Speed up Venus using radiation pressure from the sun?

Question

The amount of energy required to change the rotational velocity of Venus in any meaningful way is immense. Requiring far more energy than humanity can muster at the present date. But I wonder if we can use the most powerful thing in our solar system, the sun, to affect the Venutian rotation? Can we turn Venus into a radiometer?

Would the rotational velocity of Venus change if we shaded half of the planet? Shade the half rotating toward the sun and only allow sunlight to strike the half rotating away from the sun? Would the radiation pressure of the sun on the lighted half help to increase the rotational velocity of the planet? And if so, how long would it take for the rotation to match that of Earth?

Answer 1

This would be difficult to do, but it's easy to make an order-of-magnitude estimate of how difficult it is. We can estimate the angular acceleration this would produce on Venus by calculating the radiation pressure at its orbit, in an ideal scenario: $$P_{\text{rad}}=\frac{2G_{\text{SC}}}{c}\left(\frac{r}{\text{AU}}\right)^2\approx1.74\times10^{-5}\text{ Pascals}$$ with $G_{\text{SC}}$ the solar constant and $r$ the orbital radius of Venus. The force is then $P_{\text{rad}}$ multiplied by half of the cross-sectional area of Venus: $$F=P_{\text{rad}}\cdot\frac{\pi}{2}R^2\approx10^9\text{ Newtons}$$ We can estimate the torque applied to Venus by $\tau\approx F\cdot(R/2)$ and calculate the angular acceleration by dividing this by the moment of inertia, giving $$\alpha\approx\frac{\frac{1}{2}FR}{\frac{2}{5}MR^2}\approx4.24\times10^{-23}\text{ radians s}^{-2}$$ Venus currently has a rotation speed of $\omega=3\times10^{-7}\text{ radians s}^{-1}$, so you'd need timescales of $$\Delta t=\frac{\omega}{\alpha}\approx300\text{ million years}$$ to make any significant change.