The sun\'s mass is 1.989*10^30 kg and it radiates at a rate of 3.827*10^23 kW. (

Question

The sun's mass is 1.989*10^30 kg and it radiates at a rate of 3.827*10^23 kW. (a)Over time, must the mass of the Sun increase, remain the same, or decrease?
(b)Estimate the lifetime of the Sun from this data, assuming it converts all its mass into energy.
(c)The actual lifetime of the Sun is predicted to be much less than the answer to part B, even though its energy emission rate will remain constant. What does this tell you about the 100% conversion assumption?
(d)Theoretical calculations predict the Sun's lifetime (in its current stage) to be about 5 billion years. During that time, what percentage of its mass will it lose?

Explanation / Answer

I'm not going to do the calculations for you but I will set them up for you with some explanation. a. We know by relativity that mass and energy are fundamentally related quantities as is demonstrated by E = mc^2. If you're radiating energy, you're losing mass. b. You can figure out the mass lost per second by converting this equation into Power = mass per time * c^2. Essentially divide the rate of radiation by c^2 and that will you give you the mass lost per time. From this it's easy enough to figure out the lifetime of the sun. Just divide the mass of the sun by mass lost per time. c. Clearly it is not necessary for the sun to lose all of its mass before it goes supernova. 100% conversion of mass to energy is not the point at which a star dies. d. Simply multiply the mass loss per second by 5 billion years converted into seconds. This is the amount of mass it will have lost in five billion year. If you divide this by the total mass you will have your percentage.

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