Line Segments Oriented Radially Around A Center Point?

I'm attempting to play armchair starship designer, and I'm having trouble figuring out how to more quickly draw a LOT of small lines and orienting them so they "radiate" outward from a central point. Not actually coming from the point--they're farther out, but they're nodes/direction arrow in point-edit mode all point to that center. Hope I'm explaining this right. 

See photo below. I need to make the lines for the floor grates, but I don't want to have to make each one separately and orient it by hand--there's hundreds of them.

I thought I could use the two-color pattern fill method, but none of the single lines radiate out from the central point. I also thought there was a way to simply draw all the lines anchored to the center point, and then somehow grab the nodes in point-edit mode in the center and draw them out so that then center moved out, shrinking the length of the lines from the center out without actually moving the entire grouping instead? No joy.

Here, you see how the floor grates on either side of the corridor are supposed to look, circled in red.

And here, you see how I want them to orient. Note, I am using the scanned drawing I made on a locked layer to "trace" over. Is there a quicker way of accomplishing this?? Please help! This is the last piece I need to complete this.