A typical white dwarf has a radius of R = 10,000 km and mass comparable to the S

Question

A typical white dwarf has a radius of R = 10,000 km and mass comparable to the Sun (MSun = 2 x 1033 grams). Calculate the average density (density = Mass / Volume). Give your answer in grams per cubic centimeter. Recall that the volume of a sphere is Volume = (4/3) ? R3 .

Calculate the escape speed from the surface (Vesc = [2 GM / R]0.5). Give your answer in km/sec.

A typical neutron star has a mass of about 1.0 MSun and a radius of 10 kilometers. Calculate the average density (density = Mass / Volume). Give your answer in grams per cubic centimeter.

Explanation / Answer

apply the formula for density as D =   mass/Volume

Volume V = 4pi R^3/3

here R = 685800 + 10000 = 6.95 e 8 m

so

Density D = 3M/4pi R^3

D = 3 *1.99 e 30 /(4*3.14 * 6.95 e8 * 6.95 e8 * 6.95 e8)

D = 1.415 *10^3 Kg/m^3

--------------------

use the formula for escape speed Vesc^2 = 2GM/R

Vesc^2 = 2* 6.67 e -11 * 1.99 e 30/(6.95 e8)

Vesc^2 = 38.19 *10^10

Vesc = 6.17 e 5 m/s

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