Jude Rook

Okay, I haven't posted anything here in ages (super-demanding new job), but I have to make a note of this!  After all, it's ALPHA CENTAURI!!!

http://blogs.smithsonianmag.com/smartnews/2012/10/alpha-centauri-has-a-planet/

Here is a link to some basic info on the 40 Eridani system, home to Mr. Spock's planet Vulcan.  40 Eridani A, the largest star in the system, has a luminosity of 0.38, giving it a life zone stretching from 0.38 to 0.92 AU.  If Vulcan is Earthlike, it's probably around 0.61 AU from its primary, with a year that's 175 Earth days long, just under half an Earth year.

Basic information on this popular star can be found here.  It has a luminosity a little under half of Sol's, 0.46 to be precise.  Its life zone extends from 0.48 to 1.02 AU, with an Earth twin distance of 0.62.  A planet in the sweet spot would have a year equivalent to 205 Earth days.

Astronomers are closing in on those sunless planets that drift through interstellar space.  The ones featured in such SF novels as George R.R. Martin's Dying of the Light...

http://www.nytimes.com/2011/05/19/science/space/19planets.html
http://www.space.com/11699-rogue-alien-planets-milky-common.html

There may be more sunless planets than there are stars!  However, the latest data indicate they are more likely to be gas giants than terrestroid worlds. 

Here is a link to some basic data on this orange star.  As it seems to have a luminosity of 0.29, its life zone ranges from 0.38 AU on the inside to 0.81 on the outside.  Earth twin distance comes out to 0.54.  An Earth twin’s “year” would be around 45 Earth days long.  Note that Epsilon Eridani may have some giant planets that lie far beyond the life zone – the jury of astronomers is still out on their actual existence.

 

In previous entries I've dealt with the age and metallicity of various nearby (i.e. within 100 light years) stars, since these appear to be the main factors in determining whether a star is a good candidate to have a habitable planet.

But let's say you've weighed these factors and decided on a particular star as the primary for your fictional planet.  You're now going to want to figure out some basic data, such as how far the planet is from the star and how long its year is. 

Here are a couple of formulas that will let you make these calculations.

1. How far should your planet be from the star?

Well, if humans are going to live there without needing special protection all the time, it needs to be somewhere in the habitable zone.  If you want a hot planet, you'll put it closer to the inner edge of this zone; if you want a cold one, you'll put it near the outer edge, and if you want one that's in the middle, well, you know what to do.

To figure out where the boundaries of the habitable zone lie, start with the visual luminosity (L) of the star.  Luminosity means "how bright the star is relative to Sol," so a star with a luminosity of 0.8 would be 80% as bright as Sol.  The luminosity for stars within 75 light years or so should be readily available on such sources as the Internet Stellar Database or Solstation.com.  (If you happen to know a star's mass but can't find out its luminosity, you can get a rough approximation by raising the star's mass to the power of 3.5.)

All right, now that we've got the star's luminosity, let's do a little basic math to find the boundaries of the habitable zone.

Sol's habitable zone is generally believed to be from 0.7 to 1.5 AU.  For any other star that might have a terrestrial planet:

The inner edge in AU is the square root of L x 0.7
The Earth twin distance in AU is the square root of L
The outer edge in AU is the square root of L x 1.5

(There are more involved formulas you can use to determine these values, but this method will do for rough-and-ready calculations.)

2. Now that you know the planet's distance from its primary, how long would its year be?

Start with the distance of the planet in AU.

Cube this number.

The planet's year (in Earth years) will equal the square root of the distance cubed.  (Google "Kepler's Third Law" for more information on why this is so.)

Let's go through this exercise for the three stars of the Alpha Centauri system.

Proxima Centauri is a red dwarf.  Its luminosity is a mere 0.0017 -- that is, it's 0.17 percent that of Sol.

The square root of 0.0017 is 0.041231.

Thus, the inner edge of the habitable zone is 0.7 of 0.041231, or 0.029 AU.

The Earth twin distance is equal to the square root of L, so a planet with Earthlike temperatures would likely be located about 0.041 AU from Proxima.

And the outer edge of the habitable zone is 0.062 AU out from the star.

