- #1
physiks
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The basic idea is that from the Virial Theorem, if the gravitational potential energy of the sun decreases by a certain amount X, it gains thermal energy equal to half of this, 0.5X, and radiates away this same amount of energy too, 0.5X. This is from the relations
E=U+T and 2U+T=0 (energy E, PE U, KE T).
Then this is used to find the time the sun could continue to radiate at its current luminosity for. The problem is everywhere I read about this, the total PE of the sun is calculated in terms of its current state. They all say that the sun can continue contracting until its PE becomes zero (they say all the PE is 'radiated away'), so if we say half of the current PE is radiated away from the above, we can easily do the calculation.
However surely the PE of the sun is currently negative, and as it contracts, its PE gets more and more negative (and goes to negative infinity which obviously means my argument is flawed). If this is the case, why is the above method acceptable, because it's PE doesn't 'radiate away' and go to zero - it get's more negative. Another issue with my thinking is that because my PE is going to negative infinity, the star can continue to radiate forever at this luminosity by contracting - I'm obviously being very silly but can't figure out why!
Thanks for any help :)
E=U+T and 2U+T=0 (energy E, PE U, KE T).
Then this is used to find the time the sun could continue to radiate at its current luminosity for. The problem is everywhere I read about this, the total PE of the sun is calculated in terms of its current state. They all say that the sun can continue contracting until its PE becomes zero (they say all the PE is 'radiated away'), so if we say half of the current PE is radiated away from the above, we can easily do the calculation.
However surely the PE of the sun is currently negative, and as it contracts, its PE gets more and more negative (and goes to negative infinity which obviously means my argument is flawed). If this is the case, why is the above method acceptable, because it's PE doesn't 'radiate away' and go to zero - it get's more negative. Another issue with my thinking is that because my PE is going to negative infinity, the star can continue to radiate forever at this luminosity by contracting - I'm obviously being very silly but can't figure out why!
Thanks for any help :)