|Venus and Jupiter in conjuction after sunset.|
Mike suggested we consider light from a star reflecting off an orbiting planet this past Monday at our weekly group meeting. Simple enough... But while rattling off some fun facts, he posed what seemed to be a quite dubious scenario. When pressed, he added that beer was the answer. I do like beer, but I remained obstinate.
I've been convinced that when objects are in motion they can appear different than you expect; my foolings around with cosmic ray muons as a wee laddie had a big influence. These effects are well described by Einstein's special theory of relativity: moving objects are shorter than if they are not moving, clocks run slower, inertia is greater. But I've mostly filed away these "relativistic" effects in everyday life as the magnitude of these phenomena are scaled by the speed of the moving object as a fraction of the speed of light.
For reference, Usain Bolt reached approximately a few hundred millionths of the speed of light during his world record 100m sprint.
But every once and a while you come across something that is both "relativistic" and conceivable within the realm of everyday experience (here comes the BEER part). Consider for a moment the minuscule reflex motion of a Sun-like star due to an Earth-like planet orbiting it; it's on the order of human walking speed (~ 1 m/s). According to standard, classical physics this shouldn't induce any change in the brightness of that Sun-like star.
However, according to relativity it's brightness should change by about 1 part in a hundred million due to this tiny motion. At first this may seem too small to be relevant (I'm sure you did not notice Usain becoming brighter during his sprint), but consider the fraction of light from the Sun-like star that is reflected off the planet. Simple physics and math will tell you that it is a few parts in a billion.
Yet we see reflected light off planets all the time. So, what was Mike saying? The gravitational influence of Venus on the Sun causes the Sun to get brighter in an amount greater than brightness of Venus?... due to some wacky relativistic effect?!? That's just craziness.
Yeah, but it's true. It's true for all the planets in the sky. And while you may find BEER useful in quantifying this effect, you don't need beer to be convinced.