# B What does this equation mean?

1. Apr 3, 2017

### Enis

Specifically, what does each of the letters denote in this solar sail equation?

"The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the Sun (unless extremely close to the Sun[17]), and by the square of the cosine of the angle between the sail force vector and the radial from the Sun, so

F = F0 cos2 θ / R2 (ideal sail)

where R is distance from the Sun in AU. An actual square sail can be modeled as:

F = F0 (0.349 + 0.662 cos 2θ − 0.011 cos 4θ) / R2"

From Wikipedia.
Thanks in regards!

2. Apr 3, 2017

### Bandersnatch

F is the resultant force per square metre of the sail, F0 is the force per square metre of a hypothetical sail at 1AU and perpendicular to solar rays. θ is the angle between the direction towards the Sun and the direction perpendicular to the sail (so 0° is face-on and 90° is edge-on). R is distance to the Sun in units of AU.

3. Apr 3, 2017

### woody stanford

Even getting this equation from WIkipedia I think it would be a good idea to work it out manually one's self to both verify and understand what it means.

The part about the force being imparted to the whole sale being proportional to the distance away from the Sun is common sense and follow the inverse R^2 relationship of light energy from a point source. The part that might be throwing you though is where the cosine comes in. Now don't quote me on this (as I haven't read this carefully enough) but I think their point has to do with the angle of incidence of the rays of light hitting the sail.

Usage of cos(x) is the typical way of calculating the portion of 100% light that effectively hits the sail and is also used in the calculation of drag (looking at wind instead of photons but the same principle). Just draw out the geometry of it on paper and you'll see this is true remembering tan theta = Opposite/Adjacent (and its related identities, especially for cos).