How can we be so precise with our calculations of the universe? Example...?

Question

Sirius Bs' calculated average density is 92,000 times that of Sol's, so that one cubic inch of its material would weigh about 15 tons at the surface of the Earth. How can we know this? What are the odds that it is wrong? I assume we base the equations plugging Sols density and mass vs density and mass of the star we are studying. But how can we be sure these type of metals exist?

Answer 1

I have no idea where your numbers come from; they have no resemblance to reality. The actual average density of matter in the universe is far less than one gram per cubic kilometer. The size and masses of things in the universe are determined by measurements, showing how things change over time; any textbook on astrophysics will give details, which are too lengthy to relate here.

Answer 2

Density is a derived quantity from mass and radius.

Mass is (relatively) easy to obtain, especially for a star like Sirius B that is in a binary system. You simply observe the orbits of the stars around each other and Kepler's Laws immediately give you the mass.

Radius is determined by knowing the distance to the stars (in this case, directly by parallax) and the apparent brightness. Knowing these two things allows you to calculate the intrinsic brightness. The temperature is obtained directly from the spectrum, and temperature, luminosity, and radius are directly related to each other through the Stefan-Boltzman equation.

The trickiest of these measurements to make is the distance, except that in this case it can be directly observed with parallax (in most cases you have to use some indirect method). The measurements are all therefore certain, and thus so is the density.

It makes no difference whatsoever what Sirius B is made out of; the required observations are independent of chemistry.

Answer 3

You are correct in saying that they use equations based on density and mass. Stars are typically made up of 70% hydrogen and 28% helium. We know this because stars need this much fuel to keep burning. The remaining 2% of the star's composition is assumed to be trace quantities of metals. Even assuming they are much heavier or lighter than Sol's, it still would not throw off the equation too much. Keep in mind that this is an estimated density.

Answer 4

I'm afraid you'll need at least the 475 pages of the reference, including a strong foundation in calculus and tensors, to really answer your question. Perhaps our best clue is the mass-luminosity relationship. Plotted on a log-log scale, it's extremely linear. The various stellar mechanisms are rather well understood. We take measurements of all kinds, including luminosity, spectral composition, red shift, orbital/gravitational behavior, magnetic fields, and more. We make estimates of the composition and properties of each star. Then, massive simulations and calculations make predictions. If those predictions are well matched to observations, we are confident in the estimates. Each estimate includes accuracy and confidence ranges. Science has been doing this for quite a while, and is good at it.

Answer 5

I´m not sured about mass, but the size of "not very distant" starts can be determined quite exactly (using interferometry). I think the mass could be somehow determined by the radiance of the star and spectrum of its radiation. So I think those data are pretty exact. Those data are really experimental one.