A Problem book in Astronomy and Astrophysics by Aniket Sule

By Aniket Sule

It is a compilation of difficulties from the overseas Olympiad in Astronomy and
Astrophysics (2007-2012).

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3 / Middle of exposure 2. 3) which contains the pixel values of an image during the given exposure time. This image, which is a part of a larger CCD image, was taken by a small CCD camera, installed on an amateur telescope and using a V band filter. 4 shows this 50 × 50 pixels image that contains 5 stars. 3 the first row and column indicates the pixels’ x and y coordinates. 1 gives the telescope and the image specifications. EA: In the IOAA 2009, this table was printed on a single A3 sheet as 50 × 50 grid.

As a result of mutual gravitational force, stars are deformed from perfect sphere to the prolate spheroid with a = 2b, where a and b are semi-major and semi-minor axes (the major axes are always colinear). The inclination of the orbital plane to the plane of sky is 90◦ . Calculate the amplitude of light variation in magnitude ((∆m)) as a result of the orbital motion of two stars. Ignore temperature variation due to tidal deformation and limb darkening on the surface of the stars. Hint: A prolate spheroid is a geometrical shape made by rotating of an ellipse around its major axis, like rugby ball or melon.

The way the sunlight is reflected by the surface of the asteroid depends on its texture and on the angle between the Sun, the asteroid and the observer (phase angle), which varies as the Earth and the asteroid move along their orbits. , when they are close to the opposition). – Since the observed flux of any source decreases with the square of the distance, the observed magnitude of an asteroid also depends on its distance from the Sun and from the observer at the time of the observation. 1) where mr is usually called reduced magnitude (meaning the magnitude the asteroid would have if its distances from the Sun and the Earth were reduced both to 1 AU) and depends only on the visible illuminated surface area and on phase angle effects.

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