MacroQuantum

Mmmmm. According to the article that I quoted in my last post, an earth-like planet has an albedo of 0.37. What exactly that means, I don't know, but what would happen then, is the inner radius should be, as a last step, multiplied by said albedo (I think). So that what you would have would be: Inner=(SQRT(Luminosity)/Temperature^2)*Albedo Inner=(SQRT(0.79)/0.92^2)*0.37 Inner=(0.89/0.85)*0.37 Inner=1.05*0.37 Inner=0.39 AU While the article does make mention of the greenhouse effect, it actually doesn't give any sort of parameters, so I guess I will have to live with just the straight formula. Outer=SQRT(0.79)/1.27^2 Outer=0.89/1.61 Outer=0.55 AU Thus, with a G5 type star, and a desired temperature range of 260K to 360K, we have a range of 0.39AU to 0.55AU. But wait a moment. Earth should fall somewhere in that range, having an average temperature of 283K. So, working the formula once more.... Radius=SQRT(0.79)/1^2 Radius=0.89/1 Radius=0.89 Huh?

Mmmmm. According to the article that I quoted in my last post, an earth-like planet has an albedo of 0.37. What exactly that means, I don't know, but what would happen then, is the inner radius should be, as a last step, multiplied by said albedo (I think). So that what you would have would be: Inner=(SQRT(Luminosity)/Temperature^2)*Albedo Inner=(SQRT(0.79)/0.92^2)*0.37 Inner=(0.89/0.85)*0.37 Inner=1.05*0.37 Inner=0.39 AU While the article does make mention of the greenhouse effect, it actually doesn't give any sort of parameters, so I guess I will have to live with just the straight formula. Outer=SQRT(0.79)/1.27^2 Outer=0.89/1.61 Outer=0.55 AU Thus, with a G5 type star, and a desired temperature range of 260K to 360K, we have a range of 0.39AU to 0.55AU. But wait a moment. Earth should fall somewhere in that range, having an average temperature of 283K. So, working the formula once more.... Radius=SQRT(0.79)/1^2 Radius=0.89/1 Radius=0.89 Huh? I'm not sure why this posted twice but you see my problem. A temperature that should fall into that range, didn't.

Okay, I understand what we are doing here. But I'm not sure of the reference, because the original article (http://www.ess.sunysb.edu/fwalter/AST101/habzone.html) suggests that it should be possible to determine a range, or corridor, where life would be expected to survive. However, working from this percentage of earth temp, I don't see how to generate that. That is why I made the attempt to convert from 'percentage of earth' to a more generic range. Shouldn't it be possible to convert that luminosity into something that is not a percentage of earth?

What? Radius = SQRT(L)/T^2 Radius = SQRT(2.1)/1.1^2 Radius = 1.45/1.21 Radius = 1.2 (Whats?) Okay, let's see if I can do this right now. According to a reference I found the bolometric luminosity of earth's sun = 3.83 * 1026W or 3929.58. Also the temperature range that water is liquid at 273K to 360K (actually 373). Last, but not least, the albedo of an earth type planet would be equal to 0.37. Assuming that I am working with a G5 type star, this should work: Inner = (SQRT(Luminosity * Percentage)/Temperature^2)*Albedo Inner = (SQRT(3929.58*0.79)/273^2)*0.37 Inner = (SQRT(3104.37)/74529)*0.37 Inner = (55.72/74529)*0.37 Am I making this harder than it should be? Because obviously this doesn't work, either. This is starting to get real frustrating.

Sisyphus has given me a straight forward formula that will determine the diameter that I am looking for. However, in that formula, what I am lacking is Luminosity. So the question (that I understand) becomes how do I determine the Solar Luminosity given the facts that I have (Star temperature, mass, radius)? But every time I try to figure out what Martin is trying to tell me I get lost. Anyone want to clarify?

That being my general point, and why I was looking at that other page (http://www.ess.sunysb.edu/fwalter/AST101/habzone.html). My goal is to find the habitable range. This way I can set two planets into that range (if possible). Then I can determine the temperature of both of those planets (and hopefully some other minor details) and then continue on about my way. The next step would be to see if I could get some sort of concept of the visible here. Perhaps I have not stated my goal correctly, or perhaps I don't follow what you are saying.

So let me see if I got this right. Given a G5 type star which has an average temperature of 5770K (according to http://curriculum.calstatela.edu/courses/builders/lessons/less/les1/StarTables.html) and has a radius of .893 earth suns or 69,600,000,000m or 69,600,000km then solar lumonisity = 4 * sigma * 5770^4 (Although I'm not exactly sure what sigma represents here? If I'm not mistaken though sigma should be representing the solar constant which is 1.37 kW/m^2, the results being: solar lumonisity = 4 * 1.37 kW/m^2 * 5770^4 But I'm not sure how to simply this into something that I can work.) Given Sisyphus's formula then it should be possible to say that our planet (at the equator since that is the closet the planet comes to the sun) should have a temperature of 273K to 360K (since we don't actually want it turning into steam) which means that: Inner = (SQRT(4*1.37kW/m^2*5770^4)/273^2)*Albedo (or 0.37 for earth-like) Outer = SQRT(4*1.37kW/m^2*5770^4)/360^2 Okay how far off am I?

Does this article basically imply that solar luminosity, like planetary luminosity is equal to [surface] Temperature^4? (A site that details the approximate surface temperatures of the various types of stars I already have, but I don't beleive the site specs the luminosity.) And we start talking about diameters, or radii, are we talking the planet should be X number of planetary raddii, or solar radii, from the sun? [i'm getting lost again in possibilities!] Or do I still not have a clear picture? I think given those two items, I should be able to plot the placement of a planet that should be within the describeded habitable zone. Since most scientist agree that liquid water is required for life. Thus the upper and lower temperature range of the planet would be the temperature at which water would remain a liquid (at the equator). And obviously, thanks for your help.

At this site: http://www.ess.sunysb.edu/fwalter/AST101/habzone.html the author makes some fairly innocent statements that should arrive at a quick formula. However, my english to math translations have never been good. What I am looking for should be two formulas, one to determine the inner and outer diameter. Would anybody care to take a shot at making the translations?

At this site http://www.ess.sunysb.edu/fwalter/AST101/habzone.html he makes several statements which should yield two simple formulas. Those formulas being a Outer and Inner boundaries. My problem is in translating his english to math. As near as I can tell I=(S^4/(1/L))*A should determine the Inner boundary. Where S= The sun's temperature, L is equal to the lower end temperature of the planet (most likely at equator), and A is equal to the Albedo of the planet. Likewise, as near as I can determine O=(S^4/(1/U)) should determine the Outer boundary, where S = Sun's temperature and U is the upper end of the temperature range. While I'm at it, anybody care to take a stab at ranges those distances are in? I'm not sure how a mile, or kilometer would translate to radii Anybody care to doublecheck me?