March 5 Information

Let a given photon, move perpendicular to a given gravitational field created by a given star. According to General relativity, the photon's trajectory will be deflected by the angle ${\displaystyle \theta ={\frac {4GM}{v^{2}r}}}$ toward the star, whereas: ${\displaystyle v}$ denotes the photon's velocity (i.e. ${\displaystyle v=c}$), ${\displaystyle G}$ denotes the universal constant of gravitation, ${\displaystyle M}$ denotes the star's mass, and ${\displaystyle r}$ denotes the distance between the star and the photon.

Question: What will the angle be, if we replace the photon by a massive particle, its properties being the same as before (except its velocity ${\displaystyle v}$ which will be slower than ${\displaystyle c}$ of course). Will the angle be a half of the angle mentioned above? HOTmag ( talk) 15:11, 5 March 2024 (UTC) reply

There's no distinction - energy and mass are equivalent. The deflection of the light is just a much greater version of the same effect as the prcession of Mercury. NadVolum ( talk) 18:54, 5 March 2024 (UTC) reply

Thx.

Here you've written "there's no distinction", but you've also written "No big difference" in the edit summary (see the history page), so I wonder what's more exact.

Additionally, what do you mean by "a much greater version"? HOTmag ( talk) 19:43, 5 March 2024 (UTC) reply

Massive particles are deflected by half that angle. Ruslik_ Zero 19:56, 5 March 2024 (UTC) reply

Now I'm a bit confused, because of the contradiction between your reply and the previous reply above yours. Of course, if anyone of you could supply a source (or any argument analogous to a source), I would be much less confused (if at all). HOTmag ( talk) 20:23, 5 March 2024 (UTC) reply

The general formula, for massless and massive particles, is: ^[1]

${\displaystyle \theta ={\frac {2GM}{v^{2}r}}\left(1+{\frac {v^{2}}{c^{2}}}\right),}$

where ${\displaystyle v}$ is the velocity at a large distance, before any acceleration due to the gravitational attraction. When ${\displaystyle v=c,}$ the factor in parenthesis equals ${\displaystyle 2.}$ When ${\displaystyle v\ll c,}$ it approaches ${\displaystyle 1.}$  -- Lambiam 10:47, 6 March 2024 (UTC) reply

Thanks. HOTmag ( talk) 10:37, 13 March 2024 (UTC) reply