Red Dwarf at Eris

[mishalak]

If a red dwarf star was as distant from earth as Eris is at it's current distance (96 AU or 14 billion km, from earth 97 from the Sun) it would have less gravitational influence on Earth than Jupiter. The largest red dwarf being about 40% of the mass of the Sun. Indeed a star of that mass could be as close as 80 AU and still not perturb the Earth's orbit. Even with the much lower luminosity of a red dwarf it would easily be the brightest object in our sky. And for me it is easy to conceive of a life bearing world in such a set up, the question is if the gravitational evolution of a disk nebula could produce the result of both an approximately earth mass terrestrial planet around an approximately sun mass star with a much more distant star 80 or more AU away.

At the bottom end a near brown dwarf star of .076 of the Sun's mass could be as close as 5.2 billion km or 34.7 AU. That is just a bit farther out than Neptune's 29 AU from Earth.

The math was actually very easy. Gravitational attraction equals (G*M1*M2)/D^2 where G is the gravitational constant, M1 & 2 are the masses involved, and D is the distance. But I did not need the first two terms because I wanted to get the same force as Jupiter at its closest approach to an earth sized mass. So I simply eliminated the first two terms since they'd be the same and I was solving to find an unknown D. Jupiter at its closest is about 544 million km away. Then I used earth masses for size since that was easier to work with than kilograms. And both the Sun and Jupiter have their earth masses listed all over the place. So Jupiter is 317 Earths / 544^2, which is a very, very small number. The Sun is 332,946 Earth and .076 of that is 25303.896, round up. Divide that by the very, very small number and then take the square root.

If I were really, really ambitious I might try to understand how relative magnitude is calculated and figure out the relative brightness of these two theoretical red dwarfs. Though I'm pretty darn sure that the larger example would be brighter than anything else in the heavens, except perhaps the moon. I plugged in 10% of the brightness of the sun into a formula and got (3.9 * (10^25)) / (4 * 3.14159 * (1.43229194 * (10^26))) = 0.0216682362, but I do not know what this means. It should be lumins per square meter, if I have not made a mistake. But I have no idea what this is in terms of how bright the star would be on earth.

Comments

Magnitudes

[ionlylurkhere.livejournal.com]

(here from your comment on james_nicoll's post ...)

Right ...

To compare with other objects in the night sky, it's probably easiest to use magnitudes.{*} There's a thing called the distance modulus (http://en.wikipedia.org/wiki/Distance_modulus) which makes life relatively easy for us, as long as we know the absolute magnitude (defined as the magnitude the object would have if it was 10 pc from Earth). The distance modulus is -5 + 5logD, where D is measured in parsecs. You add that quantity on to the absolute magnitude to get the apparent magnitude.

High end: 0.4 solar masses

Here D is 80/206265 ('cos there are 206265 AU in a parsec by the definition) giving a distance modulus of almost exactly -22. High end red dwarfs seem to have absolute magnitudes of about +10, judging by the labels on various HR diagrams I can find (can't be bothered to calculate from first principles, sorry), giving us an apparent magnitude of -12. The Moon is slightly brighter at -12.7, so you're bang on there.

Low end: 0.075 M_solar

Here the distance modulus is around -24 but the absolute magnitude is down at +20 for the very low end red dwarfs (again, going off online HR diagrams). So we come out at -4, about as bright as Venus (so still brighter than all the other stars).

{*} Magnitudes are one of those units like decibels that are supposed to match on to our subjective perceptions. It's a logarithmic scale that's supposed to go from 0 for the brightest stars to 6 for the faintest ones visible with the naked eye and higher to ones only visible with binoculars/telescopes/what have you. A negative number is brighter than any star, in theory, but the system's not quite perfect so the very brightest stars actually have slightly negative magnitudes.

It'd be interesting to see whether we'd be able to resolve them as anything other than a dot, but it's getting late for me to start trying to calculate stellar radii.

Caveat: I'm sure there is at least one howler in the above, 'cos I suck at this sort of thing.

Re: Magnitudes

[mishalak.livejournal.com]

Now I think I have enough information to get myself into real trouble when writing a story set around another star! Thanks! <grin> And if I get ambitious I might even use it in a story. Though I would have to figure out how.