Remember, however, that these numbers are just approximations, and you would have to take other factors into consideration, such as the fact that Proxima is a flare star, in deciding what distance your planet would be... or if you think Proxima could have a habitable planet at all.

Let's say there is a planet at 0.041 AU.  The cube of this number is 0.00007, and the square root of 0.00007 is roughly 0.008.  So this planet's year would be 0.008 years long, or 3.056 days.  (Of course, the planet would not be likely to rotate on its axis in one Earth day -- the figure in Earth days is just to give a better idea of how long the year is.)

Alpha Centauri A is much more Sol-like, with a luminosity of 1.1.

The square root of 1.1 is 1.048809.

So the inner edge of the habitable zone is at 0.734 AU; Earth twin distance is 1.049 AU; and the outer edge is at 1.573 AU.

Finally, let's take Alpha Centauri B, an orange dwarf with a luminosity of 0.5.

Inner edge of the habitable zone is at 0.495 AU; Earth twin distance is 0.7 AU; and the outer edge is at 1.061 AU.  The Earth twin's year would be 0.59 Earth years, or 217 Earth days, long.

These calculations are only meant to apply to planets that are at least somewhat Earthlike.  They would not apply to planets that harbored liquid water under a thick crust of ice, as may be the case with one or more of Jupiter's moons, or planets that were self-warming because of radioactivity, or... well, think up your own offbeat scenarios.

The Occurrence Rate of Earth Analog Planets Orbiting Sunlike Stars
Authors: Joseph Catanzarite, Michael Shao (Jet Propulsion Laboratory, California Institute of Technology)

Abstract: Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine the fraction of Sunlike stars that have planets like Earth... Here, we show that 1.4% to 2.7% of stars like the Sun are expected to have Earth analog planets, based on the Kepler data release of Feb 2011.

The full paper is at http://arxiv.org/ftp/arxiv/papers/1103/1103.1443.pdf.  Note that by "sunlike" the study means FGK stars.

Let's say the actual percentage is 2.05%, which is the halfway point between the upper and lower limits.  Solstation.com tells us there are 303 known F stars within 100 light years of Sol, 512 G stars and 947 K stars.  That comes to 1762 stars.  If 2.05% of them have Earth analog planets, that's 36 of them within 100 light years.  Note that there are likely to be many sunlike stars that haven't been discovered, particularly K stars more than 50 light years out.

Keeping it closer to home, there are at least 254 FGK stars within 50 light years.  2.05% of that would give us 5 Earth analogs.

Finally, in case this week’s postings have inspired you to write a story about two or more of these interstellar empires and you want to know how far they are from each other, here’s a distance chart for the capital stars:

 

	475	67	853	616	882
Sol	27.3	41.2	44.4	45.7	50.1
475		51.3	70	45	66.1
67			68.2	79.5	32.8
853				60.2	57.6
616					74.9

18 Scorpii is a G1V star 46 light years away.  It may have a binary companion and is also known as Gliese 616.

As the pickings are a little slim within 10 light years, here are the stars within 15 light years of 18 Scorpii:

Gliese 606: 3.11498 light-years, class M0V
Luyten Palomar 684-17 (no Gliese number I could find): 8.9 light-years, class M4.5 or 5V
Psi Serpentis/Gliese 596.1: 11.1 light-years, class G5V
Wolf 635/Gliese 653: 13.8 light-years, class K5V
Gliese 668.1: 14.1 light-years, class G9V
Gliese 641: 14.5 light-years, class G8V
Lambda Serpentis/Gliese 598: 14.6 light-years, class G0V
12 Ophiuchi/Gliese 631: 14.8 light-years, class K0V

And here’s the chart:

	606	LP	596.1	653	668.1	641	598	631
616	3.1	8.9	11.1	13.8	14.1	14.5	14.6	14.8
606		8.8	9.6	15.3	16.3	16.8	13.6	15.3
LP			17.5	22.3	22.1	13.5	19.2	23.1
596.1				19.9	21.1	17.2	10.2	18.6
653					4.1	20.6	15.1	5.5
668.1						18.4	17.8	9.5
641							22.3	23.6
598								11.6