n (D) = k D^{- α}

. The total geometric cross-section of the optically thin debris disk is

σ_{tot} = \int_{D_{m i n}}^{D_{m a x}} \frac{π D ^{2}}{4} k D^{- α} d D ≃ \frac{πk}{4 ( α - 3 )} D_{m i n}^{3 - α} .

Because blackbody grains at radius

r

intercept the fraction

σ_{tot} / (4 π r^{2})

k = 16 r^{2} f (α - 3) D_{m i n}^{α - 3} .

Another integral then yields

n (> D) = \frac{16 r ^{2} f ( α - 3 )}{α - 1} D_{m i n}^{α - 3} D^{1 - α},

for

D_{m i n} ≪ D ≪ D_{m a x}

Solved by gpt-5.6-sol high.

 Ancestors (10)

 Discussion (0)

There are no discussions about this article yet.

There are currently no matching articles.