Re: 130: deep jumps vs. white dwarves
Posted: Sat Jun 09, 2018 9:47 am
I wrote a whole nice thing about the misconceptions and confusion in this thread, but it was eaten by the auto log-off.
So I'm going to do this again a whole lot less fancy and talky-like because my brain hurts now.
See the above picture? Same mass, different radius. We don't care what goes on 'inside' the radius because if you're there you are dead - inside a star, or inside a black hole, or inside a rock. Or about to be.
Note that both possess different gravitational values at their 'surfaces' (r=1's surface was cut off when i made the image - but it's down there) - like how white dwarves have greater surface gravity than equivalent red dwarves, and differently sized black holes have different tidal forces at the event horizon.
Now note that both possess the same curve, except where the radius intersects the gravitational curve. From this we can deduce that it is mass, not size, that will be the largest determinate of how an object defines the jump-routes leading to it. And the only determinate of the precise shape of the gravity well in places outside the radius.
Except size does matter - sufficiently large objects have less 'room' for travelers to land when they jump, compared to smaller objects of the same mass. Deep jumps may or may not be easier - but there is less room for defenders to be uncertain about.
Caveat for my model and math: I looked at the masses as point masses - looking at them as proper 3d masses may result in changes for especially large AND heavy objects.
Finally: For gravity wells which are small and heavy to not follow this, generally, the gravitational constant must change as a function of something.
While the system's white dwarf may appear to have a 'narrow but deep' gravity well, it is actually just a regular gravity well for its mass, but with lots and lots of 'free space' to 'land' in. As an aside - I'm surprised we don't see any Umiak vessels in the space between the deep jump and regular jump groups - some ships coming up short wouldn't have been a surprise.
My math, done on Desmos:
I apologize for the use of constants like that. The gravitational constant was omitted/rolled into m2 for ease on my eyes.
So I'm going to do this again a whole lot less fancy and talky-like because my brain hurts now.
See the above picture? Same mass, different radius. We don't care what goes on 'inside' the radius because if you're there you are dead - inside a star, or inside a black hole, or inside a rock. Or about to be.
Note that both possess different gravitational values at their 'surfaces' (r=1's surface was cut off when i made the image - but it's down there) - like how white dwarves have greater surface gravity than equivalent red dwarves, and differently sized black holes have different tidal forces at the event horizon.
Now note that both possess the same curve, except where the radius intersects the gravitational curve. From this we can deduce that it is mass, not size, that will be the largest determinate of how an object defines the jump-routes leading to it. And the only determinate of the precise shape of the gravity well in places outside the radius.
Except size does matter - sufficiently large objects have less 'room' for travelers to land when they jump, compared to smaller objects of the same mass. Deep jumps may or may not be easier - but there is less room for defenders to be uncertain about.
Caveat for my model and math: I looked at the masses as point masses - looking at them as proper 3d masses may result in changes for especially large AND heavy objects.
Finally: For gravity wells which are small and heavy to not follow this, generally, the gravitational constant must change as a function of something.
While the system's white dwarf may appear to have a 'narrow but deep' gravity well, it is actually just a regular gravity well for its mass, but with lots and lots of 'free space' to 'land' in. As an aside - I'm surprised we don't see any Umiak vessels in the space between the deep jump and regular jump groups - some ships coming up short wouldn't have been a surprise.
My math, done on Desmos:
I apologize for the use of constants like that. The gravitational constant was omitted/rolled into m2 for ease on my eyes.