Question

In this question, you’re asked to estimate the pressure inside a white dwarf by integrating the hydrostatic equilibrium equation. For simplicity, assume constant density and spherical symmetry, so that = 4π3rho/3 and rho= 3/4π3. Derive the analytical solution for pressure at a radius of r for a white dwarf with a mass of M and a radius of R. By setting r = 0, we get the central pressure Pc. Write down the analytical solution for the central pressure as well.

Answer 1

The acceleration of gravity at the surface of a white dwarf with given mass and radius can be found using the formula g = GM/R^2.

Step-by-step explanation:

We are given the mass (M) of the white dwarf as 2 × 1030 kg and the radius (R) as 6.4 × 106 m. To find the acceleration of gravity at the surface of the white dwarf, we can use the formula for gravitational acceleration: g = GM/R2, where G is the gravitational constant.

Substituting the given values, we have g = (6.67430×10-11 m3 kg-1 s-2) × (2 × 1030 kg) / (6.4 × 106 m)2.

The acceleration of gravity at the surface of the white dwarf is 1.93 × 105 m/s2.