Wrong formula

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Wrong formula

Post by Sedna on 26th August 2009, 11:01 am

Hello everybody,

It's me... again. But this time it's not for a question, it's for a mistake. I found that the following equation, A = ((1329x10^(-H/5))/D)^2 where A is the albedo, H is the absolute magnitude of the star and D is the diameter of the planet in kilometers, is entirely wrong. Using it with Sun and Earth, the result is A = ((1329x10^(-4.85/5)/12,756)^2 = 0.000124629 (the albedo of the Earth is supposed to be approximatively 0.35).
So I replaced the diameter by the surface facing the Sun, giving A = ((1329x10^(-H/5)/2piR)^2, but the formula is still wrong. There's another way to calculate the albedo (radiation reflected back to space/incident solar radiation), but I cannot find the equation. If someone has something about that, he's welcome.

Bye

Sedna

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Re: Wrong formula

Post by Lazarus on 26th August 2009, 12:50 pm

Where did you get that formula from? There doesn't seem to be much physical motivation behind it... the term in the absolute magnitude looks like it ought to be proportional to the luminosity, but usually in these kind of things the planet's diameter ought to cancel out.
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Re: Wrong formula

Post by Sedna on 26th August 2009, 1:44 pm

I get the formula from Wikipedia, the only place where I can find formulas. It seems that the guy who wrote that formula is stupid or he was drunken when we wrote the article.

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Re: Wrong formula

Post by Lazarus on 26th August 2009, 1:53 pm

Ah-ha. Check the reference on that formula (assuming you got it from the Albedo article), it gives a link here to a formula used to compute sizes of asteroids.

You have H = the absolute magnitude of the asteroid, which is not the same as a star's absolute magnitude, as it is defined for a reflective body rather than one that is self-luminous. In this case, the absolute magnitude is for the case when the object is located 1 AU from the observer, 1 AU from the Sun at phase angle = 0 (full phase)

The Wikipedia page on albedo should go further in explaining this formula and how it is applied, at present it is somewhat misleading.
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Re: Wrong formula

Post by Sedna on 27th August 2009, 9:45 am

I took the formula in the link, and after a few tries, it seems to be correct with asteroid sized bodies. I tried with a bigger body, the Moon, and the formula is still correct (looks good Smile ). Now it remains one unknown data, the absolute magnitude for asteroids (more generally planetary bodies). I checked the only unnoticable place where I can find detailed informations about celestial mechanics. It tells that, to get the absolute magnitude of a planetary body, subtract 31.57 from the stellar one. This sentence is, one again, wrong.

At least, I made one step forward in the "albedo process" and I thank you for that.

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