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The Sun (\SI{1.99e30}{kg}) radiates energy at a rate of about \SI{4e26}{W}. \begin{abcliste} \abc How much does the Sun's mass decrease in one day? \abc How long does it take for the Sun to lose a mass equal to that of Earth (\SI{5.97e24}{kg})? \abc Estimate how long the Sun could last if it radiated constantly at this rate. \end{abcliste}
\begin{abcliste} \abc The Sun radiates in one day an energy of: \begin{align} E &= Pt\\ &= \SI{3.456e31}{J} \end{align} This amount of energy is equivalent to a massloss of: \begin{align} m_d &= \frac{E}{c^2}\\ &= \frac{Pt}{c^2}\\ &= \SI{3.845e14}{kg}\\ &= \SI{3.845e11}{\tonne} \end{align} This is equal to almost 400 billion metric tons! \abc For the Sun to lose Earth's mass, it takes: \begin{align} t &= \frac{m_\EarthIndex}{m_d}\\ &= \SI{1.55e10}{d}\\ &= \SI{4.253e7}{a} \end{align} This is around 42 million years. \abc At this rate, the Sun could last for: \begin{align} t' &= \frac{m_\SunIndex}{m_d}\\ &= \SI{5.17e15}{d}\\ &= \SI{1.418e13}{a} \end{align} That is around one thousand times longer than the age of the universe. \end{abcliste}
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