Consider the deflection of light by a star. For light, the deflection is twice as much as you'd expect from Newtonian gravity, It's the exact thing that propelled Einstein into stardom.

You must see this gem: http://www.einstein-online.info/spotlights/light_deflection.html

I explained OP Newton mechanics, if he wishes not to update his trajectories based upon that, good for him. That means make black hole massive and photon light- as much as numbers allow. Leaning towards 1/r^2 bahavioral

You'll know that your gravitation is working where photons form a circular orbit at the photon sphere. Good luck.

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

Hmhm, you could fire straight ahead and hit your own behind ?

Fascinating, has that not yet been brought up in star trek ? ?

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Newton's formulas don't work at all, because they require a force and acceleartion variable, while lasers have no such thing here. I've said this already.

Photons don't change speed, but they change direction, therefore they change velocity, therefore they have acceleration.  A decent two-step approximation of the effect of gravity on a photon would be:

1. Calculate the effect of gravity on the photon as if it were a Newtonian particle with a small non-zero mass.
2. Normalize the speed of the photon to the speed of light, applying red- or blue-shift proportional to the adjustment in speed.

3 hours ago, midn said:

Newton's formulas don't work at all, because they require a force and acceleartion variable, while lasers have no such thing here. I've said this already.

They are a poor approximation, like they are in the real world.

Do you want realism ? Then maybe you want to read about general relativity and all that, the papers linked above are a start. I know my mind would melt under the effort. A ship could have fired long in the past close to the black hole at a passer by who from his frame wasn't even there then ...

You could scan over the papers above, i would assume we're back to 17th/18th century newtonian afterwards ?

I ended up simply interpolating the beam's direction depending on the distance on each step, and it produces a good enough result, will improve later on.