earth, 53 minutes earlier — and from its position at the moment of observation, over the day of the 2002 pass. In those 53 minutes Jupiter moves 40998 km, 0.57 of its own radius, and the deflection, a vector of 1.14 mas pointing away from the planet, turns and shrinks by up to 46 µas — about one twenty-fifth of itself. That small term was what the experiment was designed to see. The VLBA measured 51 ± 9 µas, the value general relativity predicts for a deflection pointing away from the position light reveals.

The bend a moving planet gives

Jupiter bends starlight by sixteen thousandths of an arcsecond at its edge, a hundredth of what the Sun manages, and in 2002 radio telescopes spread across a continent measured the bend on a quasar three and a half arcminutes from the planet. The experiment was designed to see something smaller still: the fact that Jupiter moves, by half its own width in the time light takes to reach the Earth, so that the bend depends on where the planet was when the light went past. The measured term was announced as the speed of gravity, and the argument over whether it was anything of the kind is the clearest lesson there is in what an experiment's number is a number of.

astrophysics · Light deflection

Named alongside it

The objects these essays reach for when they reach for this one.

Impact parameterLight deflectionAberrationBlack hole shadowCapture cross-sectionEffective potentialEvent horizonNull geodesicPhoton sphereRetarded timeSchwarzschild metricSpeed of gravity

All concepts