Hello there!

I have a mathematical question that I would appreciate if someone could check my answer to.

What is the sun’s mass that must be converted to energy each second to produce the sun's luminosity?

Note to self: Luminosity is a measure of the total energy radiated by a star in one second.

If the luminosity of the sun equals (3.826 * 10^26 J/s), attempting to solve using E=mc^2:

E is simply the luminosity of the sun, if I am not mistaken.
m is what I am solving for.
c is the speed of light, namely 299,792,458 m/s

Therefore:

(3.826 * 10^26) = m * (299,792,458)^2

(3.826 * 10^26) = 89,895,517,870,000,000 m

Divide by that long number (I prefer to do it the long way!) and get:

4,256,052,015 ???

What unit of measurement should 4,256,052,015 be? This certainly doesn't sound like the correct answer!

Help me get on the right track.

Many thanks!

Kilograms is the unit. (Don't you just love metric?) And about 4 million tons a second sounds about right off the top of my head.

You've chosen to do this in MKS units, so the answer is in kilograms per second.

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Forming opinions as we speak

Thank you both very much!

It's reassuring to know that my answer is correct (with kilograms per second added).

One day, I'm just going to create a program to perform all these metric conversions... Actually, I'm sure there are several thousand out there already! *is too lazy to check Google*

Many thanks again! You folks rock.

Now say that I wanted to find the life expectancy of the sun with the former data I gathered.

The mass of the sun is about 1.989 x 10^30 kg.

If I divide the mass of the sun by 4,256,052,015 kilograms per second, I get

467,334,514,000,000,000,000 !!!!

What does this answer represent? Is it in seconds?

If so, how would I convert that figure to years?

(I know the life expectancy of the sun is circa 10 billion years.... but I'm trying to solve for it. )

Many thanks again!

Look up dimensional analysis. It's a technique for dealing with units.

For instance, in your latest formula, you have solar mass M in kg, and a rate of loss R in kg/s. Dividing the mass by the rate is M kg / (R kg/s), or M kg * (1 s / R kg). The kg cancel out, and you are left with M/R s.

For your second question, you have to figure seconds per year. There are 60 seconds per minute, 60 minutes per hour, 24 hours per day, and 365.2422 days per year. The rest, as they say, is left as an exercise for the student.

Fred

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"For shame, gentlemen, pack your evidence a little better against another time."
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Much appreciated, Fred!

I did the conversion by dividing as follows:

(467,334,514,000,000,000,000 / 60 / 60 / 24 / 365)

I came up with approximately 14,800,000,000,000 years.

15 trillion years??

That doesn't sound right, compared to the 10 billion estimate on the main sequence!

Did I make an error in my arithmetic perhaps?

Thanks again.

The sun will not, of course, convert all the mass to energy. Since it converts hydrogen to helium, you can look at the difference in their mass from a periodic table and realize that this is the amount that was converted to energy. [4 hydrogen atoms compared to 1 helium atom]

Also, the sun has around 71% to 75% hydrogen by mass. So this reduces the life of the sun based on hydrogen fusion.

Can you think of other factors that might increase of decrease the life of our star?

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

This is the single best piece of advice given so far in this thread. You will always be asking these questions about units and conversions until you get a firm grasp of dimensional analysis. A nice side-bonus is that it gives a very nice check for your work. If your dimensional analysis comes out with the wrong units, you have done something wrong setting up the equation.

A key is knowing which units are derrived, and the underlying base units.

I'm not sure, but isn't there a certian ammount of helium and/or hydrogen atoms even in the "vaccum" of space? If so, wouldn't the sun's gravitational pull "collect" some of these? (unless solar wind is enough to overcome the gravity?)

Not that this would change the figures by a huge ammount, but it could perhapse be a factor.

also important would be if the luminosity/energy burn is constant or if it flucuates (wish i could spell), and how that rate would change as the hydrogen/helium levels change.

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I'm like one of those idiot savants...well, except for the savant part.

I think this is the key here, not mathematical errors. Also remember that nuclear fusion doesn't occur throughout the whole mass of the Sun, but only in the core (where it is hot enough), IIRC...

That is good thinking because it takes into consideration that which is outside the sun. However, the bulk of the hydrogen in interstellar space is in tiny molecular form which is blown away by the solar wind. There is a shock boundary at the heliopause where the outer edge of the solar atmosphere (heliosphere) encounters the interstallar material as we plod along in our path around the Milky Way's center.

Yet, this does not mean the sun does not gain any hydrogen material, comets contribute some hydrogen to the sun. SOHO has seen now more than 1,000 comets, sungrazers, burn into the sun. [Interestingly, it was amateurs that scrutinized the imaging to find most of them.] [Edit: make that more than 1,200 comets.]

If it suddenly does become a factor, we are all in trouble.

Good, now you're thinking in more thermodynamic terms. Only in the sun's core are conditions favorable to fusion. Things will change as the hydrogen levels diminish.

Yes. This will greatly affect the life of the sun, too, since the sun will not be able to selectively pull all the hydrogen into its core.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Thank you all very much for your continued help and discussion. I really appreciate it, and its been very educational for an amateur student of astronomy such as myself.

And I've learned something new: I never knew that comets can provide additional hydrogen to the sun. Thanks for posting that!

Well, I do recall that once the sun has used up its hydrogen supply, it will turn to fusing helium. If I recall correctly, this may allow the sun to continue to generate energy for another 100,000 years or so (don't quote me on that!) So, that is one factor that will increase the lifetime of our sun.

It is more interesting than it is effective at restoring any real portion of the hydrogen supply, I would bet.

From what little I know, it gets a little trickier during this evolutionary phase. Their is helium fusion in the core, initially, but this fusion process then moves out to a shell near the core. Hydrogen fusion continues in a shell a little further out. It is a little unstable, too. This process lasts in the millions of years, I think.

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.

Hydrogen added from a comet will not get fused to Helium in the Sun. It *might* cause a little more Hydrogen deeper down to get fused, simply by adding mass to an outer layer.

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Forming opinions as we speak

Yes. I would assume this small amount of new hydrogen would be limited to the outer convective zone and would not enter the radiative zone.

Now that such a large number of comets have been found, courtesy of SOHO, has anyone estimated the mass contribution these comets have made compared to the mass loss?

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Lighten up! This is a stellar board! Author: duh.

"The Sun, with all the planets revolving around it, and depending on it, can still ripen a bunch of grapes as though it had nothing else in the universe to do..." Author: Galileo supposedly.