Thread: Birch World
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Old April 8th, 2021, 05:56 PM
Werner Werner is offline
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Originally Posted by BackworldTraveller View Post
n.b. Only applies if the body is solid and (for hollow bodies) is small enough for R-squared not to be significant.
Birch is neither solid nor small

Take a planet the mass of earth...1G
Take two planets each half the mass of earth and separate them by 1 diameter...No longer 1G at any point on either surface.
Solid is a relative term, a white dwarf is much more solid than the Earth.
A typical white dwarf has the mass of our Sun and the radius of Earth. Since our Sun has 333,000 times as much mass as the Earth, its surface gravity will be 333,000g in direct proportion to its mass, and it will also be 333,000 times as dense as the Earth. The Earth and this hypothetical white dwarf both have the same radius, 6400 km. Now let's say we wanted to blow up this white dwarf to a large enough size so that it has 1g on its surface. The radius of the new object is the square root of its mass multiplied by an Earth radius 6400 km. The new radius is 3,693,194 km. The surface area is 333,000 times that of Earth, it's volume is 192,161,487 times that of Earth. We can find its density relative to Earth by 333,000/192,161,487=0.0017 times that of Earth, if the mass is uniformly distributed under its shell, meaning that every square kilometer has the same amount of mass under it, it doesn't matter whether its hollow or filled with a diffuse gas, it will still be 1g on its surface, if more mass is packed towards one side of the sphere, obviously the uniform gravity won't hold. One can have an expanding sphere and so long at added mass distributed uniformly equal the increasing surface area, the gravity will remain the same.
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