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- (a) Using Einstein's famous equation for rest-mass energy, E = mc², undergoing nuclear energy that could be extracted from 1 kg of hydrogen a star (HINT: the efficiency of this process is n = = 0.7%). calculate the amount of fusion in the core ofIf a circular accretion disk around a 1.4 M, neutron star has a radius of 8.00 x 10° km as measured from the center of the neutron star to the edge of the disk, what is the orbital velocity (in km/s) of a gas particle located at its outer edge? (The mass of the Sun is GM 1.99 x 1030 kg. Hint: Use the circular orbit velocity formula, V. = -; make sure to express quantities in units of meters, kilograms, and seconds.) km/sAs a mass m of gas falls into a black hole, at most 0.1mc2 is likely to emerge as radiation; the rest is swallowed by the black hole. Show the Eddington luminosity for a black hole of mass M is equivalent to 2*10-9 Mc2yr-1. Explain why we expect the black hole's mass to grow by at least a factor of e every 5*107 years. Where Edding Luminicity is defined as LE=(4piGMmpc)/(sigmaT), where G is the gravitational constant, M is the mass of the black hole, mp is the mass of a proton, c is the speed of light, and sigmaT is Thomson scattering where sigmaT=6.653*10-25 cm2.
- (Astronomy) Supernova Ejection Times. Observations show that the gas ejected from SN 1987A is moving at about 10,000 km⁄s. How long will it take to travel one astronomical unit in hours? (Note that 1 AU equals 1.5 × 108 km)1) a) Calculate the Jeans length for the dense core of a giant molecular cloud with T=10 K, n = 1010/m³, and µ=2. b) Estimate the adiabatic sound speed for this core, using y=5/3. c) Use this speed to find the amount of time required for a sound wave to cross the cloud t3=2Rj/vs. d) Compare your answer with the free-fall scale and comment your results.. The radius of the nebula is about 0.401 light-years. The gas is expanding away from the star at a rate of about 37 kilometers/second . Considering that distance = velocity x time, calculate how long ago the gas left the star if its speed has been constant the whole time. Make sure you use consistent units for time, speed, and distance. Answer in years.
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