Einstein's Field Equations - SF Writer needs general answer

[Ring Gate]

I am working on a novel that uses 'gates' that for lack of space here let’s just call worm holes (any excuse works for this question). But these gates cannot bridge to each other if located in a region of space that is warped too much.
So I'm looking for a proportional answer, not a calculated exact one.
Example: If light (like from a star) diminishes by the inverse square law, then a similar situation of what I am looking for would be: If I arbitrarily chose the amount of light hitting the Earth to be what I want for some other planet, then if I know how bright its star is compared to the Sun I can figure the distance that planet has to be to get the same amount of light as our Earth does. So a star four times as luminous would require its planet to be twice as far from it as the Earth is from the sun. Looked at this way, I don't need to know units in lumens, distances in meters, etc. Just arbitrary general units and a quick ratio.
NOW
If I were to say for instance that a gate could work if it orbited the Sun at a distance like that of earth, which is 1 AU (only an example) is there a simplified ratio that the Field Equations can be roughly equal to for at least 2 or 3 digit accuracy to be able to say another star of so many solar masses would equal some minimum distance away then for a gate at that star?
I do know that it is simpler for calculations outside of a massive object rather than inside, but it is still too complicated for this Sci-Fi writer. I hope that some rough proportion can be used for distances several times the radius of the sun, again only 2 or 3 digits at least, but if 4 or more, fantastic! The story is NOT a dry textbook to be checked for accuracy, but I do not want to write in things that to someone knowledgeable would laugh at as clearly off.
Thank you very much for any help provided.

 

[PAllen]

I am working on a novel that uses 'gates' that for lack of space here let’s just call worm holes (any excuse works for this question). But these gates cannot bridge to each other if located in a region of space that is warped too much.
So I'm looking for a proportional answer, not a calculated exact one.
Example: If light (like from a star) diminishes by the inverse square law, then a similar situation of what I am looking for would be: If I arbitrarily chose the amount of light hitting the Earth to be what I want for some other planet, then if I know how bright its star is compared to the Sun I can figure the distance that planet has to be to get the same amount of light as our Earth does. So a star four times as luminous would require its planet to be twice as far from it as the Earth is from the sun. Looked at this way, I don't need to know units in lumens, distances in meters, etc. Just arbitrary general units and a quick ratio.
NOW
If I were to say for instance that a gate could work if it orbited the Sun at a distance like that of earth, which is 1 AU (only an example) is there a simplified ratio that the Field Equations can be roughly equal to for at least 2 or 3 digit accuracy to be able to say another star of so many solar masses would equal some minimum distance away then for a gate at that star?
I do know that it is simpler for calculations outside of a massive object rather than inside, but it is still too complicated for this Sci-Fi writer. I hope that some rough proportion can be used for distances several times the radius of the sun, again only 2 or 3 digits at least, but if 4 or more, fantastic! The story is NOT a dry textbook to be checked for accuracy, but I do not want to write in things that to someone knowledgeable would laugh at as clearly off.
Thank you very much for any help provided.

For this level of question, other than that you are proposing a wormhole, the rest of your question is just about strength of gravity = curvature in Newtonian sense. In which case, you have an inverse square law, just like your light example. The same reasoning would apply for the ballpark level you seek.

You might want to ask questions like this also in the Science Fiction writing subforum of Science Fiction and Fantasy, under PF lounge.

Oh, Welcome to Physics Forums!

 

[Ring Gate]

Why thank you very much PAllen! I hoped it might have been that simple or maybe some square to cube ratio like orbital periods. Excellent, and thank you for mentioning the subforum too. I was unaware of it.

Thanks again!

 

[elfmotat]

As long as nothing's moving near the speed of light (and you're not near anything like a black hole or a neutron star), Newton's law for gravitation will suffice. So if you have a star which is four times as massive as another, the gravitational fields are equivalent when you're twice as far away from the larger star.

 

[pervect]

One could also make a case for "space warping" being tidal forces. In which case they'd fall off faster - M/r^3 But you can make up pretty much anything you want -- As far as I know, GR wormholes don't really mind being in curved space-time.Which leads to some interesting features, which you may or may not want to know about. I'd suggest reading Cramer's SF column on wormholes from Analog just for background.

http://www.npl.washington.edu/av/altvw33.html

is one, there are more

 

[Czcibor]

Ring Gate:

Technical question - how do your gates move in relation to the rest of universe? Do they orbit their stars? Or luckily just float nearby, untouched by any gravity, so for most of their time they should are in empty space, far from stars? (just curious)