## Gm

Another interesting effect comes from the fact that g changes very quickly with radius R. Differentiating the expression for g gives dg/dr = -2GM/R3

If we use the numbers in the above example, we find dg/dR = -1.1 X 108 (cm/s2)/cm. This is equal to a change of 105 times the acceleration of gravity on the Earth per centimeter. If you were floating near the surface, your feet would be pulled in with a much greater acceleration than your head. Your body would be pulled apart by these tidal forces. By tidal forces, we mean effects that depend on the difference between forces on opposite sides of an object. Some astrophysicists have jokingly noted that if an astronaut visits a neutron star, it should be in a prone position to minimize the tidal effects.

The large acceleration of gravity also has another interesting effect. The equation of hydrostatic equilibrium (equation 9.44) tells us that the rate at which the pressure in the atmosphere of a neutron star falls off, dP/dR, is proportional to g. The atmospheric pressure on a neutron star thus falls off very quickly. This leads to an atmosphere that is only about 1 cm thick. (The thin atmosphere is another reason for an astronaut to stay in a prone position.)

### 11.2.2 Rotation of neutron stars

In the process of the collapse of a core to become a neutron star, any original rotation of the core will be amplified. If the angular momentum of the core is conserved, the core must rotate faster as it becomes smaller. Since the core shrinks by a large amount, the rotation speed is increased by a large amount.

The angular momentum is given by

(1.5 X 106 cm)2 = 8.3 X 1013 cm/s2 This is almost 1011 times the acceleration of gravity J = (2/5)MR2w where I is the rotational inertia and a is the angular speed. If we put in the rotational inertia for a uniform sphere, we find

at the surface of the Earth! (With such strong gravitational fields, we should really use general relativity to calculate particle motions.) You can calculate your weight on the surface of a neutron star.

To get a feel for how fast a neutron star can rotate, let's assume that the angular momentum of a neutron star is equal to that of the Sun. (This is probably a conservative estimate since the Sun