Question

10. At the end of the Sun’s life it will use up the hydrogen and helium in its core and become a white dwarf. The Sun’s mass is 2.0 × 1030 kg, its radius is 7.0 × 105 km, and it has a rotational period of approximately 28 days. If the Sun should collapse into a white dwarf of radius 3.5 × 103 km, what would its period be if no mass were ejected and a sphere of uniform density can model the Sun both before and after?

11. Much more massive stars than the Sun will collapse into much smaller objects known as neutron stars after exploding . If a star 15 times more massive than the Sun with 8 times the radius had the same initial rotation rate and collapsed into a neutron star with a radius of 15 km, what would its period be if 90% of its mass were ejected taking 90% of its angular momentum. Assume a sphere of uniform density can model the star both before and after?

Answer 1

10) I = 2mR?, L-IW , 6-2 M= 2.0 x1030kg , R, = 7.0X105 km : R2 = 3.5x105 km , T, = 28 days - L=Lz (Conservation of Angular Momen I, w, = Iz CO2 > (3 M}(25) = (3 MB3%CE T = T (B) = 28 days X-SX0 km)? 1 T2 = 7 days) 11) m = 15m, R=8R, M₂ = 10 x 15m= 1.5m R₂ = 15 km, Ti = 28 days = 2419200 s also L2 = 10% of Li (90% of monentum taken 22 = 0.16 0.1L, = 22 Ool I, co, = I2 CO₂ I aix 2 x 15m x R x 27 = 2 x 15 MX R2 x 25 100 away) Rx = 8xR = 8x 7.0X105km = 56.0x10km *3 = 29192008 (sekin ton)= 11-786X0S