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Astrophysics/How many stars in this area?

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Question
Greetings, Mr. Stahl.

I am working on a fanfic of a science fiction franchise I am fond of.

So here is the question.

In the fanfic humanity possesses every star visible from Earth in the galaxy.

Now as I understand it the farthest stars we can see are 4000 light years away.

So how many stars would be in an 8000 light year ''bubble'' around Earth? And how many habitable planets would said area have?

Answer
Hello,

First, let's change the units to parsecs instead of light years. Currently, the star density near the galactic center is estimated at 100 per cubic parsec - so that in the Earth's vicinity two-thirds of the way out to the galactic edge it is more like 0.5 per cubic parsec.

Converting light years (radius = 4000 ly) to parsecs we get a radius R = 1.23 x 10^3 parsecs.


We use this to get a total volume of interest:

V = 4/3 pi R^3  =  7.8 x 10^9 cubic parsecs


If there are 0.5 stars on average per cubic parsec then the stellar density is:

(0.5) (7.8 x 10^9 cubic parsecs)  =  3.9 x 10^9 (approx.)

(This would be the same number as in your "8000 light year ''bubble'' around Earth")

The next question (how many habitable worlds)  is much more difficult because the data is extremely sketchy.  Assuming a habitable planet requires an early spectral type G star (the Sun is G2) then perhaps only 1 out of 100 stars fit that bill. "Habitable" means within the so-called "Goldilocks" zone - i.e. within a suitable temperature sphere about the star.

So far only about 1 in 100 fit that distribution according to a sampling of the Kepler space telescope exoplanet findings.

So, given these limiting parameters (fractions), the estimated (again 'ball park') number of habitable planets in that *volume* (not "area")  would be: ~   40,000


One must take care, however, to distinguish "habitable" from actually inhabited. The latter, may be one thousand times less - again, or only 40.  

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Philip A. Stahl

Expertise

I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars as well as the magnetohydrodynamics of sunspots and solar flares. Sorry No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

Experience

Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

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

Publications
Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

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. Barbados Astronomical Society award for service (1977-91) as Journal editor.

Past/Present Clients
Caribbean Examinations Council (as advisor, examiner), Barbados Astronomical Society (as Journal Editor 1977-91), Trinidad & Tobago Astronomical Society (as consultant on courses, methods of instruction, and guest speaker).

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