Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 315 / 2 / d

Table of contents
- Solution d

Solution

For a geometrically thin isothermal ideal-gas atmosphere, set

g = G M_{p} / R_{p}^{2}

and

H = \frac{k _{B} T _{0}}{μ m _{H} g} .

Hydrostatic balance gives

P (z) = P_{0} e^{- z / H}

. The observed transit photosphere at

P_{phot}

is consequently at the isothermal pressure-level transit radius

R_{obs} = R_{p} + H ln \frac{P _{0}}{P _{phot}} .

This assumes

P_{phot} < P_{0}

, constant

T_{0}

, composition, and gravity, and an opacity that selects the stated pressure.

 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