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.) ___________ AU

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.) ___________ AU

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If an X-ray binary consists of a 10-solar-mass star and a neutron star orbiting each other every 20.8 days, what is their average separation? (Hints: Use the version of Kepler's third law for binary stars, M, + M3 = ; make sure you express quantities in units of AU, solar masses, and years. Assume the mass of the neutron star is 1.6 solar masses.) a3 AU
Finally estimate the lifetime of an M0 spectral type star if the total mass of the star is M = 0.51M⊙ , and it has a total luminosity L = 7.7× 10−2L⊙. Make the same assumptions as the previous two problems. How does your calculated Main Sequence lifetime for the M0 type star compare to the Main Sequence lifetime you calculated for the Sun?
A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.
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)
Why are Cepheid variables important? O Cepheids variables are pulsating stars whose pulsation periods are directly related to their true luminosities. Therefore they can be used as distance indicators. O Cepheids variables are supermassive stars that are on the verge of becoming supernovae. Therefore they allow us to choose candidates to watch if we hope to observe a supernova. O Cepheid variables are stars that vary in brightness because they harbor a black hole. Therefore, they provide direct evidence for black holes. O Cepheids variables are a type of irregular galaxy, much more common in the early universe. Therefore they help to understand how galaxies formed.
What is the escape velocity (in km/s) from the surface of 1.1 M neutron star? (hint: Use the formula for the escape velocity Ve = 2GM/R ; make sure to express quantities in United of meters, kilograms, and seconds. Assume a neutron has a radius of 11 km and assume the mass of the sun is 1.99 x10^30 kg.) 1.1 M neutron Star = _________ km/s 3.0 neutron Star = __________ km/s
A 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%
Consider a neutron star as a very dense sphere of matter. Assuming that the star has a mass of 1*(mass of sun) and a radius of 0.05*(radius of sun), then how much would a 85.1 kg person weigh on the surface of this star? (enter your answer in Newtons). See the test reference sheet for applicable constants. HINT: Remember what we learned about the force of gravity and the gravitational field (Ch. 13 of the textbook)
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.