Question
In: Physics
An exoplanet is discovered through careful Doppler shift analysis of the spectrum of the star it...
An exoplanet is discovered through careful Doppler shift analysis of the spectrum of the star it is orbiting. The star’s spectrum allows us to conclude with some confidence that the star has a mass M = 0.60 solar masses, and a luminosity L = 0.13 of the solar luminosity. Assuming the orbits are circular and observed edge-on, the Doppler shift tells us that the star has a speed about the centre-of-mass of V = 250 m/s and the period of the orbit is 0.35 years.
(a) What is the semimajor axis of the planet’s orbit in AU? [ It is reasonable to assume that the planet’s mass is much less than that of the star.]
(b) What is the planet’s circular speed in km/s? [In the units we use for the solar system GM = 900 (km/s)2-AU but this will have to be modified to 540 for this star.]
(c) What is the ratio of the star’s mass to that of the planet?
(d) Estimate the planet’s surface temperature, assuming that its black-body emission balances the energy it receives from the star. Take the albedo to be 0.50 and assume no greenhouse gases. Note that the star’s luminosity is 0.13 times that of the Sun.
Solutions
genius_generous answered 2 years agoRelated Solutions
An exoplanet is discovered through careful Doppler shift analysis of the spectrum of the star it...
An exoplanet is discovered through careful Doppler shift
analysis of the spectrum of the star it is orbiting. The
star’s spectrum allows us to conclude with some confidence that the
star has a mass M = 0.60 solar masses, and a luminosity L = 0.13 of
the solar luminosity. Assuming the orbits are circular and observed
edge-on, the Doppler shift tells us that the star has a
speed about the centre-of-mass of V = 250 m/s and the period of...
Imagine two planets orbiting a star with orbits edge-on to the Earth. The peak Doppler shift...
Imagine two planets orbiting a star with orbits edge-on to the
Earth. The peak Doppler shift for each 75 m/s, but one has a period
of 7 days and the other has a period of 700 days. The star has a
mass of one solar mass. Assume 1 solar mass equals 2∗10^30.
1.) Calculate the mass of the shorter period planet.
(Hint: See Mathematical Insight Finding Masses of
Extrasolar Planets)
2.) Calculate the mass of the longer period planet.
To understand the terms in the Doppler shift formula. The Doppler shift formula gives the frequency...
To understand the terms in the Doppler shift formula.
The Doppler shift formula gives the frequency fL
f
L
at which a listener L hears the sound emitted by a source S at
frequency fS
f
S
:
fL=fSv+vLv+vS
f
L
=
f
S
v
+
v
L
v
+
v
S
,
where v
v
is the speed of sound in the medium, vL
v
L
is the velocity of the listener, and vS
v
S
is the velocity...
Blackbody Spectrum Question (a) Examination of the spectrum of a star shows that it is brightest...
Blackbody Spectrum Question
(a) Examination of the spectrum of a star shows
that it is brightest at the frequency 1.5 × 10^14 Hz. What is its
temperature? How does this compare to the Sun’s temperature? What
color will this star appear to be?
(b) How does the surface brightness of this
star compare with Sun’s surface brightness, according to the
Stefan-Boltzmann law?
(c) Somewhat surprisingly, the star in question
appears extremely bright, much brighter than the Sun would appear
at...
You have $5,000 to invest. After a careful fundamental analysis, you have discovered an undervalued stock,...
You have $5,000 to invest. After a careful fundamental analysis,
you have discovered an undervalued stock, which is currently
selling at $50 per share. The possible cash
investment strategies for you are either to buy the stock or buy
the stock call option selling at $5 per share (that is, the option
premium or cost) in an option contract with a strike price of $52
per share. Compare these two strategies in terms of % rate of
return under these...
Predict and interpret the effects of Doppler shift Relate the three types of spectra to the...
Predict and interpret the effects of Doppler
shift
Relate the three types of spectra to the physical
situations that form them
Relate spectral lines and atomic structure
Relate stellar properties and the OBAFGKM classification
system.
Identify the major steps of stellar evolution in name and
on the HR diagram.
Predict the ages of stellar clusters based on their
color-magnitude diagrams.
Relate supernovae and compact objects to the stars that
produce them.
Predict how light moves near massive objects.
Explain how...
The Doppler effect - the shift in frequency/wavelength of a sound source when there is relative...
The Doppler effect - the shift in frequency/wavelength of a
sound source when there is relative motion between source &
observer - and a Sonic Boom - a conical region of compression that
forms around the sound source when its speed exceeds the speed of
sound in the medium of the source, and results in an observed
"boom" when part of the cone passes the observer's location - are
two interesting, common, as well as connected phenomena seen this
week....
calculate the doppler shift in the frequency of photon traveling along y axis with respect to...
calculate the doppler shift in the frequency of photon
traveling along y axis with respect to moving observer along x axis
with velocity v ,explain brielfy how does doppler effect of light
in relativistic approach differ from non relativistic approach
.
Why does the Doppler effect lead to a shift in the atomic emission frequencies of hydrogen...
Why does the Doppler effect lead to a shift in the atomic
emission frequencies of hydrogen atoms in a star but a broadening
of the atomic emission frequencies of hydrogen atoms in a gas?
We can easily hear the Doppler shift of a car passing by but we do not...
We
can easily hear the Doppler shift of a car passing by but we do not
notice the Doppler shift of light from its headlamps. Why is
that?
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