Exam 33: Astrophysics and Cosmology

Suppose a 70-kg student were to be compressed to form a black hole. What would be the Schwarzschild radius of this black hole? (G = 6.67 × 10-11 N · m2/kg2, c = 3.0 × 108 m/s)

To what radius would the sun have to be compressed in order for it to become a black hole? The mass of the sun is $1.99 \times 10 ^ { 30 } \mathrm {~kg} , G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 }$ , and $c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$

In terms of the mass M of our sun, what is the Chandrasekhar limit of stellar mass, below which a star will eventually collapse into a white dwarf?

When a distant source emits light of a particular wavelength in the visible, and the source is moving away from us, the color of the light appears to us to be shifted toward the

Four different main-sequence stars are colored blue, orange, red, and yellow. What is their rank from coolest to hottest?

The cosmic background radiation corresponds to a temperature of about

Estimate the observed wavelength for the $656 \mathrm {~nm}$ line in the spectrum of a star which is 100 million light-years from us if $H = 20 \frac { \mathrm { km } / \mathrm { s } } { \mathrm { Mly } }$ ? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

About $1 \mu \mathrm { s }$ after the Big Bang, the temperature of the universe was about $10 ^ { 13 } \mathrm {~K}$ . What particle kinetic energy (in $\mathrm { eV } )$ does this correspond to? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , k = 1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } \right)$

The earth's orbit has a mean radius of $1.5 \times 10 ^ { 8 } \mathrm {~km}$ . Over a six-month period, the apparent position of a particular star varies by $0.00014 ^ { \circ }$ due to parallax. How many light-years is this star from Earth? (1 ly $= 9.46 \times 10 ^ { 15 } \mathrm {~m}$ )

A Hertzsprung-Russell diagram shows stars on a plot of

Estimate the speed of recession of a galaxy that is 10 billion light-years away if $H = 20 \frac { \mathrm { km } / \mathrm { s } } { \mathrm { Mly } }$ ? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

A star has absolute luminosity equal to that of the sun but is 10 pc away from the Earth. By what factor will it appear dimmer than the sun? The earth is $1.5 \times 10 ^ { 8 } \mathrm {~km}$ from the sun, and 1 parsec is equal to $3.09 \times 10 ^ { 16 } \mathrm {~m}$ .

It can be shown that the approximate age of the universe is $1 / H$ , where $H$ is the Hubble constant Taking $H = 20 \frac { \mathrm { km } / \mathrm { s } } { \mathrm { Mly } }$ , estimate the age of the universe, in years. (1 ly $\left. = 9.46 \times 10^{15} \mathrm {~m} \right)$

Many supernovas are thought to result in

What is the parallax angle for Proxima Centauri, which is Earth's nearest star at $4.3$ ly? The earth's orbit has a mean radius of $1.5 \times 10 ^ { 8 } \mathrm {~km}$ , and $1 \mathrm { ly } = 9.46 \times 10 ^ { 15 } \mathrm {~m}$ .

Pulsars are rapidly spinning

The earth's orbit has a mean radius of $1.5 \times 10 ^ { 8 } \mathrm {~km}$ . Over a six-month period, the apparent position of a particular star varies by $0.00014 ^ { \circ }$ due to parallax. How many kilometers is this star from Earth?

What mass would have to be compressed to a radius of $1.0 \times 10 ^ { - 15 } \mathrm {~m}$ (the order of magnitude of the radius of an atomic nucleus) in order for it to become a black hole? ( $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N}$ . $\mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } , c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ )

Black holes

The appearance of the great range of brightness among stars is due to