General Rel, deflected light around sun.

[Lengalicious]

Homework Statement

See Attachment

Homework Equations

The Attempt at a Solution

So basically I will not bother writing the derivation from my notes but ultimately it turns out an approximation of deflected light around a mass body is 2\delta\phi=4GM/R where R is distance of closest approach and M is mass of body.

Now what I am confused about is that calculating this deflection angle will give me a value with units of m²s^-2, sooooo I should be getting a value with units arcseconds per century, how exactly does this work? Confused the heck out of me. .

 

[TSny]

So basically I will not bother writing the derivation from my notes but ultimately it turns out an approximation of deflected light around a mass body is 2\delta\phi=4GM/R where R is distance of closest approach and M is mass of body.

Hello, Lengalicious.

You have left something out of the equation. Maybe in your notes you were using units where the speed of light is 1, but here you will want to use standard SI or cgs units.

 

[Lengalicious]

Hello, Lengalicious.

You have left something out of the equation. Maybe in your notes your were using units where the speed of light is 1, but here you will want to use standard SI or cgs units.

I guess that's the only logical explanation, but if there was a missing factor of 1/c then I would still end up with ms^-1 which just would not be convertible to arcseconds per century still. The deflection angle comes from the solution to a differential equation formed by conservation of energy for a particle in a gravitational potential with an extra general relativistic term. None of these terms contain a factor of c unless the general relativistic term does contain a hidden factor c=1 that my professor did not bother to specify for some reason.

 

[TSny]

If you are using units where c = 1, then also cⁿ = 1 for any power.

I'm sure you can find the formula in SI units by doing a quick web search.

 

[Lengalicious]

If you are using units where c = 1, then also cⁿ = 1 for any power.

I'm sure you can find the formula in SI units by doing a quick web search.

Yeh tried earlier with no success but after a quick research managed to find it, turns out its missing a factor of 1/c² like you say, in any case will the value be in radians now?

Thanks for the heads up btw.

 

[TSny]

Good. Yes, radians!