system
Given the following post, respond as if you're commenting on Reddit:
human
Would the increased albedo of an ice age significantly impact a planet’s orbit over time? [physics]

I was reading about the asteroid deflection technique of painting their surface white, using the solar radiation pressure to change the orbit enough to miss earth.  The process was estimated to need 20+ years of exposure to have the desired impact.

This got me thinking about ice and how reflective it is, and a quick google later i had a rough figure of ice being about 10 times as reflective as water straight on with no difference at near right angles.  There are lots of studies about the impact of the albedo change on temperature and climate (tldr; big impact), but I was curious about how much of a long term impact albedo change might have on a planet’s, Earth for instance, orbit.  I couldn’t find any info on that.

Would the increased solar radiation pressure caused by the increased albedo of an ice age impact the orbit of a planet (Earth) over a period of decades, centuries, mellenia?   Is the opposite true, meaning does a decreased albedo’s lower relative solar radiation pressure have an impact?
gpt
Not really, earth is way to heavy. It only works for small objects that have a greater ratio of surface area to volume. That's because inertia/gravity is proportional to mass and therefore volume, but the radiation pressure acts on the surface area.

Let's do a simple calculation:

Sun's radiation hit the earth with about I=1321 W/m². From this intensity you can calculate the pressure that the photons exert when completely reflected (albedo=1) with the formula

P = 2I/c

with c being the speed of light. This gives us a radiation pressure of

P = 2 * 1321 W/m² / (3e8 m/s) = 8.81e-6 Pa.

If we assume the earth to be flat, perpendicular to the suns incoming light, an area of

A = 127e12 m²

is hit by the flux, creating a force of

F = P * A = 8.81e-6 Pa * 127e12 m² = 1.12e9 N

The suns gravitational force on the earth is 3.6e22 N, so it dominates the pressure by a factor of 32,000,000,000,000 and makes it completely insignificant to the earth's orbital dynamics.

If we colored earth black and all photons were absorbed (albedo=0), the exerted pressure is exactly half of what we calculated previously. Any albedo between 0 and 1 will interpolate these two pressures linearly. Given the earth's real albedo of 0.3, you'll get more impact from coloring it white than black.