# How effective are solar sails to deflect an asteroid?

This answer states that solar sails may deflect asteroids. I understand that the goal is to deflect an incoming asteroid enough to avoid collision. I assume painting the asteroid white may also deflect it. Let's say we discover this 10km wide asteroid on year before impact. How much can we deflect it during this year using white painting and solar sails? Is it enough to avoid collision?

EDIT: This question assumes all raw materials to build and put in place solar sails and painting are available and ready to use as I don't want to take into account all the inherent preparation steps to space missions.

• This depends entirely on its speed, where it is in its orbit, how far it would need to be moved to avoid the target etc. Could you update your question with some more info. Sep 11, 2017 at 19:00
• @ManuH - Then clarify the question. The question specifically says "Let's say we discover this 10 km wide asteroid one year before impact." It doesn't matter if the materials are ready to be used immediately. That huge size of an asteroid coupled with that little lead time is too late for nukes, let alone white paint or solar sails. The Earth (or at least human life on Earth) will be dead, one year later. You've chosen a point in time that is past the point of no return. Sep 12, 2017 at 21:34
• I wrote of nukes because those are by far the best way (currently) of diverting an asteroid. A nuclear explosion near the surface of an asteroid will cause a large amount of material to vaporize, propelling the asteroid away from the site of the explosion. Sep 13, 2017 at 7:11
• @ManuH - All of the answers to that question are incorrect. "Nuclear standoff explosions are assessed to be 10-100 times more effective than the non-nuclear alternatives analyzed in this study." A standoff explosion is intended to provide an impulse but keep the asteroid together. Sep 13, 2017 at 7:27
• @DavidHammen This is the essence of the question. Is this technique efficient with one year? You say no, so write it in an answer. If you want to end your answer by "there is other means to deflect the asteroid", you still can (I think another propulsion system might be more effective than a nuke, but commentaries are not the place the place to discuss about it) Sep 13, 2017 at 8:05

Simply white-painting an asteroid probably isn't enough to avoid a predicted collision in typical cases according to my back-of-the-envelope math.

A 10km diameter asteroid has a mass of around 1e15kg.

According to Wikipedia, at 1 AU from the sun (i.e. in an orbit near that of Earth) you get about 9 µN/m^2 of radiation pressure via perfect perpendicular reflection. The cross section of the asteroid is about 8e7 m^2; so if this was a perfect flat mirror facing the sun you'd get 720 N of force. I'm too lazy to work out the corresponding pressure for a sphere, so let's say it's 100 N. That force divided by the mass of the asteroid gets you 1e-13 m/s^2 of acceleration.

1 year lead time is about 3e7 seconds; d = 1/2 at^2 gives you a displacement of around 45 meters. This is well inside the error bars for prediction of an asteroid's trajectory that far out; you wouldn't even know if you'd made things better or worse.

The smaller the asteroid, the bigger the impact of solar pressure -- mass varies as the cube of the diameter, but cross section and thus pressure varies as the square, so the displacement goes inverse-linear with the size of the asteroid. By the time you reach a possibly-significant ~500km displacement, your asteroid is a non-threatening 1m across.

You'd need a solar sail vastly larger than the asteroid, say 1000km x 1000km, to be able to deflect it within a year. You'd probably do better by using nuclear warheads to nudge the asteroid.

• The white paint technique does not depend on radiation pressure. It instead depends on the Yarkovsky effect. Radiation pressure provides a tiny thrust in the radial direction while the Yarkovsky effect provides an even tinier transverse thrust. Sep 13, 2017 at 8:18
• Those statements seem contradictory to me. Wouldn't white paint reduce absorption, thus heating and Yarkovsky? Wouldn't immediate reflection of light concentrate the effect of momentum more than thermal emission, which would be spread (albeit not uniformly) over a wider arc, depending on rotation speed? Sep 13, 2017 at 8:30

The National Academy of Sciences undertook a study, funded by NASA, regarding near-Earth object detection and mitigation. This study looked at four mitigation techniques: nuclear, kinetic impactors, gravity tractors, and civil defense. The study did not address paint or solar sails due to the extremely low level of technology readiness of those techniques.

The results of this study were published in 2010 at https://www.nap.edu/catalog/12842/defending-planet-earth-near-earth-object-surveys-and-hazard-mitigation . The graph below portrays key aspects of their findings.

Source: Chapter 5 of the previously cited study.

The nuclear option comes in two forms: Disruption and standoff explosions. The intent of the disruptive explosions is to cause the asteroid to break into tiny parts, almost all of which will be placed on a trajectory that avoids collision with the Earth. Unfortunately, this approach will most likely leave at least one large mass that remains on a collision course.

The intent of the standoff approach is to have the weapon explode some distance from the asteroid, thereby avoiding disruption. The gamma rays and energetic neutrons produced by the explosions will cause surface material on the asteroid to vaporize, generating an impulsive change in the velocity of the asteroid body, which remains intact. The disadvantage of the standoff compared to disruptive explosions is that a standoff explosion delivers less than half of the weapon's energy to the asteroid while the disruptive approach delivers almost all of the weapon's energy to the asteroid. The advantage of the standoff approach is that it isn't disruptive. A disruptive explosion is the last resort.

Kinetic impactors are non-nuclear devices that collide with the threatening object at a very high relative velocity, thereby imparting an impulsive change in the velocity of the threatening object. These are orders of magnitude less effective but orders of magnitude more acceptable than the nuclear options.

Gravity tractors are devices that maintain a somewhat largish mass close to the threatening object by means of a low-level thrust. Gravitation makes the threatening object accelerate toward the tractor. The low-level thrust keeps the tractor and its massive payload from falling into the asteroid. This is a very slow but steady approach. Multiple decades of operational time are needed to be effective. In addition to the long time span, another downside of this and related approaches is that these approaches require rendezvous, significantly increasing the delta V requirements of such missions compared to the nuclear options or kinetic impactors.

Note that in the above graph, the level of shading indicates the effectiveness of the technique. For an object 10 km across, the only effective technique is the nuclear option, and then only if there is a decade or more advance warning. The question asks about using paint or solar sails for an object that is 10 km across, with only one year of advance warning. Nothing is effective in this extreme case.

What about using paint or solar sails? These techniques (along with a myriad of others) were dismissed out of hand by the National Academy of Sciences study due to impracticality, lack of knowledge, or lack of technology readiness. The Yarkovsky effect, which is what using paint relies upon, is something that suffers from lack of knowledge. Scientists don't quite know the magnitude of the Yarkovsky effect on asteroids. Studying this is one of the key aspects of the ongoing OSIRIS-REx mission. The extremely low technology readiness of this approach also contributes to making this a technique that, at least currently, can be dismissed out of hand from an engineering perspective.

Solar sails might be effective as an alternative to using thrusters in the gravity tractor. An extremely large solar sail to accomplish this, making this a TRL 1 (idea on paper) kind of approach. Tethering the solar sail to the threatening object falls into the sub TRL 1 territory.