Paul Mainwood, Degrees in Physics and Philosophy, Doctorate in Philosophy of Physics
Written 6 Nov 2015
Laser beams travel in straight lines. The earth is a sphere. So, assuming you're pointing the beam horizontally, the beam will continue in a straight line and head out of the atmosphere as the earth curves away beneath it, unless there other effects come into play to bend it.
I can think of only two effects that would change this straight line path: Atmospheric refraction and gravitational bending of light (as predicted by general relativity).
Let's check out and see if they're significant enough to bend the laser beam even an appreciable amount.
1) Atmospheric refraction: There will be a small amount of bending as the laser goes through thinner and thinner atmosphere and exits into space. This is the same effect that means the sun is "actually" below the horizon a good while before we see the sun set. Bennet's empirical formula for visible light gives:
R=cot⁡(ha+7.31ha+4.4)" role="presentation">R=cot(ha+7.31ha+4.4)
Where h is the "apparent angle" of a distant object on the horizon, and R is given in arcminutes. Setting ha" role="presentation">ha as zero (meaning that we fire our laser beam in a horizontal line) we get a correction of around 34 arcminutes. i.e., half a degree. Not much, but it's there.
2) Gravitational bending of light: The earth's gravity will bend the light slightly. We should expect this effect to be very, very small indeed since it was not noticed until after general relativity was proposed. Let us calculate nevertheless.
Using the Schwarzchild solution for a massive body, we get:
α=4GMc2R" role="presentation">α=4GMc2R
For the angle in radians. For earth, M=5.97×1024kg" role="presentation">M=5.97×1024kg and R is the closest approach to the mass, i.e., the radius of the earth = 6371 km. Plug these in and convert to degrees and you get something stupendously small: 1.6×10−7" role="presentation">1.6×10−7 degrees. This really is not much at all. We're safe discarding it, as expected.
So, the laser will continue straight out of the atmosphere, with a tiny half a degree bend by its interaction with the atmosphere, before continuing straight on in space forever.