Relativistic mass increase due to high temperatures inside stars?

[kahoon]

Wikipedia says that the core temperature of our Sun is 15.7×10^6 Kelvins.

I don't know what that means in terms of protons' velocities inside the core, but I bet they move pretty fast. Could they move that fast that they have a noticeable increase in mass due to their relativistic speed?

Could this influence the overall gravitational pull of a star?

Could this be an explanation for dark matter?

 

[Ich]

They move at ~0,1% light speed, that doesn't contribute noticeable to the star's mass. Maybe one part in a million.

 

[Matterwave]

Because E=mc^2, a massive amount of energy is needed to resemble a small amount of mass both inertial and gravitational.

Let's look at how much mass the Sun "sheds" every second due to it's luminosity. The solar luminosity is 3.85*10^26W. That's equivalent of only 4.27*10^9kg/s. Considering the Sun's mass is 1.99*10^30kg, the mass of the sun is 21 orders of magnitude larger than the "luminosity mass". To be in equilibrium the Sun's energy production is roughly equal to the energy output (or else it would get hotter and hotter and eventually explode as all that energy built up!).

The other important point to note; however, is that this "mass" is already included in our calculations. We calculate the mass of massive stellar bodies from the orbits of objects orbiting them. We cannot tell if this gravitational mass is sourced by actual rest mass or by energy. In general relativity, both mass AND energy source gravity. To us, making these calculations, they are the same. We can't tell a shred of difference.