Imagine you observe a Cepheid variable star with an apparent V-band magnitude of 18.0 in the direction of the Andromeda galaxy which is at a distance of d = 850 kpc from us. The period of the star is 8 days and you know that the period-luminosity relation is My = −2.81 log P – 1.43. Verify if the star belongs to the Andromeda galaxy or not.
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- If an X-ray binary consists of a 16 solar mass star and a neutron Star orbiting each other every 15.4 days, what is their average separation? (Hint: Use the version of Keller's third law for binary stars, Ma + Mb = a^3 /p^2 ; make sure you express quantities in unites of AU, solar masses, and years. Assume the mass of a neutron Star is 1.6 solar masses.) ___________ AUTwo stars-A and B, of luminosities 0.5 and 4.5 times the observed to have the luminosity of the Sun, respectively-are same apparent brightness. Which star is more distant, and how much farther away is it than the other?Problem Set on Binary Systems: 1.Consider two stars in orbit about a mutual center of mass. If a1 is the semimajor axis of the orbit of star of mass m, and a, is the semimajor axis of the orbit of star of mass m2, prove that the semimajor axis of the orbit of the reduced mass is given by a = a, + a2. points)
- Time left 1:45:56 A star has initially a radius of 680000000 m and a period of rotation about its axis of 33 days. Eventually it changes into a neutron star with a radius of only 45000 m and a period of 0.3 s. Assuming that the mass has not changed, find Assume a star has the shape of a sphere. (Suggestion: do it with formula first, then put the numbers in) [Recommended time : 5-8 minutes] (a) the ratio of initial to final angular momentum (Li/Lf) Oa. 2.17E+15 Ob. 24 Oc. 0.0416 Od. 4.61E-16 (b) the ratio of initial to final kinetic energy Oa. 4.85E-23 Ob. 396000 Oc. 2.53E-6 Od. 2.06E+22A star has initially a radius of 640000000 m and a period of rotation about its axis of 20 days. Eventually it changes into a neutron star with a radius of only 50000 m and a period of 0.2 s. Assuming that the mass has not changed, find Assume a star has the shape of a sphere. (Suggestion: do it with formula first, then put the numbers in) [Recommended time : 5-8 minutes] (a) the ratio of initial to final angular momentum (Li/Lf) Oa. 1.42E+15 Ob. 19 Oc. 0.0527 Od. 7.06E-16 (b) the ratio of initial to final kinetic energy Oa. 8.18E-23 Ob. 456000 Oc. 2.19E-6 Od. 1.22E+22 52%A cepheid star is located at a distance of 24.8kpc from the Earth and has an apparent visual magnitude of 13.3. Determine its pulsation period in days. Consider the following expression of the Leavitt relation My -2.78 log Pdays - 1.35, where My is the absolute visual magnitude and Pdays the pulsation period in days to 2 decimal places.
- Imagine that the Earth is orbiting a white dwarf star, whose surface temperature is 20000 K. What is the apparent angular size of this white dwarf as viewed from Earth? (Express your answer in arcseconds)Consider two stars on the main sequence, A and B. Star A has a mass of 6 M⊙. Star B has a mass of 0.3 M⊙. Compute the ratio of main sequence lifetimes for the two stars, TB/TA .A star with spectral type A0 has a surface temperature of 9600 K and a radius of 2.2 RSun. How many times more luminous is this star than the Sun? (if it is less luminous enter a number less than one) 36.854 This star has a mass of 3.3 MSun. Using the simple approximation that we made in class, what is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.