The appearance of theqg:0d +wd.0 uaogwa+ mxbe8d0 great range of brightness among stars is due to

  The absolute luminosity for most stars depwj 9(nb*k p*g7 epvt:gt,c,q9l5*rbaori uj. ends on the

  Four different main-sequence stars are col t(. ;dwo(ksyhored blue, orange, red, and yellow. What is theik(oy.(t hw;ds r rank from coolest to hottest?

  A Hertzsprung-Russell diagram shows sh o7 w:p y1-:r(oqvekvtars on a plot of

  A white dwarf star with f(j,pp*7d j eqql(j+ ua mass equal to that of the Sun is about the size of

  The Chandrasekhar limit -:tq--kmmz r*v .rxi cof stellar mass (below which a star will collapse into a white dwarf) is, if the mass of our Sun is M, aboutm . :ivczt*k --qxrrm-

  Supernovas are thought to always result aiau pe:v.0pley2, gkwy/a :2 in

  Black holes

  Pulsars are rapidly spiqkhh6*. k/js5 .q ue xlbee.f1nning

State Einstein's principle of equivalence2n5ri/ m8y462; l kkgkgaeb tr.

  The Schwarzschild radius of a black hole is that radial distance from)nliw c/2u/ kub4lm,i the center of a sphere within which not even light can escape. It was )2kw//bn4muci l lu,ifirst discovered mathematically by Schwarzschild in 1916 after Einstein published his general relativity theory. It can be calculated from a star's mass M as: $R = 2GM/c^2$. Take the radius of both stars A and B as the Schwarzschild radius. If the mass of star A is twice as much as the mass of star B, the average density of star A, compared to star B will be

  When a distant source emits light of a particur(fv8 2 )cvvjalar wavelength in the visible, and the source is moving awaac(8v jv)rvf2y from us, the color of the light appears to us to be shifted toward the

  The cosmic backgroune)cb:e44ptthgh 2n8l d radiation corresponds to a temperature of about

  The Sun has apparent brighx. ,2cj a7jz/02-iagzcaiwgatness at Earth ($1.5 \times 10^{8} \; km$ away) of B. What would be the apparent brightness of the Sun at Pluto, which is $6.0 \times 10^{9} \; km$ from the Sun?

  A star has absolute luminosity equal to that of the ly hr)yf2h5*j Sun ($1.5 \times 10^{8} \; km$ from the Earth) but is 10 pc away from the Earth. By what factor will it appear dimmer than the Sun?

  The Earth's orbit has a:yffc 8j),mcont: wr- mean radius of $1.5 \times 10^{8} \; km$. Over a six-month period, the apparent position of a particular star varies by $0.00014^{\circ}$ due to parallax. How distant is the star, in km?

  The Earth's orbit has a mjusq t,:nd:f0 2 l,resean radius of $1.5 \times 10^{8} \; km$. Over a six-month period, the apparent position of a particular star varies by $0.00014^{\circ}$ due to parallax. How distant is the star, in ly? (1 ly = $9.46 \times 10^{15} \; m$)

  What is the parallax angle for Proxima Centauridbff5ehq7. ba,ag a :dm.m+uh.w9uf2 , which is Earth's nearest star at 5bmeau.mh7+ 2f.qgb9d:h aaf., duf w4.3 ly?

  The apparent brightness of ly:mqa731w csa star is $1.0 \times 10^{-12} \; W/m^{2}$ and the peak wavelength is 600 nm. Estimate its distance from us.

  It can be shown that the approximate age of the universe is 1/H, whereri-3 vbvnu:mq;rs u5q;vmb 71i,zw+ p H is the Hubble constant. Taking H = 20 km/s/Mly, estimate the agnqwm ;pvq7:vmri z ;,rib+u - 3b1suv5e of the universe, in years.

  If a galaxy is moving away from us at 1.0% of thegmmk85if6ij . speed of light, how far away is it from u8m6 im.5j kfigs?

  Estimate the speed of a pjva +)rc s8.hc;dx2vgalaxy that is 10 billion light-years away.

  Estimate the observed wavelength for the 656 nm line 8sj 0 asxn 6fuvm )r:nk)7/kfbin the spectrum of a star which is 100 million light-years frou87nvmf) rxa)jbk:ssn k/0f6 m us.

  About 1 ms after the Big Bang, the temperature of the universe was abod4,u0ur r0q zout 1013 K. W4rrqz od u,u00hat energy (in eV) does this correspond to?