Astrophysicists in the 1960s tried to explain the existence and thestructure of pulsars â extremely regular astronomical sources ofradio pulses whose periods ranged from seconds to milliseconds. Atone point, these radio sources were given the acronym LGM, standingfor âLittle Green Men,â a reference to the idea that they might besignals of extraterrestrial civilizations. The explanation giventoday is no less interesting. Consider the following. Our Sun,which is a fairly typical star, has a mass of 1.99x10^30 kg and aradius of 6.69x10^8 m. Although it does not rotate uniformly,because it isnât a solid body, its average rate of rotation isabout 1 rev / 25 days. Stars larger than the sun can end theirlives in spectacular explosions called supernovae, leaving behindcollapsed remnants of the stars called neutron stars. Neutron starshave masses comparable to the original masses of the stars, butradii of only a few kilometers. These stars emit beams of radiowaves. Because of the rapid angular speed of the stars, the beamssweep past Earth at regular, very short, intervals. To produce theobserved radio-wave pulses, the star has to rotate at rates fromabout 1 rev/s to 1000 rev/s.
a. Estimate the rotation rate of the Sun if it were to collapseinto a neutron star of radius 10 km. The Sun is not a uniformsphere of gas, and its moment of inertia is given by I = 0.059MR2.Assume that the neutron star is spherical and has a uniform massdistribution.
b. Is the rotational kinetic energy of our Sun greater of smallerafter the collapse? By what factor does it change, and where doesthe energy go to or come from?
Astrophysicists in the 1960s tried to explain the existence and thestructure of pulsars â extremely regular astronomical sources ofradio pulses whose periods ranged from seconds to milliseconds. Atone point, these radio sources were given the acronym LGM, standingfor âLittle Green Men,â a reference to the idea that they might besignals of extraterrestrial civilizations. The explanation giventoday is no less interesting. Consider the following. Our Sun,which is a fairly typical star, has a mass of 1.99x10^30 kg and aradius of 6.69x10^8 m. Although it does not rotate uniformly,because it isnât a solid body, its average rate of rotation isabout 1 rev / 25 days. Stars larger than the sun can end theirlives in spectacular explosions called supernovae, leaving behindcollapsed remnants of the stars called neutron stars. Neutron starshave masses comparable to the original masses of the stars, butradii of only a few kilometers. These stars emit beams of radiowaves. Because of the rapid angular speed of the stars, the beamssweep past Earth at regular, very short, intervals. To produce theobserved radio-wave pulses, the star has to rotate at rates fromabout 1 rev/s to 1000 rev/s.
a. Estimate the rotation rate of the Sun if it were to collapseinto a neutron star of radius 10 km. The Sun is not a uniformsphere of gas, and its moment of inertia is given by I = 0.059MR2.Assume that the neutron star is spherical and has a uniform massdistribution.
b. Is the rotational kinetic energy of our Sun greater of smallerafter the collapse? By what factor does it change, and where doesthe energy go to or come from?
