By Aniket Sule
This can be a compilation of difficulties from the overseas Olympiad in Astronomy and
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Extra resources for A Problem book in Astronomy and Astrophysics
Calculate the distance of the satellite from the center of the Earth (in the Earth radius unit). (I09 - T14 - B) 8. Assuming that Phobos moves around Mars on a perfectly circular orbit in the equatorial plane of the planet, give the length of time Phobos is above the horizon for a point on the Martian equator. (I11 - T04 - B) 9. Assume that you are living in the time of Copernicus and do not know anything about Kepler’s laws. You might calculate Mars-Sun distance in the same way as he did. After accepting the revolutionary belief that all the planets are orbiting around the Sun, not around the Earth, you measure that the orbital period of Mars is 687 days, then you observe that 106 days after opposition of Mars, the planet appears in quadrature.
According to the Astronomical Almanac, the solar diameter on that day is 32’. 2 Data Analysis active region in unit of millionth of solar hemisphere (msh)? 2 25 (I08 - Data Analysis 1. 1 presents a negative image of sky taken by a CCD camera attached to a telescope whose parameters are presented in the accompanying table (which is part of the FITS datafile header). 2A) is an enlarged image of the same part of the sky taken some time earlier. 3 presents a sky map which includes the region shown in the CCD images.
I11 - T05 - A) 3. The Galactic Center is believed to contain a super-massive black hole with a mass M = 4 × 106 M⊙ . The astronomy community is trying to resolve its event horizon, which is a challenging task. For a nonrotating black hole, this is the Schwarzschild radius, R⊙ = 3(M/M⊙ ) km. Assume that we have an Earth-sized telescope (using Very Long Baseline Interferometry). What wavelengths should we adopt in order to resolve the event horizon of the black hole? (I10 - T08 - B) 4. What is the minimum diameter of a telescope, observing in the visible and near ultraviolet bands and located at one of the Lagrangian points L4 or L5 s of the Sun-Earth system, in order to be able to detect the Earth’s wobbling relative to the ecliptic plane caused by the gravitational action of the Moon?