Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 315 / 1 / b

Table of contents
- Solution b

Solution

Put

μ = cos θ

. For

I_{ν} = A_{ν} + B_{ν} μ^{3}

, the mean intensity is

J_{ν} = \frac{1}{2} \int_{- 1}^{1} I_{ν} d μ = A_{ν},

because the cubic term is odd. The K-integral, or second angular moment, is

K_{ν} = \frac{1}{2} \int_{- 1}^{1} μ^{2} I_{ν} d μ = \frac{A _{ν}}{3},

because the

μ^{5}

contribution is also odd. Hence

K_{ν} = \frac{1}{3} J_{ν} .

This intensity obeys the Eddington closure approximation even though it is not isotropic.

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version