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The Sun loses about 5.5 million tonnes of mass every second, does this mean Sun's volume is also going down? If so can we tell by how much every year?

E: "by how much" I mean can we tell if sun's radius is going down too

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    $\begingroup$ No, this amount is completely insignificant compared to the solar mass. On the main sequence the sun's radius is slowly growing, as hydrostatic reaction to the increasing mean molecular weight in the fusing core. $\endgroup$ May 28 at 7:59
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Is the sun shrinking currently?

It's the other way around: The Sun is slowly growing hotter and thus is slowly expanding. The Sun accumulates ever more helium in its core as it ages. This growing amount of fusion ash results in the core getting hotter, which in turn results in the Sun expanding in volume. This completely overwhelms what one would expect from looking only at the mass loss due to fusion and solar winds.

The solar mass loss rate currently is on the order of $10^{-13}$ solar masses per year. At that rate, it would take on the order of ten trillion years for the Sun to consume or expel all of its mass. That's a much longer time span than the Sun's much faster aging process. The Sun has five to seven billion years or so left on the main sequence. Shortly before the time the Sun leaves the main sequence, it will be about twice as luminous and considerably larger than it is now. Shortly after the the Sun leaves the main sequence, it will be much more luminous and even larger than it was just before it left the main sequence.

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    $\begingroup$ I think there are about 200 million years left before it's curtains for life on Earth due to increased solar output. That's not long, Indeed 200 million years ago is as recent as the the latest supercontinent assembly. Earth is practically over. $\endgroup$ May 29 at 21:56
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    $\begingroup$ @DavidTonhofer - en.m.wikipedia.org/wiki/Future_of_Earth gives us up to 600my. $\endgroup$
    – peak
    May 30 at 16:46
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    $\begingroup$ Why is accumulation of "ash" increasing the temperature? I would think adding things which are not contributing to the reaction would slow the reaction down, i.e. cool the sun? $\endgroup$ May 30 at 20:59
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    $\begingroup$ @PaŭloEbermann The core of a non-convective star (stars between ~0.5 and ~1.5 solar masses) maintains an equilibrium balance between pressure, temperature, and fusion rate. As a star ages, its fusion rate would decrease if the core temperature remained the same. But that is a non-equilibrium condition as the reduced fusion rate would result in a reduced temperature and hence a reduced pressure. The core would contract (which it does), increasing pressure, temperature, and fusion rate so as to maintain that equilibrium state. $\endgroup$ May 31 at 11:28
  • $\begingroup$ To clarify, does the surface temperature of a star like our Sun increase as it ages (while still on the MS)? Or does the increase in temperature of the core lead to overall expansion of the star, which then cools the outer layers, decreasing surface temperature? $\endgroup$
    – YiFan
    Jun 1 at 11:12
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Sun's mass is almost $M_\odot = 1.9*10^{30}$ kg.
The mass-loss scale you are talking about is around $\delta M \approx 10^{10}$ kg/s.
I'm guessing this mass-loss is due to both stellar winds and nuclear fusion.

So, if the Sun evolves only using this mass-loss, it will last for $t=\frac{M\odot}{\delta M} = 10^{20} seconds.$
This time scale is almost 3 trillion years, which is much longer than the expected life of the sun. Such a mass loss will barely affect our Sun's radius.

Moreover, during the main sequence stage (which is what our Sun is going through), the radius remains roughly the same. This is because the star is in equilibrium between radiation pressure and gravitational pull. Whenever a star starts to shrink, the core reaction rate increases and thus, the radiation pressure increase. As a result, the star expands again until the equilibrium is reached again.

During its main sequence stage, and through a process of many changed equilibriums, the stellar radius and luminosity increases steadily over its main sequence stage.

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    $\begingroup$ In fact, there is a slight expansion as the sun moves along the main sequence since the luminosity increases a bit over time. This effect is definitely dwarfing the mass loss effect. $\endgroup$ May 28 at 10:07
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    $\begingroup$ Indeed, the Sun is getting bigger quite significantly. The radius doubles over the MS lifetime. $\endgroup$
    – ProfRob
    May 28 at 11:30
  • $\begingroup$ Yes, thanks for the comment. Although the expansion will not be comparable to the RGB phase, a star in MS does indeed grow larger over its MS lifetime. I will edit m aanswer. $\endgroup$ May 28 at 20:21
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In case you are interested in "apparent shrinkage", then you might want to know that the Earth is moving away from the Sun by about 15 centimeters per year, while the Sun itself is growing by about 5 centimeters per year. However, as the Earth-Sun distance is about 100 times the Sun's diameter, apparent growth (between these two factors) easily wins.

However, those slow long term factors are lost in seasonal noise.

The orbit is elliptical which means that the Sun is apparently shrinking half a year and apparently growing the other half a year, as we travel away from and then back toward the ball of fire.

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