I know that light can be affected by gravity. But what if there was a planet where if you shone a light in a direction and it could hit your back. I'm talking about a planet where light is bent around the diameter of the planet and back to the starting point. But I am not incredibly good at math so I need help.

The planet must be made of Osmium. Although that is the logical material anyway because I want this planet to be as small as possible without being compressed and Osmium is the densest naturally occurring element (assuming it won't compresses itself under its own gravity for some random reason). And it must be natural because I want this to be possible. So using this information I wanted to know the diameter of this planet for light to bend all the way around it and I would like to know the gravity of this object.

I just want a "defy all odds" answer. Many other areas of Q/A in SE have been calling me ridiculous and that my idea is useless but I don't want criticism, I just want your answers.

@Tim B has given an amazing answer but we can't do the math. If anyone could help that would be great.

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    $\begingroup$ Welcome to worldbuilding! With that kind of density, I'm pretty sure what you're talking about is some kind of black hole. $\endgroup$
    – PatJ
    Nov 23 '17 at 3:10
  • $\begingroup$ I know this, but I just want a "defy all odds" answer. Many other areas of Q/A in SE have been calling me ridiculous and that my idea is useless but I don't want criticism, I just want your answers. $\endgroup$ Nov 23 '17 at 3:16
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    $\begingroup$ To be clear, there is no criticism of you. There is nothing wrong with wondering if something is possible. But, sometimes the only answers are that you can break the laws of physics (entirely respectable sci-fi authors do this all the time), or you can find a different but similar solution to your problem because you original idea is inconsistent with the laws of physics (also no shame in this if you want to write hard sci-fi, people want something cool and don't really care that your original mechanism isn't what gets you there). Trying harder doesn't change the laws of physics. $\endgroup$
    – ohwilleke
    Nov 23 '17 at 5:04
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    $\begingroup$ Hello and welcome to Worldbuilding. What you have asked for is a black hole. No matter what size you make it, it remains a black hole. Why is it like this? Because the behaviour you have asked for — light trapped in its gravity well — is what makes the hole be black. There is no way to "defy the odds here" because the odds of this being any kind of normal planet is zero. Also a general tip: do not ask questions if you are not willing to deal with honest or — even more salient — truthful answers. If people say "this is a black hole", no amount of wishful thinking will change that. $\endgroup$
    – MichaelK
    Nov 23 '17 at 7:34
  • $\begingroup$ "assuming it won't compresses itself under its own gravity" — it will. Everything can be compressed under enough force. $\endgroup$
    – Mołot
    Nov 23 '17 at 9:11

The only place where stable photon orbits exist is the Photon Sphere. This is 3/2 of the Swarzchild radius of a black hole (or possibly an ultra-compact neutron star, so there are three approaches to this, the first two of which are nearly impossible for different reasons:

  1. Orbiting surface on a black hole. The black hole would need to be very massive (possibly even supermassive) to sustain non-spaghettified surface-dwellers. This would mean that the surface doesn’t have actual stable photon orbits. Also, the energy requirements make it completely infeasible (to maintain near light speed in an area with high atmospheric density from the accretion disk)

  2. Another option is exotic physics, in some form of exotic matter or other impossible phenomenon that would allow mass within a Swarzchild radius to not collapse into a black hole. This is only really useful if you aren’t opposed to using pseudo-science handwaving.

  3. The third option, which is feasible under our current understanding of physics, and would actually be at the photon sphere, relies on active support of a non-orbiting body (i.e. using thrusters to maintain the position of a station). The photon sphere is the lower bound for stable orbits, so any stable station at that distance couldn’t be in orbit. The thrusters’ energy costs would be incredibly massive, so something like a statite could be created. The structure itself is realistic around a black hole, but the energy would be very expensive. An accretion disk or energy output from the previously mentioned neutron star could be helpful in maintaining the station. An assisted orbit system could make the satellite/statite more sustainable and stable. This proposed system is a satellite at the photon sphere orbiting at near light speed, but with support thrusters (thrusters towards the body of gravitation). I don’t know the maths that determines the speed of acceleration at the photon sphere, but I believe that acceleration decreases with size of the black hole; therefore, habitable acceleration levels could be obtained for an incredibly large black hole.

  • $\begingroup$ There is theoretical solution for a neutron star with photon sphere: adsabs.harvard.edu/full/1993ApJ...406..590N - black hole not needed. $\endgroup$
    – Mołot
    Nov 23 '17 at 9:33
  • $\begingroup$ @Mołot Thanks. I’ll edit my answer to reflect this. $\endgroup$ Nov 23 '17 at 16:10

Sorry, it is impossible to do this with gravitational lensing without killing everyone.

