# Would the Poynting–Robertson effect ever be faster than a solar sail from a 1 AU orbit to the Sun?

In this answer to Do you need 0 km/s velocity to crash into the sun? I mention solar sails for retrograde thrust and the Poynting–Robertson as two ways an object could ever-so-slowly spiral into the Sun.

Using known materials with modest extrapolations (like they do for solar sails) and ignoring deterioration due to solar wind, radiation damage and meteorites, is there some mass regime where a configuration optimized for Poynting–Robertson effect would be faster than a configuration optimized for a vanilla solar sail to get from a 1 AU orbit to the Sun?

For example, if two teams were assigned the task of designing a passive Sun-spiraling craft and given the same mass constraint, would the SolarSailors team always win no matter what mass was choses, or are there some masses where the PoyntingRobertsons could win?

• – uhoh
Jun 6, 2020 at 13:10

No. Let's take the "tacking against the Sun" scenario.

The optimal incidence angle for a 100% reflective solar sail to reduce orbital velocity around the Sun, is 45 degrees, all of the reflected incident rays reflected 90 degrees prograde, maximum retrograde thrust. Any more or any less and some of the thrust would have useless radial component. For less than 100% reflective the angle might be slightly higher; all of the absorbed light provides useless radial-out thrust, but it will be re-radiated perpendicular to the sail (on the average), so giving it a little of prograde bias at cost of losing out some on the reflected might provide beneficial; nevertheless the reflected light provides far more momentum so the aim will be to get as close to 100% reflectivity as possible.

On the other hand, Poynting–Robertson effect is equivalent to the same but at incidence angle of $$arctan({c \over 29.7 km/s})$$, that is about 89.994 degrees. Almost but not quite the completely useless 90 degrees where none of the light would contribute retrograde thrust and in fact none would hit the sail surface.

That is even ignoring the impossible engineering challenge of having the "Poynting–Robertson sail" have the reflected light not hit any other part of the craft; doable in case of sparse loose dust, not a structurally solid macroscopic spacecraft.

• For the sail this answer says it's closer to 35 degrees. Can you cite some supporting source(s) for the arctan equation? Thanks!
– uhoh
May 6, 2020 at 13:08
• @uhoh Just me putting the second paragraph of the "Source of the effect" section of the Wikipedia article you've linked into terms of trigonometry.
– SF.
May 6, 2020 at 13:20
• oh geez all this time I've been thinking Yarkovsky effect where I've been writing Poynting–Robertson, my bad. That isn't the question I thought I'd asked but this is definitely the answer to what I did ask. (I'm seriously thinking of looking into this further) I'll let it go around the Earth a few times and likely accept this, and in the mean time see if I can ask a Yarkovsky question complementary to this one (what I'd wanted to ask). Thanks!
– uhoh
May 6, 2020 at 14:27
• I've gotten around to it finally: Would the Yarkovsky effect ever be faster than a solar sail from a 1 AU orbit to the Sun?
– uhoh
Jun 6, 2020 at 13:10