Epsilon Eridani – HD 22049 [1]

Writing this report was much more difficult but also much more fun and interesting than I imagined when I began with the project. I didn’t know a thing about luminosity, spectral classes or parallaxes. I pestered my teacher with questions when I first entered the SIMBAD database: “what does that mean?”, “what can you do with it?”, “how did they find out?”… I didn’t get all the answers but I got a pretty good start. Equations suddenly seemed useful. Luminosity… wow! To tell the truth I think I learnt more from working with this project than from a whole year of astronomy lessons.

I choose to write about Epsilon Eridani because I’ve been interested in extrasolar planets since I first heard about their discovery. I knew Epsilon Eridani was close to Sol and that they had found a planet orbiting it. Speculations of going there some day in the future or at least getting the planet on picture swirled in my mind. An interesting note might be that the Star Trek-planet Vulcan with its emotionless human-like aliens with pointy ears is claimed to orbit Epsilon Eridani. This star simply seemed like the most interesting choice

I thought pretty long about which level I should put the report on. I wanted both astronomers and people knowing only little about astronomy to get something from it, and I decided to calculate pretty many things by myself so that I wouldn’t have to trust other information sources all the time. I’ve tried to not put any information into the paper before I’ve seen it in at least two sources and I’ve tried to be critical, both towards myself and towards them. But I didn’t mention all the double-sources and I didn’t mention the sources for the most common equations. In that case, this report should have contained nothing but sources. Comparisons are done through the report, mainly with the sun because it’s easy for people to relate to.

Content

Page 1: Introduction and content

Page 2: The constellation

Page 3: Distance and stellar neighbours

Page 4: Luminosity and temperature

Page 5: Spectral class

Page 6: Mass, radius and metallicity

Page 7: Stellar life and the planet

Page 8: The planet

Page 9: The planet and the task

Page 10: The task

Page 11: The task and the end

The constellation

Phaethon, son of Helios, was once allowed to drive the chariot of the sun over the sky. But the horses wouldn’t obey the alien master and went crazy, away from the route of the sun and burning both the earth and the sky in their wild ride. To prevent a disaster, Zeus, king of the gods, threw a lightning bolt towards Phaeton, knocking him out of the chariot. He fell like a star towards the ground, falling into the river Eridanus. To console Helios for the loss of his son, Zeus placed the river on the night sky.

Another tale tells that Herakles changed the path of river Eridanus to clean the stable of king Augeias, leading it into the shitty house on one of his famous twelve missions. [2]

Eridanus, claimed to represent the Italian river Po, is a generally faint constellation but the second longest on the night sky, spanning from the south of the northern celestial sphere, southeast of Orion and right below the celestial equator, down to 30 degrees from the south celestial pole. That is almost 50 degrees in right ascension and over 2 h in declination. Because of its width and length it’s quite hard to grasp when you’re looking at the night sky, even if you watch it from an ideal position in North Africa or South America. Eridanus begins with star Cursa in the north, the second brightest star in the constellation (apparent magnitude 2.79) and ends with star Achernar in the south (magnitude 0.50), which is the 9:th brightest star on the night sky. You can watch the northern part of the constellation during the winter if you live in northern Europe or America but there is not a chance to view or photograph the whole Eridanus. [3]

HD 22049, Epsilon Eridani, is located in the upper part of Eridanus, a bit to the right of Zaurak (magnitude 2.98). Epsilon Eridani is not a very bright star (apparent magnitude 3.37) so it might be difficult to locate with the naked eye. The star’s right ascension is 3h 32m 55.846s, it’s declination -9°27'29.72 and its proper motion 0.98 arc seconds per year [4].

Located just to the left of Zaurak is the planetary nebula NGC 1535 (magnitude 9), which might be interesting to observe with a small telescope [5].

 

 

Distance

It seems like finding out information about stars is quite difficult. However, Epsilon Eridani is close enough to the Sun that its distance can be measured by the method of parallax, which gave the angle (p) 310.74 mili-arc seconds [6] = 0.31074 arc seconds. The distance in parsecs is given by the connection 1/p (where p is the parallax in arc seconds) = 1/0.31074 = 3.218 parsecs. 1 parsec is 3.26 light years, which gives us the distance 10.49 light years to Epsilon Eridani.

