# Why does light travel in a straight line and not rotate with us due to gravity?

I read somewhere that light is affected by gravity, so then why doesn't like us it move along with the earth?

• I don't follow your logic; how does one logically go from "affected by gravity" to "move along with the earth"? – Alfred Centauri Nov 23 '16 at 12:58
• The reason is the speed I think. Photons travel damn fast, they can't be attracted by the earth... Only a black hole can though.... PS: Im not a physicist lol – esQmo_ Nov 23 '16 at 13:00
• Its path is definitely affected by the presence of the sun, but the Sun's mass is not enough to make light go around like the Earth does – caverac Nov 23 '16 at 13:12
• Possibly the question relates to GR where a massive body like a satellite rotates around the earth following a geodesic in curved space-time and the question is why light doesn't do this in the same way. – freecharly Nov 23 '16 at 14:04
• Possible duplicate of Is light affected by gravity? Why? – sammy gerbil Nov 23 '16 at 18:22

The geometry of the path that light follows definitely changes in the presence of massive objects, e.g. the Sun. Eddington's experiment indeed showed that for the Sun, concluding that the light bends $\sim 1$ arcseconds when it goes near. This in contrast with the earth that goes a full $360^\circ$ around the sun.

It is possible to make light go around a full revolution, but for that you would need to shrink the Sun to a radius of $R_s \sim 3$ km, and in this case, the light will move in an orbit of radius $3R_s/2\sim 5$ km. Compare this with the actual size of the Sun $\sim 7\times 10^{5}$ km, and the size of Earth's orbit $\sim 1.5\times 10^{8}$ km!

• caverac, the equation holds only for black holes. For the sun this equation is not useable. As long as a photon could escape a body it would not be possible that it would revolve around this body. The gravitational potential does not depends of the mass density – HolgerFiedler Nov 23 '16 at 18:56
• @HolgerFiedler My point is that you would need to create a black hole out of the sun to have photon sphere – caverac Nov 23 '16 at 19:48

The effect of the Earth's gravity on light is way too tiny to care for most purposes.

https://en.wikipedia.org/wiki/Gravitational_lens

Using a classical calculation to get the size of things without getting too fancy, the orbital speed (for a circular orbit) at the surface of the Earth is about $9 \frac{km}{s}$. The speed of light is about 33 thousand times faster than that.

The the relationship between the mass of the planet and the orbital speed goes like $M \sim v^2$. So in order for the orbital speed to be 33 thousand times as fast, the Earth would have to be about 1 billion times as massive.

• I think that you should explain this more in detail. Not just refer to a link. – freecharly Nov 23 '16 at 13:58