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⎛<br />

⎜<br />

⎝<br />

Equilibrium Temperature for a<br />

Single Grain:<br />

L star<br />

4πr 2<br />

⎞<br />

⎟ πa2<br />

⎠<br />

( ) Q vis<br />

E in<br />

= E out<br />

( ) = 4πa 2<br />

( )( σT 4<br />

) Q IR<br />

( )<br />

T = 1 r<br />

⎛<br />

⎜<br />

⎝ 16πσ<br />

L star<br />

Q vis<br />

Q IR<br />

⎞<br />

⎟<br />

⎠<br />

1<br />

4<br />

K<br />

For the case where L=L Sun<br />

and Measuring r in AU:<br />

T = 278.3<br />

r AU<br />

⎛<br />

⎜<br />

⎝<br />

Q vis<br />

Q IR<br />

⎞<br />

⎟<br />

⎠<br />

1<br />

4

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