Stellar neighbours

Double stars, like the Alpha and Proxima Centauri and triple stars or more are most common in our galaxy but Epsilon Eridani is a single star just like our sun. Single stars are believed to easier develop planets because there is no external gravitation disrupting the planets, but extrasolar planets orbiting double stars have been found, like Gliese 86, also located in constellation Eridanus [7].

The star closest to Epsilon Eridani, 4.1 l.y away [8], is HIP 15689, followed by Luyten 726-8 (5.1 l.y) and Tau Ceti (5.5 l.y). HIP 15689 is a double star of magnitude 12.16 and only 0.000230 the luminosity of the sun [9]. Sirius is 8.6 l.y away from Sol and 7.8 l.y away from Epsilon Eridani.

 

 

 

 

 

 

Luminosity [10]

Luminosity is the energy per second emitted by a star and an excellent tool for later calculations of mass, temperature and radius. The apparent magnitude (m) of Epsilon Eridani is 3.73. [11] The luminosity can be calculated from the absolute magnitude (M) of the star, where m-M = 5 (log d ) –5. d is the distance in parsecs, which in this case is 3.218 parsec. M= -(5*(log d)-5-m) = -(5*(log3.218)-5-3.37) = 6.192. The sun is of absolute magnitude 4.85. [12]

To get the luminosity of Epsilon Eridani we can use the absolute magnitude 6.192, the absolute magnitude of the sun and the luminosity of the sun due to the equation M star – M sol = -2.5*log (L star /L sol ).  L = (10 ((M star -M sol )/-2.5) )*L sol.  Putting the values in gives L = 0.291*L sol , which also is what my sources indicate. So the luminosity of Epsilon Eridani is only about 29% of the suns. The luminosity of the sun is 3.86*10 26 W, which when multiplied with 0.291 finally gives the luminosity of Epsilon Eridani: 1.123*10 26 watts. Even though little compared to the sun it’s still one awfully big light bulb.

 

Temperature

A star’s colour can give an approximate surface-temperature. The more blue or white, the warmer, the more orange or red, the cooler. More than one source says that Epsilon Eridani is a red-orange star [13], but based on the temperature and spectral class stated in most other sources, I don’t trust them in this case. Epsilon Eridani is pretty much orange.

A more reliable method to calculate the temperature of a star is to study the spectrum of the star – a very useful method for astronomers - and determine the wavelength of which it emits most energy and then use Wien’s law to get the temperature. Wien’s law is  y max = 0.0029/T, where y max is the wavelength of maximum energy in meters and T is the surface temperature in Kelvin [14]. Generally, a star emits most energy at the same wavelength as its colour. The wavelength for orange light is approximately 600 nm = 6*10 -7 m. So if Epsilon Eridani indeed is orange it should have a temperature around T= 0.0029/ y max = 4800 K. That would be the average temperature for an orange star, but of course orange stars can have different temperatures anyway. Epsilon Eridani’s actual temperature has been estimated to 5100 K, [15] not very far from sun’s 5800 K.

Spectral class

Spectral classes can, like temperatures, be determined by studying the spectrum of a star. The first image [16] below shows a spectrum for an A-star with the temperature of 10 000 K, the second image a K-star like Epsilon Eridani, with typically weak absorption lines for hydrogen and stronger traces of ionised calcium and titanium-oxide.


Spectral classes are intimately bound together by temperature, colour and absorption-lines. Knowing a star’s surface temperature and colour makes you able to put it into a class, vice versa knowing it’s dominating sources of the absorption lines gives you a hint of it’s temperature, colour and chemical composition. [17]

Class

Colour

Average temperature

Strong absorption lines

O

White-blue

35 000 K

Ionized helium

B

light white-blue

21 000 K

Helium

A

White

10 000 K

Hydrogen

F

Yellow-white

7 000 K

Ionized calcium + iron

G

Yellow

6 000 K

Ionized calcium

K

Orange

4 500 K

Titanium oxide,

M

Red

3 000 K

Titanium oxide

Stars are also divided further into their classes. Sol is a G2 star, meaning that it has a high temperature for a G-star. This division spans from 0-9, where 9 is the lowest temperature of the class. And as if that wasn’t enough we have luminosity classes, a scale of roman numbers from I to V, indicating size and luminosity of the star. I is a super giant, V is a main sequence star [18]. Putting luminosity and spectrum class into a Hertzprung-Russel diagram [19] shows that Epsilon Eridani shows up together with the vast majority of stars in the main sequence. Using all this together Epsilon Eridani has been put into spectral class K2V, thus pretty warm for a K star.

