Solar and Magnetospheric Physis Physics Assignment Help

Assignment Task

QUESTION  
Antares is a red super giant with a mass of 13 M?, a radius of R = 680 R?, and a luminosity of L = 76000 L?, where M?, R? and L? denote, respectively, the Sun’s mass, radius an luminosity.
a) Derive an equation for the time it would take for matter from the surface of Antares to reach its centre under the action of gravity. Evaluate this equation.

b) Compare the gravitational potential energy of Antares with the luminosity of Antares to derive an equation for the time it would take Antares to cool through gravitational collapse. Evaluate this equation.
c) Supergiants have already exhausted all the Hydrogen in their cores, so that they rely on Helium fusion. Assuming that 10% of Antares’ mass partakes in the nuclear fusion and that 0.065% of this mass can be converted into energy by nuclear reactions, how long can Helium fusion support the current luminosity of Antares?
d) Use the times from parts a), b), and c) to explain why we can assume that Antares is in equilibrium

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