P2 =[ 4 pi2 a3 ] / [
G(M1+M2) ]
Radius_black hole = 2 G M / c2
E=m c2
G=6.67 x 10-11 m3 / kg / s2
L_sun=3.9 x 1033 ergs/sec
1. Suppose you discover a binary star. The period of the binary is 20 days. The semi major axis of the binary is 0.2 AU.
a.) If one of the stars has the same mass as the sun, what is the mass of the companion in the binary?
Hint: Convert the period from days to seconds and the semi major axis to meters.
Then use Newton's version of Kepler's 3rd law to calculate the total mass
in the binary.
b.) If the companion is a black hole, what is the radius of the black hole?
2. Suppose an alien civilization decides to turn the sun into a black hole.
a.) What will the radius of the sun be when it becomes a black hole? (Show the calculation!)
b.) What will happen to the orbit of the Earth?
c.) What will happen to the climate of the Earth?
3. What are the three possible end points of stellar evolution (i.e. what do stars become when they die)?
Compare the radii, masses, and densities of different stellar remnants. (i.e. which has the smallest radius, what has the largest density, etc.)
4. The space between stars in not completely empty. Gas and dust exist in interstellar space. Name two specific types of interstellar material. Give some characteristics of each.
5. You're now familiar with Einstein's equation E=mc2 and how nuclear fusion at the center of a star converts matter into energy (which is why a star shines). Another example of converting matter into energy is when a black hole "consumes" matter. A black hole can be the end state of a star's life. A black hole can also exist on a much, much larger scale at the center of galaxies (you may have heard of "active" galaxies like "quasars"). A supermassive black hole is only about 10% efficient at converting mass into energy. In other words, for every 10 ergs of mass that falls into the black hole, only 1 erg of radiation is emitted by the black hole. (i.e. E_black hole = 0.10 m c2 )
a.)How much energy does a black hole emit that consumes one Earth mass every day?
Hint: For an answer in units of ergs, use:
M_Earth = 6 x 1027 g
c=3 x 1010 cm/s
b.) What is the average luminosity of radiation energy emitted by that supermassive black hole in ergs/second?
Hint: convert one day into number of seconds and divide energy calculated in part a) by number of seconds per day
c.) Convert this luminosity from units of ergs/second into units of the sun's luminosity.
Hint:Divide answer to part b) by L_sun.