# Solar Pressure and Gravity

I recently read some articles and pages on Solar Sails, and the possibility of using lasers to propel spacecraft, and I had a relatively outlandish idea.

Would it be possible for a star to be outputting enough light that planet-sized (or smaller) objects caught in it's gravitational pull would not cross a certain threshold?

A sort of 'reverse blackhole' if you will, where the event horizon is an area that the matter(not light) can not proceed further into the star.

I would assume this to look like a star with a large ring around it, equidistant from any point of the star's center, where matter would coalesce.

Furthermore, would it be possible that an object could remain 'stationary' (ie. not in orbit and no acceleration in any direction beyond the pull of gravity) around this star without fear of gravity pulling it into the star?

• Possible duplicate of Will a Ball placed close to Sun fall into it? – pela May 19 '16 at 6:57
• I'd like to point out that my question is related, not a duplicate, of that and it's related answers. The Q&A you've suggested is too specific, as it deals with only our star, the sun. My question is less specific, asking if it is possible for a star (of any kind or size) to exhibit this (specific) behavior within the realm of reasonable expectations. – user11883 May 19 '16 at 16:25
• Okay, but you can actually use exactly the same formulae. Since radiation pressure is proportional to the luminosity of the star, the most luminous known star R136a1 — which has $L = 8.7\times10^8\,L_\odot$ and $M = 315\,M_\odot$ — exerts $8.7\times10^8$ times the pressure, so from the fifth equation in my answer, $m/r^2 \sim 7\,\mathrm{g}\,\mathrm{cm}^{-2}$. For the Sun, the maximum size of a ball of rocky material is of the order 0.1 to 1 $\mu$m. For R136a1 the maximum size is then $\sim1\,\mathrm{cm}$ — far from a planet. – pela May 19 '16 at 20:38

While I'm lacking the formulae, the applicable surface area of a body would have to be great enough, and it's density low enough that it's gravity remains below that threshold. So a smaller body is much more likely. If you think about it, most dust from near the sun gets pushed out by the pressure.

There wouldn't be a specific point where you would get the matter buildup, it'd be more like the Roche limit where the gravity and density are the factors of the distance from the larger body.

Without running calculations I'm also unsure as to whether it would in fact be a stable arrangement but more like an L1 style Lagrange point, where it requires some energy every now and then otherwise it drifts.

Edits are welcome, I feel that I haven't used the best language available here and may have rambled.

• Wouldn't other bodies at the limit pull the smaller objects into them anyway? Thus, the system would be relatively "clean"? – user11883 May 18 '16 at 18:13
• That depends on how much more massive they are and what the radius of their orbit is. I also forgot to mention that if the body is stationary and not orbiting the star, the pressure would have to be significantly stronger because there is less centripetal force – Tanenthor May 19 '16 at 3:43

Both the radiation and gravity follow an inverse square law, so there is no "horizon" at which gravity would overcome light radiation, they both get weaker at the same rate.

Radiation pressure affects smaller objects disproportionately. This is one factor in the formation of comet tails: dust and gas is pushed away from the heavier nucleus, which is relatively unaffected.

Very small objects can already be pushed from our sun, I did a quick estimate and found that dust with a mass of less than $10^{-16}\,kg$ the mass of a bacteria, would be more affected by the light of the sun than the gravity.

For a planet to be affected more by the radiation than the gravity of a star would be beyond realistic (though might make a good "xkcd 'what if'". Not only would be be enough to vaporise a planet, it would be enough to unbind the star. It would be a supernova.

• Do these numbers hold with a much larger or luminescent star, such as UY Scuti or R136a1? I'd 'plug and chug' but I'm unfamiliar with the second half of your equation and pretty sure any results I came across would be inaccurate at best. – user11883 May 18 '16 at 21:49
• The second half is very rough. It assumes a mass of 5000 kg/m3 and uses the numbers from the radiation pressure wikipeida – James K May 19 '16 at 5:15