|
92. Problem 16.30 (RHK) It is conjectured that a “burned-out” star could collapse to
a “gravitational radius”, defined as the radius for which the work needed to
remove an object of mass m from the star’s surface to infinity equals the rest
energy mc2 of the object. We have to show that the gravitational radius of
the Sun is
|
and
determine its value in terms of the Sun’s present radius.|
Solution: Click For PDF Version Let us consider an object of mass M and surface radius R. Work required to remove an object of mass m from the surface of the object of mass M to infinity is the negative of the potential energy of the m-M system. It is
Gravitational radius of an object of mass M is the radius
We calculate next the gravitational radius of the Sun.
We use this data and find that the gravitational radius of the Sun is
According to the Einstein’s theory of gravitation the correct value of
|
which is such as would require energy
for an
object of mass m to escape to infinity. That is
and is
called the Schwarzschild radius.