Editing Solar sail (section)

===Solar radiation pressure===
{{Main|Radiation pressure}}
The force imparted to a solar sail arises from the momentum of photons. The momentum of a [[photon]] or an entire flux is given by [[Energy–momentum relation|Einstein's relation]]:<ref>{{cite web|url=http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html |title=Relativistic Momentum |publisher=Hyperphysics.phy-astr.gsu.edu |access-date=2015-02-02}}</ref><ref name="wright-appendixA">Wright, Appendix A</ref>

:<math>p = E/c</math>

where p is the momentum, E is the energy (of the photon or flux), and c is the [[speed of light]]. Specifically, the momentum of a photon depends on its wavelength {{math|''p'' {{=}} ''h/λ''}}

Solar radiation pressure can be related to the irradiance ([[solar constant]]) value of 1361&nbsp;W/m<sup>2</sup> at 1&nbsp;[[Astronomical unit|AU]] (Earth-Sun distance), as revised in 2011:<ref>{{cite journal|author1=Kopp, G. |author2=Lean, J. L. |author2-link=Judith Lean |title=A new, lower value of total solar irradiance: Evidence and climate significance|journal=Geophysical Research Letters |volume=38 |issue=1 |year=2011|pages=n/a |doi=10.1029/2010GL045777|bibcode=2011GeoRL..38.1706K |doi-access=free }}</ref><!--DO NOT CHANGE FROM SIG FIGURES: LEADS TO MISLEADING VALUES & INCONSISTENCIES-->

*perfect absorbance: F = 4.54&nbsp;μN per square metre (4.54&nbsp;μ[[Pascal (unit)|Pa]]) in the direction of the incident beam (a [[Inelastic collision|perfectly inelastic collision]])
*perfect reflectance: F = 9.08&nbsp;μN per square metre (9.08&nbsp;μPa) in the direction normal to surface (an [[elastic collision]])

An ideal sail is flat and has 100% [[specular reflection]]. An actual sail will have an overall efficiency of about 90%, about 8.17&nbsp;μN/m<sup>2</sup>,<ref name="wright-appendixA"/> due to curvature (billow), wrinkles, absorbance, re-radiation from front and back, non-specular effects, and other factors.
[[File:Sail-Force1.gif|thumb|Force on a sail results from reflecting the photon flux]]
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<ref>McInnes, C. R. and Brown, J. C. (1989) ''Solar Sail Dynamics with an Extended Source of Radiation Pressure'', [[International Astronautical Federation]], IAF-89-350, October.</ref>), and by the square of the cosine of the angle between the sail force vector and the radial from the Sun, so

:<math>F = F_0 \cos^2(\theta) / R^2</math> (for an ideal sail)

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

:<math>F = F_0 (0.349 + 0.662 \cos( 2\theta) - 0.011 \cos( 4\theta)) / R^2</math>

Note that the force and acceleration approach zero generally around θ = 60° rather than 90° as one might expect with an ideal sail.<ref>Wright, Appendix B.</ref>

If some of the energy is absorbed, the absorbed energy will heat the sail, which re-radiates that energy from the front and rear surfaces, depending on the [[emissivity]] of those two surfaces.

[[Solar wind]], the flux of charged particles blown out from the Sun, exerts a nominal dynamic pressure of about 3 to 4 [[Pascal (unit)|nPa]], three orders of magnitude less than solar radiation pressure on a reflective sail.<ref>{{Cite web|url=http://www.swpc.noaa.gov/SWN/index.html|archive-url=https://web.archive.org/web/20141127142813/http://www.swpc.noaa.gov/SWN/index.html|url-status=dead|title=NOAA / Space Weather Prediction Center|archive-date=November 27, 2014}}</ref>