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Ignore any other effect on earth; I'm only curious about how much and in what way gravity's affect on the light would distort what is seen by the eye. :)

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closed as off-topic by L.Dutch, dot_Sp0T, Mormacil, Draco18s, Aify Jun 24 '17 at 0:40

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    $\begingroup$ Your vision would be distorded as your eyes would be squished to a few atoms thick layer of organic compounds. But I assume "any other effect on earth" includes us :p $\endgroup$ – Keelhaul Jun 23 '17 at 10:25
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    $\begingroup$ It would be distorted by the fact that you would be dead. $\endgroup$ – Sasha Jun 23 '17 at 10:27
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    $\begingroup$ I'm voting to close this question as off-topic because this boils down to 'how does gravity affect light' which in turn is asking about physics and equations. $\endgroup$ – dot_Sp0T Jun 23 '17 at 11:19
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    $\begingroup$ @secepticus This isn't high concept though and I would say it is fine. Odd but fine. $\endgroup$ – Bellerophon Jun 23 '17 at 11:40
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    $\begingroup$ It is a fairly established thought experiment. "If you were standing on a neutron star, you would see the back of your head". I'm surprised people have a problem with this question. I cannot provide an answer though. Maybe the problem is that it could be in a physics forum, but many questions here would fit someplace else as well, they are just asked by people that do not know physics very well and wouldn't be able to understand the answers they receive there. This is a perfectly legitimate (if boring) question, especially since it asks for 178k exactly which imo even makes it WB $\endgroup$ – Raditz_35 Jun 23 '17 at 12:27
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Not Much, Unless You're An Astrophysicist.

178,000 g is roughly 1.75e6 m/s^2. It's a lot. That's roughly the peak acceleration of a bullet fired from a pistol. But would it have a noticeable affect on vision? Assuming you have eyeballs to withstand being in the gravitational equivalent of a centrifuge, can you see the bending of light?

Since gravity is linear with mass, and falls off exponentially with distance from the center of mass, to have such gravity the Earth's mass would have to also increase by 178,000 while keeping the same radius. 178,000 times Earth's mass puts it roughly at 1e30 kg. That's about half the mass of our Sun, but packed into a much, much, much smaller area. It's a lot of mass, at a very high density.

But it's still pretty low by cosmological standards. A white dwarf is twice as high. The gravity on the surface of a neutron star is a million times stronger. The gravity at the event horizon of a black hole with the same mass is 3e13 m/s^2 or 20 million times stronger.

Let's do some quick and dirty calculations.

Spacetime Distortions

Such a high gravitational field would produce distortions of spacetime, but not so you'd notice. 1 second on the Earth would be about 100 microseconds slower than 1 second outside its gravity well. We already have to account for such distortions in very sensitive instruments in medium and high orbits like GPS, but this is much more extreme.

Gravitational Lensing

With such high gravity, the Earth would produce a gravitational lensing effect on distant light traveling near the surface.

$$\theta = \frac{4GM}{rc^2}$$

Right now, the Earth distorts light by $1.5\times 10^{-7}$ degrees. The deflection increases linearly with mass, so with 178,000 more mass that's 178,000 more deflection or 0.027 degrees. Not enough so you'd notice anything different looking up at the stars, but enough so astronomers would have to compensate.

Horizon

Because light near the surface is bent towards the surface, the Earth would appear just a little bit flatter than it really is. You'd be able to see things just over the horizon, but not so you'd notice.

If you're standing on the Earth's surface, and there's no obstructions, the horizon is about 5km away. A 0.027 degree bending of light toward the surface will not be noticeable to the naked eye.

Spaghettification

The force of gravity is $GM/r^2$, where G is the Gravitational Constant, M is the mass of the object, and r is your distance from the center. In very high gravity environments, small changes to r can produce large effects.

Your feet are roughly 2 meters closer to the center of the Earth than your head. This makes a difference in gravity of 1.744e6 m/s^2 to 1.748e6 m/s^2. That might not seem like a lot, but that's a difference of 4000 m/s^2 or 400g. Your head and feet will feel a difference in force higher than rocket sled.

You'll notice that.

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  • $\begingroup$ This is exactly what I was looking for, thanks! I'm gonna assume that 2 or 3 times the mass isn't gonna be MUCH different. Thanks a bunch! $\endgroup$ – Fred the John Jun 24 '17 at 7:27

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