- #1

astrostuart

- 9

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I am an astronomer with a research question:

I want to evolve this equation for planet distribution:

[itex]

\frac{{\operatorname{d}}f(P)}{{\operatorname{d} \operatorname{log}}{P}}=

k_P P^\beta \left(1-e^{-(P/P_0)^\gamma }\right)

[/itex]

as a function of period ``P'',

by using an equation for change of P.

I will actually use

this equation of change of semi-major axis ``a''

(below)

for which I will input assumed values of the

masses and radii of the star and planets, (but transforming between P and a

is not hard. The calculus confuses me, though.)

[itex]

\frac{1}{a}\frac{da}{dt}=

-\left(\frac{9}{2}{\left(G/M_*\right)}^{1/2}\frac{R_p^5M_p}{Q_*^{prime}}\right)

a^{-13/2}

[/itex]

[itex]

G M P^2= (2 \pi)^2 a^3

[/itex]

I know it's unusual to think of planets "flowing" into stars, but consider this to be in the large limit of what happens to so many planets, that each planet is like a piece of fluid. Perhaps a mathematician can suggest how to say this better.

Thanks

Stuart

I want to evolve this equation for planet distribution:

[itex]

\frac{{\operatorname{d}}f(P)}{{\operatorname{d} \operatorname{log}}{P}}=

k_P P^\beta \left(1-e^{-(P/P_0)^\gamma }\right)

[/itex]

as a function of period ``P'',

by using an equation for change of P.

I will actually use

this equation of change of semi-major axis ``a''

(below)

for which I will input assumed values of the

masses and radii of the star and planets, (but transforming between P and a

is not hard. The calculus confuses me, though.)

[itex]

\frac{1}{a}\frac{da}{dt}=

-\left(\frac{9}{2}{\left(G/M_*\right)}^{1/2}\frac{R_p^5M_p}{Q_*^{prime}}\right)

a^{-13/2}

[/itex]

[itex]

G M P^2= (2 \pi)^2 a^3

[/itex]

I know it's unusual to think of planets "flowing" into stars, but consider this to be in the large limit of what happens to so many planets, that each planet is like a piece of fluid. Perhaps a mathematician can suggest how to say this better.

Thanks

Stuart

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