Calculate the average density in kilograms [kg] per cubic meter [m3] for a White Dwarf with a mass of

1 solar mass and the size of planet Earth. Be sure to use the correct units. (b) Calculate your own weight on the surface of the white dwarf star.

(a) 2 * 10^9 kg/m^3; (b) roughly the mass of the Statue of Liberty.

Step-by-step explanation:

(a) Density of white dwarf:

D = m/V

dа ta:

1 solar mass = 2 * 10^30 kg

1 Earth radius = 6.371 * 10^6 m

Calculations:

V = (4/3) πr^3 = (4/3) π * (6.371 * 10^6 m) ^3 = 1.083 * 10^21 m^3

D = 2 * 10^30 kg/1.083 * 10^21 m^3 = 2 * 10^9 kg/m^3

2. Weight on a white dwarf

The formula for weight is

w = kMm/r^2

where

k = a proportionality constant

M = mass of planet

m = your mass

w (on dwarf) / w (on Earth) = [kM (dwarf) m/r^2] / [kM (Earth) m/r^2

k, m, and r are the same on both planets, so

w (on dwarf) / w (on Earth) = M (dwarf) / M (Earth)

w (on dwarf) = w (on Earth) * [M (dwarf) / M (Earth) ]

dа ta:

M (Earth) = 6.0 * 10^24 kg

Calculation:

w (on dwarf) = w (on Earth) * (2 * 10^30 kg / 6.0 * 10^24 kg)

= 3.3 * 10^5 * w (on Earth)

Thus, if your weight on Earth is 60 kg, your weight on the white dwarf will be

3.3 * 10^5 * 60 kg = 2 * 10^7 kg

That's roughly as heavy as the Statue of Liberty is on Earth.