Thread: Birch World
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Old April 7th, 2021, 06:00 AM
Werner Werner is offline
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Originally Posted by aramis View Post
if the area is sufficiently deep as to have significant dilation, it's sufficiently deep that people will be turned to jam.

The difference between 0.9G and 1G is measured in centiseconds per year. And a year is roughly 31536000 seconds.

To have livable for humans, the G's can't exceed 2 by much... and that's still only going to be no more than single digit seconds per year.

you're not going to get humans surviving significant gravitational dilation without having significant centrifugal pseudo-force... but that's got other issues, as well, since the gravitational gradient over 2m with significant time dilation is going to be enough that your speed won't save you from spaghettification.
Here are two real world examples. Earth and Saturn, surprisingly, Saturn has 95 times the mass of Earth, but at its "surface" the gravity is the same as Earth, although its escape velocity is much higher. If you continue increasing the radius of a sphere by the square root of its mass as its mass increases, then its surface gravity will remain the same as its escape velocity continues to increase. In order to do this, the density of the object must decrease, if you continue this trend until the radius equals 0.48 of a light year, that is a birch world, at that point the escape velocity approaches the speed of light, it is the largest possible World you can build that is held together by it's own gravity.

Gravity obeys the inverse square law with distance, and it also increases proportional to mass so is you have a planet with 1 Earth mass and 1 Earth radius you will get 1 Earth gravity on its surface. If you double the radius but keep the mass the same the gravity on its surface will be 1/4 g, and if you quadruple its mass within that same volume you are back to having 1g on its surface. Now normally if you double a planet's radius while keeping the density the same the mass is proportional to the planet's volume so you would octuplets the planets mass, but since you are only quadrupling it, the density of the planet has to be halved each time your double the planet's radius to keep the surface gravity at 1g.

Last edited by Werner; April 7th, 2021 at 09:55 AM..
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