Download ASTR 2020 Space Astronomy Homework #3 Due Tuesday, 4

ASTR 2020 Space Astronomy
Homework #3
Due Tuesday, 4 October, in class
1] Dwarf planets vs. terrestrial planets or gas giants. Give three reasons why it was appropriate
to re-classify Pluto as a “dwarf planet” in 2006 by the International Astronomical Union.
2] Black holes: Black holes are objects containing sufficient mass in a small enough region so
that the escape-speed is the speed of light, Vesc = c = (2 GM / r )1/2. Solving this for r gives the
so-called Schwarzchild radius of a black hole, rS = 2 GM / c2 , effectively the radius of the
surface from which the escape-speed is the speed of light.
[a] Consider the Sun with a mass Mo = 2 x 1033 grams. If the sun collapsed into a black hole,
what would be its Schwarzschild radius? Please give you answer in cm and in km.
[b] Consider an asteroid with a mass Ma = 1015 grams. Assuming it has a density of 1 g cm-3,
what is its radius?
[c] If this asteroid were to become a black hole, what would be its radius? How does this
compare to the radius of a proton or neutron?
[d] If the mass of the asteroid were to fill a sphere with the radius you estimated in part [c], what
would be its density?
[e] The Milky Way galaxy has a mass of about Mg = 5 x1011 times the mass of the Sun (this
mass estimate includes both baryonic and dark matter content of our Galaxy). What would be the
radius of a black hole containing the mass of the Milky Way?
[f] Consider the entire Universe, made up of roughly 1011 galaxies. How large a black hole
would the Universe make?
[g] How does this compare to the Hubble radius of the Universe? The Hubble radius is given by
the product of the age of the Universe times the speed of light, RU = ctU where tU is the current
age of the Universe, tU = 13.7 billion years (=13.7 x 109 years). Note that if you re-write the
Hubble constant H = 71 km s-1 Mpc-1 in purely c.g.s units, H = 2.3 x 10-18 s-1. Thus, 1 / H = tU
in seconds.
3] Parallax. As we discussed in class, the unit called a parsec is defined as the distance at which
the Earth-Sun mean separation (the Astronomical Unit), subtends 1 arc-second (assuming that
the Earth-Sun separation is at right angles to the line connecting the Sun to the distant object).
[a] How large is a parsec in centimeters? (Don’t just look it up ….Please show a diagram with
the various parts of the geometry labeled).
[b] The parallax-angle of a star is 1 milli-arc-second. How far is the star in parsecs and in cm?
[4] Astronomy missions. Please give a few sentence description of the following spacecraft
whose missions were primarily astronomical. What was the wavelength range? List one of two
major discoveries made by each mission and give the year of launch, and approximate duration of
operations.
[a] Copernicus:
[b] IUE:
[c] Uhuru:
[d] Chandra:
[e] Hubble:
[f] Spitzer:
[g] IRAS:
[h] COBE:
[i] Planck:
[j] Herschel:
[k] GRO:
[j] Fermi:
[k] ISO: