1. Stars spend the majority of their lives converting hydrogen into helium via fusion. The simplified reaction is: 4 H He a. How much mass is converted into energy per reaction? Express your answer in kg. b. How much energy is produced per reaction? Express your answer in Joules J = kg m2/s = 2. The star Vega is 2x the mass of the Sun. It produces 40x the power output of the Sun or 1.6 1028 Joules per second. a. How far from the Vega would we need to be in order for it to appear as bright in the sky as our Sun does today? Note: Earth is 1 AU from the Sun and you should express your answer in AU. b. How much H does Vega convert into He every second to sustain its power output? You may express your answer in tons or kg. Note: answers with appropriate justification that are correct to a factor of 2 will receive full credit. c. How long can we expect Vega to sustain H -> He fusion in years? You may assume that, like the sun, only 10% of Vega's H fuses into He. Compare this value to the sun's lifetime of 10 Billion years. Note: answers with appropriate justification that are correct to a factor of 2 will receive full credit. Quantities you may find helpful are on the second page of this document. c = speed of light = 3x108 m/s. Doppler formula A / = v/c Hint: 1 light year = 9.4x10 km 1 year = 3.1 x 107 seconds. E = m c J = Joule = kg m2/s H = hydrogen, mass = 1.6726 10-27 kg 4He = helium, mass = 6.6465 10-27 kg c = speed of light = 3 x 108 m/s Mass of sun = 2 1030 kg