	AllExperts > Astrophysics
	Search

About Philip A. Stahl
Expertise
I specialize in stellar and solar astrophysics. Can answer any questions pertaining to these areas, the spectroscopic analysis of stars – as well as the magneto-hydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions.

Experience
Have published papers on the relationship between sunspot morphology and solar flares; discovery of SID flares related to this, constructed computerized stellar models; MHD research.

Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

Publications
Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France)

Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society

You are here: Experts > Science > Physics > Astrophysics > Follow-up solution

Astrophysics - Follow-up solution

Expert: Philip A. Stahl - 11/5/2009

Question
Okay, I think I have worked this out, but can you tell me if it’s right?

From the link you gave in the previous answer, I can write:

m – M = 5 log (d/10)

where m = +8

M = +4.8 (absolute magnitude for a solar mass star) and d is the distance to the binary

So:

(8 – 4.8) / 5   =   log (d/10) = 0.64

Doing anti-logs:

4.36 = d/ 10 so    d = 4.36 x 10 = 43.6 or call it about 44 pc.

The basic relation between distance and parallax angle p is p = 1/d

So in this case: p = 1/44 = 0.”0227

The angular separation is given as a” = 1.”00

So the semi-major axis in AU is A = a”/p = 1.”00/(0.”0227) = 44 AU

Kepler’s 3rd law gives the form (for two separate masses):

(M1 + M2) = A^3/ P^2

Where we are given P = 100 yrs.

We know M1 is a solar mass star so M1 = 1 (solar mass) and need to get M2

So then: (M1 + M2) =   (44)^3/ (100)^2   = 8.5 solar masses

So that M2 = 8.5 – 1 = 7.5 solar masses

Is that correct?

Thanks!

Answer
Congrats! You have it correct! The key to the solution was in seeing that, after you obtain the distance (d) to the system via the distance modulus, then you need to obtain the parallax angle applicable, p. We know the basic definition for parallax implies a distance of 1 parsec for an angle of 1" subtended at the Earth. Since the distance obtained via the distance modulus is ~ 44 parsecs, that means the applicable value for p is 44 times *less*, or:

p = 1"/44 = 0."0227

Which is then employed to obtain A, the actual semi-major axis in A.U.. The only remaining chore was to get the unknown mass of the binary system (M2) using Kepler's law as you did.

Good job!

Add to this Answer Ask a Question