I was having a conversation with a friend about their idea for a sci-fi story, but I don't know enough orbital mechanics to give more than a basic guess of what'll happen, so I figured I'd turn to you.
Consider two-body system: a spherical planet covered with a mirror (or possibly just something like snow, with an albedo very near 1) orbiting a star. The light reflecting off the planet will, on net, push it away from the star- and so it'll rotate normally, following Kepler's laws, but as if gravity were slightly weaker than it actually is (based on the luminosity / gravity relationship of the star). That's pretty easy to work through- the luminosity of incident light varies inversely with r2
, just like gravity, and everything is radial.
Now let's make things more complicated. Instead of covering the planet with mirrors, let's cover it with fiber optics- so we can pipe the light around to wherever we want. (Alternatively, coat the planet with solar cells, and move around electrons rather than photons.) Now, shoot all the collected light from a point on the terminator
in the plane of the planet's orbit, to create a positive angular acceleration.
What happens to the orbit of the planet? All of the orbital mechanics that I know hinge on conservation of energy and angular momentum, which aren't relevant to this system (since you ignore the energy and angular momentum of departing photons). It seems obvious that the planet's angular momentum will increase. But it's not clear how much of that increase comes through increasing eccentricity, and how much comes through increasing the radius of the periapsis. (Both terms used in the context of the orbit you would have if you shut the light collection system down.)
As well, the rate at which the angular momentum increases varies inversely with r2
. That seems like it would favor eccentricity over periapsis.
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