# Solar sail questions

1. Apr 19, 2007

### JoAuSc

I did a simulation of a solar sail in Java. It seems to be accurate; when you face the sail in one direction, it approaches the sun, in the other direction it goes outward, when it's parallel to the sun's rays it moves in an ellipse and when it's perpendicular, the ellipse is elongated. (This simulation is for a solar sail whose angle relative to the sun is constant. I should also mention the solar radiation force term is something like S/r^2, split into components based on the sail angle, where S was derived with the assumption that the maximum acceleration at the Earth's distance from the sun due to the sail was 0.25 mm/s^2, which I got from a paper.)

One thing that surprised me, though, is that dr/dt (where r is the radius) seems to be roughly constant. After taking a closer look at it and letting the end time of the simulation be much longer (~100 years), r is not quite linear, but curves towards the sun the closer to the sun you get at a rate that increases as well, whether you're looking at r >> 150 million km, or r << 150 million km.

Here are my questions:

1.) Is there a way to analytically get an approximate value for the slope of dr/dt?

(This is neglecting variations due to eccentricity. My simulation has a slider which varies the intial velocity, but it assumes it's all perpendicular to the sun, so while you can smooth out an elliptical orbit to get a circular one, you can't smooth out an elliptical spiral, at least not until I allow the direction of the initial velocity to vary with sail angle.)

2.) Also, do you guys have any idea of better ways to approximate solar sail motion? My simulation solves the set of 2nd-order equations that come from Newton's 2nd law in polar coordinates, but I've heard about other methods, such as "Lagrange's planetary equations for orbital perturbations". Can anyone provide me with methods of determining the path of a solar sail that'd be better than simply solving newton's 2nd law?