1. Due to atmosphere refraction (34 angular minutes near the horizon) the object that would not rise in definite location on the Earth, does not set under the horizon, always being above. At what latitudes on the Earth this can happen?

2. Amateur astronomers observe the artificial satellite of the Earth in Saint-Petersburg. The satellite crossed the zenith twice during the New Year night - at 18.00, December, 31^th and at 05.58, January, 1^st. When will the satellite reach the zenith again? The latitude of Saint-Petersburg is equal to +60^o, the satellite orbit is circular.

3. In the New Year evening Venus reaches the maximum eastern elongation point being observed from the Earth. In the same time the spacecraft is launched from the Venus to the Mars by the orbit tangent to the orbits of Venus and Mars. What bright star is seen near to Mars in this New Year evening in the Earth’s sky?

4. Which stars from the list following will be visible in Moscow (latitude +56^o) in 13000 years: Sirius, Canopus, Vega, Capella, Arcturus, Rigel, Procyon, Altair, Spica, and Antares.

5. Bright comet comes to the opposition with the Sun, moving in the sky along the ecliptic in the straight direction (from the west to the east). Estimate the maximum possible distance between the Earth and the comet at this moment.

6. The white dwarf with radius 6000 km, surface temperature 10000 K and mass equal to solar one moves through the interstellar cluster of comet cores, each one has radius 1 km and density 1 g/cm². How many comets must fall on the white dwarf every day to increase its luminosity in two times?

7. What should be the size of hypothetical molecular hydrogen cloud with density equal to the one of near-ground air and temperature 1000 K to create the star?

The problems about total solar eclipses

8. (The problem about springtime eclipse). The total solar eclipse occurs at the spring equinox day. The path of totality crosses the North Pole of the Earth. At what latitude on the Earth will the central eclipse be observed at the maximum altitude over horizon? Please find the value of this altitude. During the eclipse the Moon is situated near ascending node of the orbit.

9. (The problem about summertime eclipse). The total solar eclipse occurs at the summer solstice day. The shadow of the Moon enters the Earth surface at the point with latitude and longitude both equal to 0^o. The totality duration at this point is equal to 1 minute. Please find the maximum totality duration for the stationary observer on the Earth, the coordinates of the point when it will be observed and the Universal Time of the middle of the longest total eclipse. The inclination of the lunar orbit, the refraction and the time equation can be neglected.

10. (The problem about solar corona). It is known that the free electrons scatter the emission almost isotropically as the metal balls with radius equal to 4.6*10^-15 meters, but heavy particles (protons, ions, atoms) scatter the light many times worse. Assuming that the corona consists of pure hydrogen, the atmospheric pressure in the lower corona layers is equal to 0.003 Pascals and the average corona temperature is equal to 1000000 K, estimate the magnitude of the Sun during the total solar eclipse on the Earth.

All Problems written by Oleg S. Ugolnikov