, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by it
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A supernova’s energy is often compared to the total energy output of the Sun over its lifetime. Using the Sun’s current luminosity, calculate the total solar energy output, assuming a 1010 year main-sequence lifetime. Using Einstein’s formula E=mc2 calculate the equivalent amount of mass, expressed in Earth masses. [Hint: The total energy output of the Sun over its lifetime is given by its current luminosity times the number of seconds in a year times its ten billion-year lifetime; ; mass of earth = 6×1024kg; c = 3×108m/s. Your answer should be 200-300 Earth masses.]
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- The flux received at the Earth from Supernova 1885 was 3.0182 x 10 10 W/m². The luminosity of the supernova is 6 x 10° Lo (or 6 x 10° solar luminosities). What is the distance to the supernova in parsecs? Take 1 pc = 3.0857 x 1016 m and Lo= 3.828 x 1026 w. d = pcThis star has a mass of 3.3 MSun. What is the main sequence lifetime of this star? You may assume that the lifetime of the sun is 1010 yr.Place the following events in the formation of stars in the proper chronological sequence, with the oldest first and the youngest last. w. the gas and dust in the nebula flatten to a disk shape due to gravity and a steadily increasing rate of angular rotation x. a star emerges when the mass is great enough and the temperature is high enough to trigger thermonuclear fusion in the core y. the rotation of the nebular cloud increases as gas and dust concentrates by gravity within the growing protostar in the center z. some force, perhaps from a nearby supernova, imparts a rotation to a nebular cloud y, then z, then w, then x z, then y, then w, then x w, then y, then z, then x z, then x, then w, then y x, then z, then y, then w MacBook Air on .H. O O O O
- Using the center-of-mass equations or the Center of Mass Calculator (under Binary-Star Basics, above), you will investigate a specific binary-star system. Assume that Star 1 has m₁ = 3.4 solar masses, Star 2 has m₂ = 1.4 solar masses, and the total separation of the two (R) is 52 AU. (One AU is Earth's average distance from the Sun.) (a)What is the distance, d₁, (in AU) from Star 1 to the center of mass? AU (b)What is the distance, d2, (in AU) from Star 2 to the center of mass? AUQuestion helpIf the sun expanded to a radius 5000 times its present radius, what would its average density be (in g/cm3?)
- 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(Astronomy) Hyades Cluster Age. This chapter states that the Hyades cluster is 650 million years old. What is the age of the cluster based on highest-mass star in the cluster that is still on the main sequence? (Hint: the figure and the table below may be helpful.)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?
- using the center-of-mass equations or the Carter of Mass Calculator (under Binary-Star Basics, abova), you will investigate a specific binary star system. Assume that Star 1 has m, 3.2 solar masses, Star 2 has m,-0.9 solar masses, and the total separation of the two (R) is 34 All (One AU is Earth's average distance from the Sun) (2) What is the distance, d. (In Au) from Star 1 to the center of mass? AU (b) What is the distance, dy On Au) from Star 2 to the center of mass AU ( what is the ratio of d, tod?The lowest mass for a true star is 1/12 the mass of the sun. What is the luminosity of this star (in units of the sun’s luminosity) based upon mass luminosity relationship? Use the exponent of 4 for easy calculations instead of 3.9A 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.