But belonging to the K class is in no way a guarantee for a small, low luminous star. Lots of super giants and giants like Aldebaran and Arcturus, belong to the class. Arcturus is a K1.5 III star [20] with 25 times the radius of the sun and 115 times its luminosity [21].

 

 

 

Mass, radius and metallicity

There is a relationship between a star’s luminosity in watts (L), the distance to the centre of the star in meters (R) and the temperature in Kelvin (T): L=4 π R 2 σ T 4 , where σ is Stefan-Boltzmann’s constant 5.67*10 -8. The distance to the centre of the star is the same as the radius if T is the surface temperature of the star. The luminosity of HD 22049 was calculated to 1.123*10 26 watts and the temperature to 5100 K. Playing with the equation gives us

R = (L/(4*π*σ*T 4 )) 1/2 , putting the values in give the radius 4,826*10 8 meters for Epsilon Eridani.

The radius of the sun is 6.960*10 8 m. [22] Thus Epsilon Eridani should have 69% the radius of the sun, but the sources I’ve found [23] say 80% = 5.57*10 8 m. Maybe it’s different because of the inexact temperature value I used. Putting the radius 0.8*R sol into the equation with the same luminosity as before would give T=(L/(4 π R 2 σ )) (1/4) ≈ 4700 K. This is also possible for a K star, just like the temperature given by Wien’s law, I guess, but it wouldn’t really be warm enough for a K2 and it would mean that my other sources would need to check their info better. Weird.

While we’re at it with luminosity-relationships there is one [24] for main sequence stars which we can use to get the mass of Epsilon Eridani: L star /L sol = (M star /M sol ) 3.5. The mass of the sun [25] is 1,989*10 30 kg, but some sources say that (M star /M sol ) 3.9 is to be used and some say (M star /M sol ) 4 , so it isn’t easy to know what to pick. L/L sol is 0.291, which when you use the 3.5 equation gives M star /M sol = 0.70 and M star /M sol = 0.73 when you use the 4 equation. So Epsilon Eridani should have about 70 % the mass of the sun = 0.7*1.989*10 30 = 1.39*10 30 kg. Again this isn’t exactly what the sources [26] say, they want it closer to 80%, and they might be right but at least it’s clear that it can be healthy to question astronomical data.

If one would consider it fun I guess you could calculate the volume of Epsilon Eridani with the help of the radius, get the density in kg/ m 3 and compare it to the density of pure hydrogen at the same pressure and temperature. A great difference would indicate that Epsilon Eridani contains lots of element heavier than hydrogen and helium, like metals. It could give a hint of a star’s metallicity, which is usually determined by studying the star’s spectrum. HD 22049 has [Fe/H] = -0.1, which means that it has 10 -0.1 = 0.79 = 79% the metal content of the sun. [27]

Stellar life

We have stated that Epsilon Eridani is a small, orange main sequence star. Orange means pretty low temperature and makes, together with the small size, that the star won’t digest its hydrogen as fast as the white-blue Sirius, as an example. So unlike its apparent fellows, the red/orange giants and the brighter main sequence stars, it can look forward to a lifespan longer than our sun’s.

Not surprising by now, there is a relationship for the lifetime of a main sequence star, parly calculated from the mass-luminosity relation. The relationship is: t = M/(M 3.5 ), where M is M star /M sol and t is the lifetime in solar lifetimes. [28] If we take M HD22049 /M sol = 0.70 and sun’s lifetime as 10 billion years, Epsilon Eridani will digests its hydrogen in 2.44* 10 000 000 000 = 24 billion years.

Epsilon Eridani is a young star, perhaps proven best by a discovery made by radio imagery in 1998: the dust ring around Epsilon Eridani at the distance of 30 AU. [29] Even though older stars may have dust rings/disks, perhaps as a consequence of planet collisions, they are most common in young, planet-forming systems where all the gas hasn’t thickened to planets yet. A planet around Epsilon Eridani has been discovered so the star can’t be totally newborn, but the planet might be in its early stages.

It sounds like it also should be possible to measure the amount of helium in relation to hydrogen within the star, perhaps through spectroscopy. The more helium, the older the star. In any case, astronomers have calculated the age of Epsilon Eridani to somewhere between 500 000 000 to 1 000 000 000 years. But it is actually quite old in comparison to other stars where dust disks have been found, like Vega and Beta Pictoris, who are under 300 000 000 years old [30].