There are ways to bend light other than gravity (e.g. prisms, reflective surfaces and fibre optics), but if you use gravity everyone dies a horrible death unless you want to change the law of physics and stick to magic.

The diameter to get the gravitational effect you want would be about 8.7 millimeters for a planet of Earth mass, or about 0.1 millimeters for a planet with the mass of the Moon.

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    $\begingroup$ Yes. This is the answer according to the laws of physics. There is exactly one answer to this question. There is no other answer that will cause light to go in circles due to gravity. It can't be larger and it can't be smaller. $\endgroup$
    – ohwilleke
    Nov 23 '17 at 3:30
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    $\begingroup$ I mean creating an object SO massive that it almost has the gravity capabilities of a black hole. Someone in Physics SE gave me an anwser but I don't know If it is right here it is though. $\endgroup$ Nov 23 '17 at 3:33
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    $\begingroup$ How are you going to stop this ball of osmium from compressing itself due to gravity? But anyway, if we do a naive calculation using the formula from Chris's answer and a density of 22590kg/m322590kg/m3, ignoring gravitational collapse, the radius is a little over 68.875 million kilometres. And using simple Newtonian mechanics the surface gravity would be about 44340 times that of Earth. Of course, both of these numbers are nonsense. $\endgroup$ Nov 23 '17 at 3:34
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    $\begingroup$ An object that is almost, but not quite a black hole is called a neutron star and for an Earth sized object would be only a fraction of a millimeter different in size and wouldn't give you light that goes in circles. You can't get the light bending effects you want for anything remotely close to that radius. Gravity has to be really, really strong to bend light that strongly - too strong for a person to survive. You can't have osmium with gravity that strong, osmium needs much weaker gravity to exist. $\endgroup$
    – ohwilleke
    Nov 23 '17 at 3:34
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    $\begingroup$ What OP is describing is the behavior of light at the event horizon of a black hole. There is no other answer $\endgroup$
    – pojo-guy
    Nov 23 '17 at 5:12

Something similar to what you are asking is theoretically possible (see this answer)

Consider a neutron star. If the radius falls below 1.76 times the Schwarzschild radius for its mass, then due to the General Relativistic bending of light in curved space, then all of the surface is visible, when viewed from any direction

If the light can be bent to show all the surface from any direction, it should be also possible to trap it around the body.

Now, I hope you agree that Osmium, though being highly dense (22.59 g/cm3), is still way out of the density of a neutron star (~4.5x1014 g/cm3). And mind that "way out" is still an euphemism when we talk about 13 orders of magnitude difference!

Therefore gravitation lensing is to be ruled out.

You can however still trap the photons if your atmosphere acts as a waveguide generating something similar to Schumann Resonances.

Schumann resonances are global electromagnetic resonances, generated and excited by lightning discharges in the cavity formed by the Earth's surface and the ionosphere. Schumann resonances occur because the space between the surface of the Earth and the conductive ionosphere acts as a closed waveguide. The limited dimensions of the Earth cause this waveguide to act as a resonant cavity for electromagnetic waves in the ELF band.

  • $\begingroup$ See all surface is still not a full circle. Close, infinitesimally close, but not exactly there. As far as I understand full circle is only possible at the event horizon, isn't it? $\endgroup$
    – Mołot
    Nov 23 '17 at 9:18
  • $\begingroup$ @Mołot, venturing into the calculations is beyond my knowledge, but I "suspect" that, somewhere in between this case and the black hole there is the closed elliptical photonic orbit, which degenerates into the circle. $\endgroup$
    – L.Dutch
    Nov 23 '17 at 9:22
  • $\begingroup$ My bad, it seems that there is theoretical solution for a neutron star with photon sphere: adsabs.harvard.edu/full/1993ApJ...406..590N $\endgroup$
    – Mołot
    Nov 23 '17 at 9:30

You can’t do it with gravity, but you could have an atmosphere that refracts the light. Long ago, I once heard that Venus’s atmosphere would do this, if it were transparent. In reality, the refraction needs to bend it in the proper direction and that direction only, so you need a gradient of density or different layers.

If you just want to see a glow from behind you, not a tight spot, you have an easier job. In fact, HAM radio operators do this on Earth, bouncing the light (not a frequency we see with our eyes though, but it’s all the same stuff) to the other side of the planet via reflections on a specific layer of the atmosphere.

You might postulate a layer that reflects visible (to them) light when a glancing angle is used. Look up total internal reflection. Two layers of the atmosphere that settle out in distinct sharp layers would allow for that.


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