Quote:
Originally Posted by Werner
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.

n.b. Only applies if the body is solid and (for hollow bodies) is small enough for Rsquared 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.