# Special relativity and stars' masses

1. Jun 22, 2013

### omiros

Hello everybody I am a first year student and I have a question about stars' masses.

I've been thinking about, what happens to a star's mass cause of the high speeds of the particles there. Do we consider the 'extra' mass, 'caused' by relativity (really high speed particles are heavier than those that are slow) or do we just think about its rest mass?

2. Jun 22, 2013

### Staff: Mentor

You're thinking about the random motion of the particles associated with the star's temperature, right? In that case, yes, one way to look at it is that the star's mass includes the "relativistic mass" of those particles.

Another way, which is more in line with the way most physicists think of mass in relativity now (that is "mass" = "rest mass"), is to say that the star's mass is its total energy divided by c2, in the reference frame in which the star as a whole is at rest (its total momentum is zero).

The star's total energy in turn consists of

• the energy associated with the "rest masses" of the individual particles
• the kinetic energies of those particles
• the (negative) potential energy that keeps all those particles together as a star

3. Jun 22, 2013

### omiros

Yes, I forgot to specify it. I've been thinking of a star with speed<<c.

So now we might say that this stars has a mass of 10kg let's say, however in reality is it more massive?

And if we had the case of fast moving star 1/3c would that affect its 'mass' too?

4. Jun 22, 2013

### Staff: Mentor

In special relativity the invariant mass (in units where c=1) of a system is given by m²=E²-p². In the star's rest frame p=0 for the star as a whole, so m=E (or in units where c≠1: E=mc²). In any frame where the star is moving both p and E increase so that m remains the same.