 

 

The planet

The planet orbiting Epsilon Eridani was discovered year 2000 with Doppler spectroscopy. The radial velocity of a star is slightly disturbed if an object is orbiting it and moves the gravitational centre of the system. This can be shown by a velocity curve. The larger planet is, the greater disturbance becomes and the easier it becomes to detect. To get good values you have to study the star during at least one orbital period for the possible planet. The closer the planet is to the star, the more periods you can observe in comparison to planets with great semi-major axis’. Because of this, most of the extrasolar planets discovered so far have been planets of 1 Jupiter mass or more in orbits close to the star.

The existence of the Eridani planet has been under debate. Epsilon Eridani has an unusuallyactive cromoshpere for a star its size and age and gives away “noise” which disturbs the readings of the radial velocity. [31] But lately the discovery has been confirmed by so many different teams of astronomers that the existence of the planet should be without doubts.

The planet of Epsilon Eridani has a mass of 1.2 Jupiter-masses, is likely a Jovian gas-giant and has an orbital eccentricity of 0.608. Thus, the orbit is egg-formed, bringing the planet closer to the warmth of the star about half of the time of its 2501-day orbit and out in the cold the rest of the period. Pluto, which we consider eccentric, has only the eccentricity of 0.248. [32] The semi-major axis of the Eridani planet is 3.3 AU, to compare with 1.52 AU for Mars and 5.3 AU for Jupiter. This system is different from our own solar system because of the eccentric orbit and its young age, but we can be sure of how similar or different it is otherwise until we get more knowledge of it.

It is very unlikely for life to evolve on this planet, or even on its eventual moons. The temperature varies too much because of the egg-formed orbit and it’s far too distant from Epsilon Eridani to be warm enough to support life, as we know it. But it might be possible for a terrestrial planet to form closer to the star where it won’t be affected by the eccentric orbit of the greater planet and where it has a more pleasant temperature. As already stated, Epsilon Eridani is a young system so it’s also possible that an earthlike planet orbiting the star looks like Earth in its youth; glowing hot from asteroid collisions or

covered by vast oceans, where proteins slowly are “mating”

with each other to produce the early stages of life...

Much of this is, of course, only speculation. We don’t have the technology to find earth-sized extrasolar planets yet. And it would take thousands of years to travel to Epsilon Eridani with today’s technology. Sorry all Star-Trek fans, reality’s Vulcan is a baby. Freeze yourselves in a cryo-chamber and you might get to greet Mr. Spock in a billion years or so.

 

 

Task – investigating the basic conditions of life on an extrasolar planet

This exercise should be done with pupils older than 16 years and with some previous information from the teacher about extrasolar planets. It can be done with any extrasolar planet discovered, or an imaginary one, if the luminosity of the star and the semimajor axis and the eccentricity of the planet are known.

Part 1 – Habitable zone

Scientists believe that liquid water is one of the requirements for life, as we know it. The distance from a star where the temperature is between the freezing and the boiling point of what, i.e. where liquid water may exist, is called the habitable zone. That would be 0-100 degrees Celsius or 273-373 Kelvin. The normal temperature empty space is –273 degrees Celsius or 0 K. The higher temperature of the star, the further away from it is the habitable zone, the lower the temperature, the closer is the habitable zone. Of course this liquid water would need a steady surface to form on, so the gas giant extrasolar planets discovered this far are unlikely to have life. But they might have moons large enough to withhold an atmosphere, which also is likely to be needed to protect the life from radiation and dampen meteorite collisions.

The temperature of a planet on a certain distance from a star can be calculated with the luminosity-equation. It can also give a rough value of the habitable zone, where the type of the planet and its ability to reflect and absorb the light hitting it has been left out.

L=4* π *R 2 * σ*T 4                  T= (L/(4*π *R 2 * σ)) 1/4            R= (L/(4*π * σ *T 4 )) 1/2

L = the luminosity of the star in watts (J/s)

R = the distance to the centre of the star in meters

T = the temperature in Kelvin

σ = Stefan-Boltzmann’s constant, 5.67*10 -8

π = 3.14159

To get the distance of the habitable zone in meters it’s just to first put T = 273 K into the last equation to get the outer edge of the habitable zone and then put T = 373 K to get the inner edge of the habitable zone.

