1) A given object will form a black hole if its radius is less than its
Schwarzshild radius. This leads to a very peculiar feature of black holes
the more massive they are, the less dense the material that forms them
needs to be. Remember that density is
1) Suppose a malevolent intelligence is trying to deceive us into thinking that a
binary system of the kind described last week exists, when in fact that isnt
the case. Suppose this evil being lives on a neutron star that is not part of
a binary system, a
1) How big a shift in the wavelength of green light will this
instrument be able to detect?
7
We know (from class) that the wavelength of green light is 5000 A (= 5 10
m).
So, if the Doppler precision of the Rocky Planet Finder is 1 m/s, that means we
nee
1) There is a relativistic
expression for the addition of
velocities (that is, for the total
observed velocity vtot of
something that moves at
velocit
y
v1
with
respect
to
another object that itself
moves at velocity v2 with
respect to the observer).
This
1) Read the homework policy (linked from the syllabus). Then answer
the following true/false questions:
a) You can drop your lowest homework score.
False
b) You can work on homework with other students, provided you split
up before you write down your ans
1) Suppose you observe a Sun-like star with a planet in an Earth-like
orbit. How massive does the planet have to be for it to be detected by the
Rocky Planet Finder?
Earth-like orbit:
a = 1AU
a3 = P 2 M
The period is then:
P = (A3/M )1/2
[yr]
P = (1AU )3/
1) Consider a binary star system consisting of two 1.5M
8
neutron
stars. Sup- pose one of the neutron stars is a pulsar with an
average observed pulse period of exactly 2 seconds. If the
orbit is circular and edge-on to our line of sight, what is the
maxi
1) The formula for the relativistic Doppler shift is
/
/0 =
1 + vR
/c 1
vR/c
1/2
1.
Show that the post-Newtonian approximation reproduces the result we
used before, namely that /0 = vR/c. What happens when vR approaches
+c or c? Does this result make se
1) a) Faint brown-dwarf stars have absolute magnitudes of around
17.5. How many times fainter than the Sun are these stars?
MBD = 17.5
Msun = 5
log
17.5 5 =
b1
5
12.52
5
b1
b2
5 = log b1
105 = b1
So brown dwarfs are 105 fainter than the sun.
b) If one obs
1) a) Suppose the entire diff
between Hubbles measurement of the
Hubble constant and the currently known value of 70 km/s/Mpc was
due to observing the wrong kind of Cepheid. What is the diff
in
absolute magnitude between the two types of Cepheids? That is