Repost from the previous forums. Here is my best guess at specifics of how hyperspace works with pictures. As far as I know it is still constant with all information provided by Arioch.
On massive wall of text coming up.
If you map our 3+1 dimensional (3 space and 1 time dimension) universe into a 2+1 dimensional membrane in a 3+1 dimensional external space where mass deforms the membrane to create a slope in external spaces 3rd dimension. For future reference the 2 dimensional membrane will be referred to as the ground brane and the external space will be referred to as the space.
Now take a 2 dimensional cross section of the space where x-axis is passes through the target and starting stars and the space's 3rd dimension is the y axis. In the cross-section the ground brane will form a curve leading from the source gravity well to the destination gravity well.
In this figure shows the approximate space time curvature of the solar system ranging from 1 au to 30 au (Earth to Neptune orbits) and neglecting the contribution of any planets.
When the ftl drive in engaged, the mass within its sphere of influence is unstuck from the ground brane (the mass is no longer constrained to remain embedded in the ground brane) and proceeds on a velocity vector that is tangent to the slope of ground brane deformation. This mass is now referred to at the transiting mass. This is shown it the following figure.
While in the external space the transiting mass is affected by gravitational forces as usual (there is an acceleration vector pointing from the transiting mass's position to all other masses embedded in the ground brane). This has the effect of creating a net force pulling the transiting mass back towards the the ground brane.
To re-embed itself back into the ground brane 2 conditions must be met.
- First the transiting mass must be coincident with the ground brane within a tolerance.
- Second the slope of the transiting mass's velocity vector must be within the a certain tolerance of the slope of the ground brane's deformation.
This is illustrated in the following figure.
In a the event of a velocity undershoot or a velocity overshoot you are most likely to re-embed inside of a star. The following figure shows why this is (In this graph I simplified by assuming that the star has a uniform density).
As you can see the gravity gradient reverses and eventually zeros out a the center of the of the star. Given that while jumping course correction is impossible. Therefor entering a stable orbit while possible is extremely unlikely. The most likely outcome is that the transiting mass will come to rest in the center of the star. At which point both re-embedding conditions will be met and the transiting mass will re-enter normal space in the center of the star.
--Aygar