A distance in meters give little information when you’re talking about astronomy. In AU, astronomical units, it’s much easier to compare with the solar system, cause the semimajor axis of Earth is 1 AU. 1 AU is 1.496*10 11 m, so 1 m is 1/(1.496*10 11 ) AU. Take your value in meters and multiply it with 1/(1.496*10 11 ) to get the distance in AU.

If one would like a more realistic value you should multiply the star’s luminosity with 0.5 before putting the luminosity into the equation. This pushes the habitable zone inwards. 0.5 is a standard value for the albedo of a planet. The albedo is the extent of which the light hitting a planet will be reflected again. Albedo 0.5 means that 50% of the incoming energy will be reflected again. Also, planets with atmospheres will probably have some sort of greenhouse effect with CO 2 preventing some of the energy from being reflected, fighting some of the effect of the albedo.

Example:

The luminosity of Epsilon Eridani is 1.123*10 26 W.

The outer edge of the habitable zone: R= (0.5*L/(4*π*σ*T 4 )) 1/2 = ((0.5*1.123*10 26 )/(4*3.14159*5.67*10 -8 *273 4 )) 1/2   = 1.19*10 11 m

In AU: 1.19*10 11 *1/(1.496*10 11 ) = 0.80 AU

The inner edge of the habitable zone: R= (0.5*L/(4*π*σ*T 4 )) 1/2 = ((0.5*1.123*10 26 )/(4*3.14159*5.67*10 -8 *373 4 )) 1/2   = 6.38*10 10 m

In AU: 6.38*10 10 *1/(1.496*10 11 ) = 0.43 AU

The zone where we might find liquid water is within 0.4-0.8  AU from Epsilon Eridani. The planet orbiting Epsilon Eridani has a semimajor axis of 3.3 AU. Thus it is well outside the habitable zone and is very unlikely to have life, even on its eventual moons.

Part 2 – Eccentricity

Even if a planet has had the luck to be born with a semimajor axis within the habitable zone of its star it is no way a guarantee for habitability. A too great eccentricity can bring the planet in and out of the habitable zone, making the planet too warm for life or too cold for life most time of its orbital period. Eccentricity is measured from 0 to 1, where 0 is a perfect circle, 0.5 similar to the shape of an egg and 1 a flat line. You can investigate if your planet remains within the habitable zone, or how high the eccentricity can be for a planet in the habitable zone with the planet remaining inside it anyway, if you know the planet’s eccentricity (e) and the semimajor axis (a). [33]

Example:

The planet orbiting Epsilon Eridani has a semimajor axis of 3.3 AU and an eccentricity of 0.608. It is well outside the habitable zone, so let’s push it inwards to 0.6 AU, the centre of Epsilon Eridani’s habitable zone. Its closest distance to the star would then be

0.6*(1-0.608) = 0.23 AU and its furthest distance 0.6*(1+0.608) = 0.96 AU.

The habitable zone of Epsilon Eridani was 0.4-0.8 AU. So even if the planet’s semimajor axis had been in the middle of the habitable zone its eccentricity would have made the conditions for life hard when it wanders 0.2 AU out of the habitable zone, both closer to the star and further away from the star. So how high eccentricity could this hypothetical planet have and still remain within the habitable zone?

Eccentricity acceptable for inner edge: 0.6*(1-e) = 0.4           e = 0.2/0.6 = 0.333          

Eccentricity acceptable for outer edge: 0.6*(1+e) = 0.8          e = 0.2/0.6 = 0.333

The eccentricity could have been up to 0.333 without seriously disrupting the life on the planet, at least theoretically. If the values had been different, like 0.333 and 0.356, the lowest value would be required for the planet cause otherwise it would have gone out of the habitable zone on one edge anyway.

3 - Conclusion

Do the basic conditions of life exist in the surroundings of your planet? Is it within the habitable zone and does it have a moderate eccentricity? Or is it possible that the conditions are right somewhere else in your system? Discuss and have fun.

The end

By Caroline Hyll

2002-10-25

Saltsjöbadens Samskola

Sweden

Supported by teacher and team member Anders Västerberg

Thanks to:

Pawel Artymowicz

Back to the content


[1] Image from Aladin. Key word HD 22049. Suvey “SERC”, origin “DSS2/STScI”, color “ER”, “global plate”. Inverted and with Aladin marks removed. Epsilon Eridani is the bright star in the upper right corner.

