Difference between revisions of "Astrophysical warm-up"

Problem 1

Obtain the non--relativistic approximation (to the first order in $V/c$) for the Doppler effect.

Problem 1

Obtain the relativistic formula for the Doppler effect.

Problem 1

What are the differences between the Doppler effect for light and the "analogous" effect for sound?

Problem 1

Using the Doppler effect, how could we demonstrate that time is running differently for observers which move relative to each other?

Problem 1

Every second about $1400 J$ of solar energy falls onto one square meter of the Earth. Estimate the absolute emittance of the Sun.

Problem 1

Assuming that the constant emittance stage for the Sun is of order of $10^{10}$ years, find the portion of solar mass lost due to radiation.

Problem 1

Why was the connection between the emittance of variable stars (Cepheids) and the period of their brightness variation discovered from observation of stars in Great Magellan cloud rather than in our Galaxy?

Problem 1

A supernova in its maximum brightness reaches the absolute stellar magnitude of $M=-21$. How often will the supernova outbursts be registered if observation is carried out on the whole sky up to the limiting magnitude $m=14$? Assume that in a typical galaxy a supernova bursts on average once per 100 years, and galaxies are distributed with spatial density of one galaxy per $10 Mpc^3$.

Problem 1

Calculate the average rate of star formation in our Galaxy.

Problem 1

• Determine the wavelengths of hydrogen resonant lines.

Problem 1

The main method for investigation of interstellar neutral hydrogen are observations in unltraviolet band. The strongest interstellar absobtion line is $\alpha$--Lyman hydrogen line ($\lambda=121.6\mbox{nm}$). This line corresponds to transition of electron from state with quantum number $n=1$ to the state with $n=2$. At the same time, the Balmer series characterized by electron transition from excited $n=2$ state are not observed. Why does this happen?

Problem 1

Hydrogen burning (hydrogen to helium transformation) in stars is realized in the so-called $p$--$p$ cycle, which starts from the reaction of deuterium formation \(p+p\to d+e^+ +\nu.\) To support such a reaction the colliding protons have to overcome Coulomb barrier (in order to enter the region where nuclear forces act: $r_{nf}\approx10^{-13}\mbox{\it cm}$.) It requires energy as high as \(E_{c}=e^2/r_{nf}\approx1.2\mbox{ MeV.}\) Typical solar temperature is only $T_\odot=10^7 \mbox{ K}\approx0.9\mbox{ keV}$. The Coulomb barrier can be overcome due to the quantum tunneling effect (classical probability to overcome the barrier for the protons in the tail of Maxwell distribution is too low). Estimate the probability of tunneling through the Coulomb barrier for protons on the Sun.

Problem 1

At present hydrogen in the Sun burns (transforms into helium) at temperature $1.5\cdot10^7\ K$, but much higher temperature will be required to synthesize carbon from helium (when hydrogen is exhausted) due to higher Coulomb barrier. What physical mechanism could provide the increase of the Sun's temperature at the later stages of its evolution?

Problem 1

Accretion is the process of gravitational capture of matter and its subsequent precipitation on a cosmic body, i.e. a star. In such a process the kinetic energy of the falling mass $m$ transforms with some efficiency into radiation energy, which leads to additional contribution to the brightness of the accreting system. Determine the limiting brightness due to accretion (the Eddington limit).

Problem 1

Masses of stars vary in the limits \[0.08{{M}_{\odot }}<{{M}_{star}}<100{{M}_{\odot }}.\] How could this be explained?

Problem 1

How many quantities completely determine the orbit of a component of a double star?