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Re: Is the Sun losing mass?

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Thomas 'PointedEars' Lahn wrote:

> Simon Roberts wrote:
>> Considering all this and the equation E = Mc^2 what is the rate of loss
>> of mass of the Sun?
> 
> Not much.  Google is your friend. [psf 6.1]
> 
> BTW, unless one wants to emphasize a larger mass in relation to a smaller
> mass, one uses “m” as the symbol for mass in physics, not “M”.
>  
>> I did a rough calculation near a year ago.
>> 
>> I must have made a huge mistake in my calculation since I still see the
>> Sun.
> 
> Yes.
>  
>> It's mass hasn't diminished so that it does not exist.
> 
> Correct.  And that is not going to happen.  The end of the Sun (as we know
> it) and of all the inner planets, including Earth, will come in a far more
> spectacular way in any case (in about 2 to 5 billion years, short scale).

FWIW, since I also always tell people that Usenet is not the Web, I thought 
it would be interesting and fun to do the calculation here myself (with a 
little help from Wolfram|Alpha).

The energy released by Sol through nuclear fusion can be roughly obtained 
from her luminosity, which has units of power (watt):

  L☉ ≈ 3.848 × 10²⁶ W

 1 W = 1 J∕s

So the energy released per second is (trivially)

  ∆E ≈ 3.848 × 10²⁶ J.

This corresponds [as a point of note, *exactly* as in Einstein’s 1905 
formulation in “Does the Inertia of a Body Depend upon its Energy-Content?”, 
although he used different symbols, and words [1]] to a loss of mass *per 
second* of

  ∆m = ∆E∕c² ≈ 4.281 × 10⁹ kg,

where c is the speed of light (in vacuum).

This may seem much, but consider that the current mass of Sol is

  M☉ ≈ 1.988435 × 10³⁰ kg.

10⁹ is 21 *magnitudes* less than 10³⁰, or less than *one sextillionth* of 
the current mass (if I know my numerals correctly).

So if Sol would only continue to lose mass through nuclear fusion, and I did 
not miscalculate, it would take

  ∆t = M☉∕((∆m)∕s)
     ≈ 1.988435 × 10³⁰ kg∕(4.281 × 10⁹ kg∕s)
     ≈ 4.667 × 10²⁰ s
     ≈ 1.479 × 10¹³ a

or ca. 14 trillion years (short scale), for her to "evaporate" this way.

However, as astronomer Phil Plait points out [2], Sol also loses mass 
through the solar wind (stream of charged particles) that it emits.  
Ignoring electrons because of their comparably small mass, Plait calculates 
that Sol loses “1.5 million tons of material” (protons) or 1.5 × 10⁹ kg per 
second through that.  Again, that is a lot in human measures – but consider 
what she is that we are talking about.

So it would take Sol "only"

  ∆t ≈ 1.988435 × 10³⁰ kg∕((4.281 + 1.5) × 10⁹ kg∕s)
     ≈ 3.44 × 10²⁰ s
     ≈ 1.09 × 10¹³ a

or ca. 11 trillion years to lose all her mass in both ways.  (No wonder 
she’s still around, yes? ;-))

<http://www.wolframalpha.com/input/?i=luminosity+of+sun>
<http://www.wolframalpha.com/input/?i=3.848%C3%9710%5E26+J+in+kg>
<http://www.wolframalpha.com/input/?i=4.281%C3%9710%5E9+kg+%2B+1.5+*+10%5E6+t>
<http://www.wolframalpha.com/input/?i=mass+of+Sol%2F5.781%C3%9710%5E9+kilograms>
<http://www.wolframalpha.com/input/?i=mass+of+Sol%2F(5.781%C3%9710%5E9+kilograms%2Fs)>

But as I alluded to, and Plait also mentions, she is not going to live a 
thousandth of that time.  Because once all the hydrogen is exhausted in 
about 5 billion (5 × 10⁹) years, helium fusion is going to set in where she 
will grow to be a red giant that extends beyond the orbit of Mars.  Once 
helium fusion is done, there will not be enough mass left to ignite fusion 
again, and the core is going to shrink to leave a white dwarf.

<https://en.wikipedia.org/wiki/Sun#After_core_hydrogen_exhaustion>

Sol’s death (as we know her) might come even earlier as the Andromeda Galaxy 
and the Milky Way are on a collision course and projected to merge in ca. 
_4.5_ billion years (_not_ 2).  Distances between stars are huge, and so it 
is unlikely that two stars would collide, but it remains a possibility.  
Certainly gravitational influence of other astronomical objects such as 
other stars could cause Sol to have a very different fate than a white 
dwarf.

<https://en.wikipedia.org/wiki/Andromeda_Galaxy>

HTH.


PointedEars
___________
[1] 
<http://www.slate.com/blogs/bad_astronomy/2014/07/14/solar_wind_versus_fusion_how_does_the_sun_lose_mass.html>
[2] <http://einsteinpapers.press.princeton.edu/vol2-trans/186>

-- 
Q: What did the nuclear physicist order for lunch?  
A: Fission chips.

(from: WolframAlpha)

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Thread

Is the Sun losing mass? Simon Roberts <retenshun@gmail.com> - 2018-03-14 00:21 -0700
  Re: Is the Sun losing mass? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-14 21:47 +0100
    Re: Is the Sun losing mass? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-14 23:50 +0100
  Re: Is the Sun losing mass? Simon Roberts <retenshun@gmail.com> - 2018-03-14 15:51 -0700
    Re: Is the Sun losing mass? Simon Roberts <retenshun@gmail.com> - 2018-03-14 17:15 -0700
      Re: Is the Sun losing mass? Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2018-03-19 03:34 +0100
        Re: Is the Sun losing mass? Volney <volney@volney.invalid> - 2018-03-19 00:04 -0400

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