Question 02/02
MAXIMAL GRAVITY
Consider a celestial body (planet) of mass M
and volume V consisting of material of uniform
density M/V. If the body is spherical, then its
radius is R=(3V/4{pi})1/3, and the free-fall
acceleration on its surface is
g=GM/R2=GM(4{pi}/3V)2/3,
where G is the gravitational constant. Consider all
possible shapes of the body. What is the largest g,
that can be achieved at one point on a surface, and what is
the shape of the body for which such acceleration is achieved?
Back to "front page"