[2] Myths from the book Alla våra stjärnbilder ( All our constellations ) by Bengt Rönde and Björn Stenholm. Published by Liber Utbildning in 1995

[3] Constellation image from http://www.earthvisions.net/bcp/aster/constellations/Eri.htm with some modifications

[4] Declination, right ascension and proper motion from http://www.stellar-database.com/Scripts/search_star.exe?Name=Epsilon+Eridani

[5] Information about the constellation and its objects from SIMBAD and the book Alla våra stjärnbilder ( All our constellations ) by Bengt Rönde and Björn Stenholm. Published by Liber Utbildning in 1995.

[6] Parallax from SIMBAD, http://simbad.u-strasbg.fr/sim-id.pl?protocol=html&Ident=epsilon+Eridani&NbIdent=1&Radius=10&Radius.unit=arcmin&CooFrame=FK5&CooEpoch=2000&CooEqui=2000&output.max=all&o.catall=on&output.mesdisp=N&Bibyear1=1983&Bibyear2=2000&Frame1=FK5&Frame2=FK

[7] Gliese 86 information from http://www.eso.org/outreach/press-rel/pr-1998/pr-18-98.html

[8] Nearby stars of Epsilon Eridani from http://www.solstation.com/stars/eps-erid.htm

[9] HIP 15689 information from http://www.johnstonsarchive.net/astro/nearstar.html

[10] Image of Epsilon Eridani from Aladin database (http://aladin.u-strasbg.fr/java/nph-aladin.pl?frame=launching&-rm=14.1&-server=Aladin) with key word “HD 22049”, survey “SERC” and origin “DSS2/STScI”. Inverted.

[11] Apparent brightness from SIMBAD, same adress as before.

[12] Absolute magnitude from http://joy.chara.gsu.edu/RECONS/TOP100.htm

[13] Among them http://www.solstation.com/stars/eps-erid.htm

[14] Wien’s Law from the book Universe , by Roger A. Freedman and William J. Kaufmann. The sixth edition.

[15] Temperature from http://www.astro.uiuc.edu/projects/sow/epseri.html, by professor Jim at the University of Illinois' Department of Astronomy

[16] Image from Armagh Observatory, http://www.arm.ac.uk/~csj/pus/spectra/spek.html

[17] Spectral class table created with help from Columbia University Press; http://ph.infoplease.com/ce6/sci/A0846213.html

[18] University of Illinois; http://www.astro.uiuc.edu/~kaler/sow/spectra.html

[19] Diagram homemade with the help of Abell’s Exploration of the universe and the table

[20] Spectral class from SIMBAD, http://simbad.u-strasbg.fr/sim-id.pl?protocol=html&Ident=arcturus&NbIdent=1&Radius=10&Radius.unit=arcmin&CooFrame=FK5&CooEpoch=2000&CooEqui=2000&output.max=all&o.catall=on&output.mesdisp=N&Bibyear1=1983&Bibyear2=2002&Frame1=FK5&Frame2=FK4&Frame3=G&Equi1=2000.0&Equi2=1950.0&Equi3=2000.0&Epoch1=2000.0&Epoch2=1950.0&Epoch3=2000.0

[21] Radius and luminosity from http://www.solstation.com/stars2/arcturus.htm

[22] Radius from Abell’s Exploration of the universe

[23] Percentage from http://www.obspm.fr/encycl/eps-Eri.html and http://www.solstation.com/stars/eps-erid.htm

[24] Equation from http://zebu.uoregon.edu/~imamura/208/jan23/ml.html, http://tesla.phys.unm.edu/phy536/3/node2.html, http://ceres.hsc.edu/homepages/classes/astronomy/spring99/Mathematics/sec22.html

[25] Mass from Abell’s Exploration of the universe

[26] Mass in percent from http://www.solstation.com/stars/eps-erid.htm and http://www.obspm.fr/encycl/eps-Eri.html

[27] Metallicity from http://www.obspm.fr/encycl/eps-Eri.html

[28] Lifetime equation from Freeman’s Universe , sixth edition, by Roger A. Freedman and William J. Kaufmann

[29] Image from http://www.jach.hawaii.edu/~jsg/kbelt.html (EpsEri.gif) and distance from http://www.extrasolar.net/mainframes.html

[30] Ages for Epsilon Eridani, Vega and Beta Pictoris info from http://astron.berkeley.edu/~kalas/disksite/pages/epseri850.html

[31] Velocity curve from http://exoplanets.org/esp/epseri/epseri.shtml

[32] Eccentricity of Pluto from Abell’s Exploration of the universe , page 655

[33] Eccentricity image homemade