34.1 Cosmology and Particle Physics

Find the approximate mass of the luminous matter in the Milky Way galaxy, given it has approximately $\text{10}^{\text{11}}$ stars of average mass 1.5 times that of our Sun.

(a) Estimate the mass of the luminous matter in the known universe, given there are $\text{10}^{\text{11}}$ galaxies, each containing $\text{10}^{\text{11}}$ stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mass? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then…

On average, how far away are galaxies that are moving away from us at 2.0% of the speed of light?

(a) What is the approximate speed relative to us of a galaxy near the edge of the known universe, some 10 Gly away? (b) What fraction of the speed of light is this? Note that we have observed galaxies moving away from us at greater than $0 . 9 c$.

Assuming a circular orbit for the Sun about the center of the Milky Way galaxy, calculate its orbital speed using the following information: The mass of the galaxy is equivalent to a single mass $1 . 5 \times \text{10}^{\text{11}}$ times that of the Sun (or $3 \times \text{10}^{\text{41}} \text{kg}$), located 30,000 ly away.

Andromeda galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity $\text{10}^{\text{12}}$ times that of the Sun and lies 2 Mly away.

The average particle energy needed to observe unification of forces is estimated to be $\text{10}^{\text{19}} \text{GeV}$. (a) What is the rest mass in kilograms of a particle that has a rest mass of $\text{10}^{\text{19}} \text{GeV}/ c^{2}$? (b) How many times the mass of a hydrogen atom is this?

(a) What Hubble constant corresponds to an approximate age of the universe of $\text{10}^{\text{10}}$ y? To get an approximate value, assume the expansion rate is constant and calculate the speed at which two galaxies must move apart to be separated by 1 Mly (present average galactic separation) in a time of $\text{10}^{\text{10}}$ y. (b) Similarly, what Hubble constant corresponds to a universe approximately $2 \times \text{10}^{\text{10}}$-y old?

The core of a star collapses during a supernova, forming a neutron star. Angular momentum of the core is conserved, and so the neutron star spins rapidly. If the initial core radius is $5 . 0 \times \text{10}^{5} \text{ km}$ and it collapses to 10.0 km, find the neutron star’s angular velocity in revolutions per second, given the core’s angular velocity was originally 1 revolution per 30.0 days.

Distances to the nearest stars (up to 500 ly away) can be measured by a technique called parallax, as shown in the figure. What are the angles $\theta_{1}$ and $\theta_{2}$ relative to the plane of the Earth’s orbit for a star 4.0 ly directly above the Sun?